阅读说明：本技术 超导转变边缘热传感器 (Superconducting transition edge thermal sensor ) 是由 迪米特里·埃费托夫 保罗·塞弗特 卢晓波 若泽·杜兰 彼得·斯捷潘诺夫 于 2020-11-09 设计创作，主要内容包括：本发明涉及一种超导转变边缘热传感器,包括超导膜,该超导膜限定用于在其上入射量子的有效区,其中,所述超导膜由超导体制成,在所述超导体的临界温度T-c处该超导体展示出低于10～(13)cm～(-2)的电荷载流子密度和低于10～3k-b的电子热容量,其中,超导体由彼此叠置的至少两层二维晶体形成。(The invention relates to a superconducting transition edge thermal sensor comprising a superconducting film defining an active region for incident quanta thereon, wherein the superconducting film is made of a superconductor, at a critical temperature T of the superconductor c The superconductor exhibits less than 10 13 cm ‑2 Charge carrier density of less than 10 3 k b Wherein the superconductor is formed of at least two layers of two-dimensional crystals stacked on top of each other.)

1. A superconducting transition edge thermal sensor comprising a superconducting film defining an active region (SC) for incident quanta thereon, characterized in that the superconducting film is made of a superconductor, at a critical temperature T of the superconductor_cSaid superconductor exhibits less than 10¹³cm^-2Charge carrier density of less than 10³k_bWherein the superconductor is formed of at least two layers of two-dimensional crystals stacked on top of each other.

2. The superconducting transition edge thermal sensor of claim 1 wherein the at least two layers are two graphene layers that are twisted relative to each other by an angle of 1.1 ° ± 0.1 ° such that they form a molar superlattice.

3. The superconducting transitioning edge thermal sensor of claim 1 wherein the at least two layers are two bilayer graphene twisted relative to each other by an angle of 1.3 ° ± 0.1 ° such that they form a molar superlattice, wherein the graphene layers in each bilayer are aligned at 0.0 ° relative to each other.

4. The superconducting transition edge thermal sensor of claim 1, wherein the at least two layers are two bilayer wses₂The two bilayers WSe₂Twisted relative to each other by an angle in the range of 1 ° to 4 ° so that they form a molar superlattice with WSe within each bilayer₂The layers are aligned at 0.0 deg. with respect to each other.

5. The superconducting transition edge thermal sensor of claim 1, wherein the at least two layers are three graphene layers aligned at a twist angle of 0 ° with respect to each other, wherein the stacking order of the graphene layers corresponds to an ABC stacking order, forming three layers of graphene.

6. Superconducting transition edge thermal sensor according to any of the preceding claims, wherein the at least two layers are hermetically and watertightly sealed by means of a sealing material.

7. The superconducting transition edge thermal sensor of claim 6 wherein the at least two layers are encapsulated by the sealing material, wherein the sealing material is an air and water impermeable van der Waals material.

8. Superconducting transition edge thermal sensor according to claim 6 when dependent on claim 5, wherein the at least two layers are encapsulated by the sealing material, wherein the sealing material is an air and water impermeable van der Waals material, and wherein the air impermeable van der Waals material is hexagonal boron nitride forming a heterostructure in which the three layers of graphene are embedded and a molar superlattice is generated due to lattice constant mismatch.

9. Superconducting transition edge thermal sensor according to any of claims 1-5, wherein the encapsulated at least two layers are patterned on a substrate (Su) to form nanostructures.

10. Superconducting transition edge thermal sensor according to any of claims 1-5, further comprising at least two electrodes (E1, E2) arranged and in electrical contact with respective locations of the active region (SC) of the superconducting film longitudinally spaced from each other, wherein the at least two electrodes (E1, E2) are operatively connected with a control unit to current-or voltage-bias the superconducting film and/or to read out electrical signals caused or modified by transitions between superconducting and non-superconducting phases occurring in the active region upon incidence of the quanta on the active region.

11. The superconducting transition edge thermal sensor according to any one of claims 1 to 5, wherein the active region (SC) of the superconducting film is configured and arranged to: quanta included in electromagnetic radiation having a wavelength of interest undergo a transition between a superconducting phase and a non-superconducting phase upon incidence.

12. The superconducting transition edge thermal sensor according to claim 10, wherein the active region (SC) of the superconducting film is configured and arranged to: undergoes a transition between a superconducting phase and a non-superconducting phase upon incidence of a quantum comprised in electromagnetic radiation having a wavelength of interest, and wherein:

-the at least two electrodes (E1, E2) are configured and shaped to form an antenna for allowing or improving electromagnetic coupling between the active area (SC) and the electromagnetic radiation; and/or

-at least the active region is embedded in a ring resonator, fabry-perot cavity, photonic crystal cavity or other type of optical cavity for optical coupling with the electromagnetic radiation.

13. The superconducting transition edge thermal sensor of claim 11 wherein the wavelength of interest is in the range of visible spectrum to THz radiation.

14. Superconducting transition edge thermal sensor according to any one of claims 1 to 5, constituting a calorimeter configured and arranged to measure the energy of a single quantum incident on the active region (SC) of the superconducting film.

15. The superconducting transition edge thermal sensor according to any one of claims 1 to 5 constituting a bolometer configured and arranged to measure an energy flux of a quantum incident on the active region of the superconducting film.

Technical Field

The present invention relates generally to superconducting transition edge thermal sensors, and more particularly to sensors including superconducting films made of superconductors exhibiting ultra-low electron thermal capacity.

Background

Today, it is desirable to detect quanta, and in particular single photons, with high sensitivity and is therefore a key enabling technology in many areas of research including quantum sensing, quantum key distribution, information processing and radio astronomy. Due to scientific needs and technical feasibility, Single Photon Detectors (SPDs) have been developed and even commercialized that will be used for wavelengths ranging from visible light to communication wavelengths, including near infrared (nIR).

Prior art SPD techniques rely on thermally induced destruction of the superconducting state in nanostructured Superconductors (SCs). Here, superconducting Transition Edge Sensors (TES) and Superconducting Nanowire Single Photon Detectors (SNSPD) have been developed as SPDs with the highest detection efficiency and the lowest dark count rate. Prior art SNSPDs and TES have so far demonstrated the most advanced SPD technology with the highest sensitivity and lowest dark count rate in the visible to near Infrared (IR) wavelengths.

However, although both SNSPD and TES operate with high efficiency in visible to near Infrared (IR) wavelengths, detection of low energy photons in mid-IR and terahertz (THz) wavelengths cannot be performed efficiently using detectors known in the art, and such detectors have not been developed as is well known so far. In other words, extension of broadband detection of single photons from nIR to infrared or even to terahertz (THz) is to be demonstrated for SNSPD and TES. The performance of single photon detectors at these wavelengths is currently limited by the material properties of the SC thin films used, which are disordered, bulky and have high electron heat capacity.

In particular, with respect to TES, these types of sensors utilize the steepness of temperature-dependent resistance at the superconducting transition edge, which enables a detectable voltage pulse to occur when electrons are heated by absorbed optical quanta. Since the energy of the absorbed photon is transferred to the entire electron collection, the performance of TES is determined by the heat capacity of the calorimetric materials used. Currently, this limits the SPD operation of TES to wavelengths below 8 μm, temperatures below 100mK, and detection times above 10 μ s. Strategies to reduce heat capacity have led to the targeted development of thinner nanostructured SC thin films and the use of SC with low carrier density, so that the absorbed heat is shared between fewer electrons. However, conventional material fabrication methods have set limitations to these developments. SC thin films are highly disordered, polycrystalline, and have a thickness exceeding several nanometers, because SC thin films are obtained from SC of high electron density by sputtering and etching.

Therefore, there is a need to provide an alternative to the prior art that covers the defects found therein by providing TES, in particular superconducting transition edge thermal sensors, that does not have the above-mentioned drawbacks associated with those known in the art and that significantly breaks through the above-mentioned limitations in operating wavelength, temperature and detection time.

Disclosure of Invention

To this end, the invention relates to a superconducting transition edge thermal sensor comprising a superconducting film defining an active region for incident quanta thereon.

In contrast to superconducting transition edge thermal sensors known from the prior art, in one of the present inventions, in a characteristic manner, the superconducting film is made of a superconductor, the critical temperature T of which is at_cThe superconductor exhibits less than 10¹³cm^-2And a carrier density of less than 10³k_bWherein the superconductor is formed of at least two layers of two-dimensional crystals stacked on top of each other.

The present inventors have tested a number of superconducting materials and arrangements and performed detailed mathematical calculations (some of which will be set forth in the following document) to find out which meet the above requirements to produce the above-mentioned at least two layers with appropriate superconducting materials according to an appropriate arrangement.

For some embodiments, suitable superconducting materials and arrangements are listed below. Other embodiments comprising alternative superconducting materials and arrangements that meet the above requirements of charge carrier density and electron heat capacity are also encompassed by the present invention.

The use of superconducting materials and arrangements listed below to fabricate superconducting transition edge thermal sensors is not known in the art, and applicability to the intended purpose of use is neither known nor desired in the art. In fact, in order to find those materials having such a low electronic heat capacity, the present inventors had to conduct detailed tests and mathematical calculations, which have not been completed in the art.

For an embodiment, the at least two layers are two graphene layers, the two graphene layers being twisted with respect to each other by an angle of 1.1 ° ± 0.1 ° such that they form a molar (moire) superlattice, a material commonly referred to as magic angle graphene. Superconduction occurs at carrier densities as low as 0.5 x 10¹²1/cm²Then (c) is performed. In contrast to conventional superconductors, magic angle graphene, which is a two-dimensional single crystal with ultra-high electron mass, exhibits an electron density that is orders of magnitude lower, and as will be explained below, the present inventors have found that such materials also exhibit an electron heat capacity that is orders of magnitude lower than conventional superconductors used as single photon detectors. These properties position magic angle graphene as an absolutely superior material for single photon sensing applications, and will enable the detection of lower energy photons in mid-IR and terahertz (THz) wavelengths with high resolution and fast response times.

For another embodiment, the at least two layers are two bilayer graphene twisted with respect to each other by an angle of 1.3 ° ± 0.1 ° such that they form a molar superlattice, wherein the graphene layers within each bilayer are aligned at 0.0 ° with respect to each other. Superconduction occurs at carrier densities as low as 2.45 x 10¹²1/cm²Then (c) is performed.

For yet another embodiment, the at least two layers are two bilayers WSe2, the two bilayers WSe2 are twisted relative to each other at an angle in the range of 1 ° to 4 ° such that they form a molar superlattice, and the WSe within each bilayer is a WSe in the two bilayers₂The layers are aligned at 0.0 deg. with respect to each other. In the range between 1 ° and 4 °, flat tapes supporting superconductivity can be observed. Superconduction occurs inCarrier density as low as 7 x 10¹²1/cm²Then (c) is performed.

According to another embodiment, the at least two layers are three graphene layers, the three graphene layers being aligned at a twist angle of 0 ° with respect to each other and the stacking order of the graphene layers corresponding to the ABC stacking order, forming three layers of graphene. Superconduction occurs at carrier densities as low as 0.5 x 10¹²1/cm²Then (c) is performed.

For any of the above embodiments, the at least two layers are hermetically and watertightly sealed by means of a sealing material, thereby avoiding surface degradation caused by oxidation. The sealing ensures a high crystalline quality and protects the at least two layers from environmental influences.

According to an implementation of this embodiment, the at least two layers are encapsulated by the above-mentioned sealing material, wherein the sealing material is an air and water impermeable van der waals material and is preferably placed on a substrate (typically a flat substrate).

Alternatively, the at least two layers are not encapsulated but only covered by the sealing material, since the at least two layers are arranged on a substrate (preferably a flat substrate), which has air and water sealed the at least two layers from their bottom side.

For the implementation of the above embodiment with reference to three-layer graphene, the air-impermeable van der waals material is hexagonal boron nitride, forming a heterostructure in which three layers of graphene are embedded and which produces a molar superlattice due to the mismatch in lattice constants.

For various embodiments of the sensor of the present invention, all of the superconductor materials disclosed above are low carrier density superconductors, wherein the superconducting state occurs at a carrier density of less than 10¹³1/cm²Then (c) is performed. The present inventors have found that these materials also exhibit ultra-low electron heat capacities, which are orders of magnitude lower than the electron heat capacities in other superconductors, and have found that the main cause of such ultra-low electron heat capacities is the contribution of electrons at fermi energies up to 3/2k_BT in the energy range.

According to an embodiment, the encapsulated at least two layers are patterned on the substrate to form nanostructures, i.e. structures having a nanometer scale.

For an embodiment, the sensor of the present invention comprises a back gate that allows tuning of the charge carrier density of the superconductor by applying a gate voltage thereto.

For another embodiment, the application of an appropriate gate voltage to the back gate can be used to tune the wavelength detection range, narrowing or widening the range.

For one embodiment, the superconducting transition edge thermal sensor of the present invention further comprises at least two electrodes arranged and in electrical contact with respective locations of the active region of the superconducting film longitudinally spaced from each other, wherein the at least two electrodes are operatively connected to the control unit to current-bias or voltage-bias the superconducting film, and/or to read out electrical signals caused or modified by the transition, into a transition between superconducting and non-superconducting phases occurring in the active region upon incidence of said quantum on the active region.

Although the sensor of the present invention is generally intended for the purpose of light detection, for the detection of optical photons, i.e. photons, the sensor is also suitable for the detection of non-optical photons, as long as the non-optical photons can be absorbed by the superconductor and carry energy to raise the temperature of the non-optical photons.

For some preferred embodiments, the active region of the superconducting film is configured and arranged to: quanta included in electromagnetic radiation having a wavelength of interest undergo a transition between a superconducting phase and a non-superconducting phase upon incidence.

Typically, the air-impermeable van der waals material is transparent to at least the wavelength of interest of the electromagnetic wave associated with the photon that makes up the quantum (i.e., to be detected).

According to an implementation of the above preferred embodiment, the at least two electrodes are configured and shaped to form an antenna for allowing or improving electromagnetic coupling between the active area and electromagnetic radiation having a wavelength of interest.

Additionally or alternatively, at least the active region is embedded in a ring resonator, fabry-perot cavity, photonic crystal cavity, or other type of optical cavity for optical coupling with electromagnetic radiation having a wavelength of interest.

The shape and size of the active area, i.e. the at least two layers forming the superconductor, can be adjusted to allow easy integration with different antenna and cavity designs to match the desired detection wavelength.

Preferably, the wavelengths of interest are in the range of the visible spectrum to THz radiation, although other wavelengths such as those of ultraviolet light are also encompassed by the present invention.

According to an embodiment, the superconducting transition edge thermal sensor constitutes a calorimeter configured and arranged to measure the energy of a single quantum incident on an active region of a superconducting film, implemented according to any of the embodiments and implementations of the superconducting transition edge thermal sensor of the present invention described in this document, unless explicitly described with respect to another device that is not a calorimeter.

According to another embodiment, the superconducting transition edge thermal sensor constitutes a bolometer configured and arranged to measure the energy flux of a quantum incident on an active region of the superconducting film, implemented according to any of the embodiments and implementations of the superconducting transition edge thermal sensor of the present invention described in this document, unless explicitly described with respect to another device that is not a bolometer.

In different sensors/detectors, there may be some confusion as to how different authors name their devices. Expressions such as bolometer, calorimeter, thermal detector or photon (or quantum) detector are used. In addition, coherent detectors such as heterodyne receivers may also be discussed in the context of superconducting bolometers. For some embodiments, all of those expressions are valid for defining the sensor of the present invention.

Since the use of thermal effects from absorbed single photons in superconductors represents the main detection principle in modern single photon detectors, including the sensor of the present invention with such low electron thermal capacity of the superconductor material, it can be used to advance single photon detection techniques for low energy photons.

The invention not only constitutes the first use of the two-dimensional material in the energy analysis superconducting calorimeter, but also constitutes the first use of the two-dimensional crystal molar superlattice in any practical application.

The invention has many different and possible applications. That is, it can be used for quantum communication protocols such as quantum key distribution and bell inequality testing, for quantum information, and for quantum sensing. Observation astronomy, and in particular radio astronomy, is also a possible application where it is of interest to detect the energy of long wavelength single photons (mid IR to THz wavelengths). There is no competing technology, and thus the sensor of the present invention may be an enabling technology. Further applications are thermal imaging, such as image arrays based on nano-calorimeters, and cameras for low-energy optical microscopes. The magnitude of the better energy resolution of the sensor of the present invention will drastically change the applicability of nano-calorimeters to even more advanced technologies.

The present invention encompasses combinations of two or more of any of the embodiments and implementations described in this document, where those combinations are possible and result in possible embodiments.

Drawings

Hereinafter, some preferred embodiments of the present invention will be described with reference to the accompanying drawings. They are provided for illustrative purposes only, and do not limit the scope of the present invention.

Fig. 1 relates to an embodiment of the sensor of the invention, for which the superconductor is formed by two graphene layers twisted by an angle of 1.1 ° ± 0.1 ° with respect to each other, i.e. by double-layer graphene twisted by a magic angle (hereinafter referred to as MATBG), implementing a single photon nano calorimeter. Schematic diagram of matbg sensor/device. Twisted bilayer graphene with a twist angle of 1.1 degrees was sandwiched between two pieces of hBN and embedded in the geometry of lateral gold photodetector/MATBG photodetector/gold photodetector on Si/SiO2 substrate (Su) including local graphite gate electrode (not shown). At low temperatures, the sheet resistance at optimum doping drops to zero. When a certain energy is availableThe temperature of the MATBG sheet is driven across the superconducting transition edge as photons are absorbed, producing a voltage drop proportional to the applied bias current. The voltage response relaxes with the thermal relaxation time of the system. b. Film thickness and carrier density for different two-dimensional superconductors commonly used in single photon detection applications, and selected thin film superconductors below 10 nm. The diagram includes a crystalline 2D superconductor (ZrNCl, BSCCO, NbSe)₂、MoS₂、WTe₂) Interface 2D superconductors (STO/LAO, FeSe/STO), elemental thin-film superconductors (Nb, Al), and composite thin-film superconductors of crystalline materials (NbN) and amorphous materials (WSi, MoSi), and MATBG (yellow star). The inset depicts experimentally obtained resistance of the sensor of the present invention, i.e., the MATBG apparatus, as a function of carrier density n and base temperature T, exhibiting different phases including a metallic state, a correlated state, and a superconducting state.

FIG. 2. intrinsic thermal performance of MATBG devices. a. Electron heat capacity as a function of T calculated from the density of states. The inset depicts the calculated low energy band structure at the magic angle. b. When n is 1.1.10¹²/cm²The photon absorption induced temperature rise of the superconducting dome according to the change of the photon frequency is Δ T for different base temperatures. c. When n is 1.1.10¹²/cm²The resistance R and dR/dT of the MATBG device changes according to the temperature T. The inset depicts an optical microscope image of the MATBG apparatus. The scale bar is 2 μm.

Figure 3 light response and relaxation time in magic angle graphene. a. Photon-induced voltage drop Δ V across the MATBG sheet as a function of base temperature and photon frequency at an applied 20nA bias current. The white triangles represent the maximum voltage response points. The inset shows the I/V characteristics of the experimentally obtained MATBG apparatus. b. Thermal relaxation time tau according to temperature change of equipment_thAnd thermal conduction via electron-phonon scattering G_e-phAnd Wilmann-Franz's law G_WFThe contributed heat dissipation. The inset depicts a legend of the thermal dissipation channels for the thermionic electrons in the MATBG after photon absorption. c. For from 0.5THz toFrequency of 20THz, MATBG sheet at T ═ T due to absorption of photons_cTransient voltage response.

Fig. 4 thermodynamic fluctuations and energy resolution. a. After measuring thousands of photons, a histogram of potential detected energy distributions of two different photon energies. Due to energy spreading, two photon energies can only be distinguished when their energies are separated by more than half the full width at Δ Ε maximum. b. The energy scale Δ E of the thermodynamic fluctuation calculated from the electron heat capacity and the associated relative temperature fluctuation δ T/T. c. Relative magnitude of optical response (V/V) at 1THz as a function of temperature of the device_max) And the maximum frequency resolution (Δ f) of single photon detection in MATBG in thermodynamic limits.

Fig. 5.a. the calculated band structure and density of states of the magic angle twisted bilayer graphene. b. For embodiments in which the superconductor is made of magic angle twisted bilayer graphene, the corresponding electron heat capacity as a function of temperature, calculated from the band structure and density of states in (a), of the 250nm x 250nm calorimeter according to the invention.

Fig. 6 is a sketch of a nano-calorimeter (i.e., a calorimeter having dimensions on the nano-scale) for use in the first and second embodiments of a sensor embodying the present invention. a. Top view: for the first embodiment, the active region (SC) of the nano-calorimeter, comprising a width (B) and a length (a), electrically contacts the two electrodes (E1 and E2). b. An isometric view of the first embodiment of the nano-calorimeter. c. Top view: an active region (SC) of the nano-calorimeter, comprising a width (B) and a length (a), which electrically contacts two electrodes (E1 and E2), and wherein the electrodes (E1 and E2) form a THz-antenna according to the second embodiment (only partially shown). d. An isometric view of the nano-calorimeter of the second embodiment. e. Top view: also according to the second embodiment, the electrodes (E1 and E2) form a THz antenna having a width (C) and a length (D), wherein the active region (SC) of the nano-calorimeter is a concentrated dissipative element in the THz antenna. f.e, wherein electrodes (E1, E2) forming an antenna and an active area (SC) are arranged on a substrate (Su).

FIG. 7 between superconducting domesAnd (6) comparing. a. For n is 5.10¹¹/cm²、n＝5·10¹¹/cm²And n is-1.7.10¹²/cm²Superconducting dome of time, according to temperature T₀A varying resistance R. b. For different superconducting domes, depending on the temperature T₀A varying dR/dT. c. According to temperature T₀Varying electron heat capacity. d. Thermal conduction contribution G of electron-phonon interaction_th. e. Thermal relaxation time tau according to temperature change of equipment_th. Maximum energy resolution for single photon detection in matbg.

Figure 8 relaxation time of magic angle graphene. a. The relative voltage at which the 1-THz photon is absorbed relaxes for different device temperatures. b. For T ═ T_cThe relative voltages at which photons of 1THz and 10THz are absorbed relax.

Fig. 9 transient relaxation of voltage response. a. For frequencies from 0.5THz to 20THz, the MATBG sheet at T ═ T due to absorption of photons_cTransient thermal response in time. b. A corresponding transient voltage response as a function of the temperature transient in (a).

Detailed Description

In this section some possible embodiments of the sensor of the invention will be described in detail, in particular for the implementation of the invention, the sensor is a nano-calorimeter and the superconducting film is made of superconducting magic angle twisted bi-layer graphene, also known as magic angle graphene, which will be used for energy-resolved high-speed single-photon detection.

In the MATBG calorimeter analyzed here, a "molar" pattern creates a long wavelength periodic potential by stacking two graphene layers on top of each other with opposite twist angles between the layers. The results show that for a well-defined twist angle of 1.1 °, the so-called "magic" angle, a flat band with ultra-high density of states (DOS) (compared to regular graphene) is formed and at T_c>The 3K case produces the relevant insulated and dome-shaped superconducting phases that interact to drive.

In contrast to conventional SC's, magic angle graphene, which is a two-dimensional single crystal with ultra-high electron mass, exhibits an electron density that is orders of magnitude lower, and as will be explained below, the present inventors have found that such materials also exhibit an electron heat capacity that is orders of magnitude lower than conventional superconductors used as single photon detectors. These properties position magic angle graphene as an absolutely superior material for single photon sensing applications, and will enable the detection of lower energy photons in mid-IR and terahertz (THz) wavelengths with high resolution and fast response times.

In this section, the inventors have demonstrated through electron transport experiments that the superconductor material (magic angle graphene) used to make the calorimeter of an embodiment of the sensor according to the invention exhibits the material properties necessary for single photon detection. In particular, in order to demonstrate its ultra-low electron thermal capacity, a single photon calorimeter made of magic angle twisted double-layer graphene (MATBG) was proposed. A complete detailed theoretical analysis of the theoretically implementable single photon detection performance of the calorimeter is also provided.

The inventors also demonstrated the feasibility of producing energy-resolved SPDs from MATBG by estimating their thermal response due to the absorption of single photons. Due to the steep temperature-dependent resistance at its SC transition edge, a voltage pulse can be generated which can be generated by a photon which can be directly read out.

FIG. 1(a) depicts a schematic of a sensor/detector studied herein, consisting of a material on Si/SiO₂A 250nm x 250nm superconducting MATBG sheet in electrical contact on top of the substrate Su, acting as a capacitive back gate allowing tuning of n by applying a gate voltage. For some embodiments, applying an appropriate gate voltage to the capacitive back gate may also be used to tune the wavelength detection range, narrowing or widening the range. In MATBG, for T₀→T_cThe superconducting gap will disappear, allowing in principle a wide band of light absorption even at frequencies much lower than THz, the absorption coefficient of graphene at low energies being only-2.3%. However, we can solve this problem, where several methods have been successfully developed and implemented, by combining it with photonic crystals, fabry-perot microcavities or ring resonators to operate at wavelengths in the near and mid IR, and by combining it with the methods used for THz operationThe antenna integration of the rows improves the absorption rate of the graphene to nearly 100%. Importantly, after the electrons absorb the energy of the photon, the energy is thermalized on a time scale of 100fs by electron-electron scattering within the electron bath, which is much faster than the relaxation time of the fermi energy. The subsequent photoexcited electron distribution can therefore be described by the effective electron temperature first order decoupled from the crystal lattice.

First, the temperature-dependent electron heat capacity C of MATBG electrons is calculated_e(T) to quantify the thermal behavior of MATBG electrons. The present inventors first calculated the single-particle band structure of MATBG, in which an ultra-flat band close to charge neutrality was obtained (fig. 2(a), inset, and band in fig. 5 (a)). From this band structure and DOS we can further calculate the electron heat capacity. In particular, we can extract the density of states, according to the energy dispersion of these "molar" bands, to obtain C_e(T) (see "calculation of Heat Capacity and Cooling time" below). Fig. 2(a) and 5(b) show that for n 1.1 · 10¹²/cm²C as a function of temperature T_eThis corresponds to the density of one SC dome (see fig. 7(c) for the other SC domes). Notably, the inventors have found that the low carrier density is close to SC T_cAt a temperature of about only a few hundred k, causes an electron heat capacity having a very small value_bThe ratio shows a heat capacity in the range of 10⁴To 10⁵k_b2 to 3 orders of magnitude lower than any other superconducting single photon detector. These calculations are also valid for all superconducting materials mentioned in the previous section for the different embodiments. Therefore, since the low electron heat capacity is directly proportional to the low carrier density, all those superconducting materials will show similar detection performance as MATBG when used as the active area of the sensor of the present invention.

By equating the energy of the incident photon with an increase induced by absorption of internal energyThe inventors calculated the temperature increase Δ T of electrons in the MATBG sheet based on photon absorption. FIG. 2(b) depicts the root for different temperatures TThe corresponding Δ T according to the change in photon frequency. Notably, forThe inventors have found that the value of Δ T is relatively large, on the order of a few K for mid-IR photons, but even for photons at THz and 100GHz frequencies, Δ T is quite large, on the order of 10 to 100 mK. For optimal detection performance, a sharp SC transition is highly desirable as it enables a detectable voltage pulse to occur even from a weak photon induced thermal pulse. FIG. 2(c) shows experimentally obtained R and dR/dT as a function of temperature T for 1.1.10 at n¹²/cm²Optimal doping of the superconducting dome (fig. 7(a) and (b) for other SC domes). At T_cNear the critical temperature of 0.65K, the device exhibits a very sharp transition edge with a large resistance change.

To evaluate the performance of intrinsic detectors, the inventors extracted the photon-induced voltage change Δ V across or current-biased MATBG sheets (see "calculation of detector response and energy resolution" below). This is achieved by combining the temperature dependent resistivity at the superconducting transition with the temperature change Δ T calculated due to absorption of a single photon. FIG. 3(a) is an inset showing the I/V characteristics of an experimentally obtained MATBG device, where the inventors found superconducting critical current I_c> 20 nA. To maximize Δ V, the device is current biased to just at I_cHereinafter, I ═ 20 nA. The frequency f according to T and the absorption photon is thus obtained_pThe changed Δ V is shown in fig. 3 (a). Notably, for a very wide photon frequency range from nIR up to-100 GHz, a relatively large voltage signal on the order of tens of μ V was found.

The lifetime of the voltage pulse is determined by the intrinsic thermal relaxation path of the thermally excited electrons in the MATBG sheet. Here, the inventors assume that the dominant thermal dissipation channel is the measurement of phonons (G) acoustically by electron-phonon interaction, as established for single layer graphene devices (e.g., for the case of a single layer graphene device)_e-ph) And by the Wilman-Franz law (G)_WF) From heat diffusion to electrons, corresponding to the main heat dissipation channelThe thermal conductivity is plotted in fig. 3 (b). In contrast to single-layer graphene, which has relatively small electron-phonon interactions at low T, the inventors found that G was present in MATBG at all temperatures_e-phPredominance, over G_WFSeveral orders of magnitude. The inventors do not consider cooling by optical phonon scattering and radiative cooling, since the energies involved are much smaller than that of optical phonons, and radiative cooling can be estimated as G_rad～k_BB, where B is the measurement bandwidth, 1GHz for B, yield ratio G_e-phAt least 5 orders of magnitude smaller.

Already G_e-phAfter establishing as the dominant thermal relaxation mechanism, the inventors passed the quasi-equilibrium relationship G_e-ph·τ＝C_eThermal relaxation times τ for different T were obtained as shown in fig. 3(b) (see "calculation of heat capacity and cooling time" below, and fig. 7(d) and (e) for other SC domes). Fig. 3(c) shows that for photon frequencies between 0.5THz and 20THz, at T ═ T_cThe transient thermal response of the device upon photon absorption (see also fig. 8 and 9). Significantly, the hot electron distribution relaxes within-4 ns for all photon frequencies, orders of magnitude faster than other superconducting single photon detectors that exhibit recovery times in SNSPD of about nanoseconds and even in TES of milliseconds. The inventors have noted that at lower device temperatures, the decrease in electron-phonon interactions causes a strong increase in relaxation time, exceeding 100ns at T0.3K and even 1 μ s at T0.25K (compare fig. 8 (a)).

Depending on the final detector architecture, a broadband low noise amplifier such as a HEMT may be used to further process the fast intrinsic optical response of MATBG. Another method for processing the response is dynamic inductance detection (KID), which causes a shift in the resonant frequency in the coupled microresonator based on the change in dynamic inductance in the MATBG upon photon absorption. Compared to resistance readings, KID is much less applicable than superconducting transitions that can allow even higher sensitivity. But in principle the voltage response obtained can even be so large that it is easy to read by a dedicated nano-voltmeter, allowing for direct reading on the chip.

When the amplitude of the sensor/detector response increases monotonically with increasing photon frequency, the energy of the absorbed photon can be resolved from the transient response. The final possible energy resolution of the feedback-free calorimeter is limited by the thermodynamic energy fluctuation based on the time scale of the thermal relaxation time of the system²〉＝k_BT²C. We can understand these thermodynamic fluctuations from the following aspects: the random fluctuation of the internal energy of the electron distribution is due to its statistical nature as a canonical ensemble of heat exchange with the bath. Fig. 4(a) illustrates measurement uncertainty using an exemplary histogram, which is the energy distribution of two photons that differ in energy, detected when thousands of photons are measured. Due to energy spreading, two photon energies can only be distinguished when their energies are separated by more than half the full width at Δ Ε maximum. FIG. 4(b) shows the energy scale of these fluctuations in the MATBG device as a function of device temperatureAnd associated relative temperature delta T ═ delta E/C_e. At T_cWhere the energy fluctuation is about Δ E to 1meV and the relative temperature fluctuation is about δ T<0.1T. It is important to note that δ T does not correspond to the actual fluctuation of the device temperature, but rather is a temperature scale of thermal energy between macroscopic states of the system, as the calorimeter directly measures the thermal energy. FIG. 4(c) shows the maximum photon frequency resolution in MATBGThis is limited by thermodynamic fluctuations. The relative magnitude of the optical response is depicted as f_ph1 THz. At the optimum operating temperature, the inventors found that the sensor of the present invention allows energy resolution in the 0.4THz range, which is comparable to the most sensitive calorimeter for THz applications (see fig. 7(f) for other SC domes). The inventors have noted that in calorimeters with strong electrothermal feedback, the energy resolution can exceed this thermodynamic limitA multiple of, whereinFor the device/sensor/detector of the present invention, the inventors found a to 15, which gives an energy resolution of-0.2 THz.

Calculation of heat capacity and cooling time:

to determine the heat capacity and the cooling time, we obtained a distribution function f with momentum k and electrons in band λ starting from a kinetic equation without the presence of an external field and particle flow_k,λNamely (Principi, A. et al, Super-Planckian Electron decoration in a van der Waals Stack. Phys. Rev. Lett.118,126804 (2017)):

wherein the collision integral reading of electron-phonon interaction:

where V (q, V) is the interaction between the electron and phonon modes V (e.g., longitudinal or transverse), and D_{k,λ；k',λ'}Is the modulo square of the matrix elements between the initial and final states k, λ and k ', λ' of the electronic operator to which the phonon displacements are coupled. For the determination, the operators are assumed to be electron density. Other phonon models have been addressed in the literature and will not be discussed here, with the emphasis on providing an order of magnitude estimate for the cooling time. In equation (2), ε_k,λAnd ω_q,νRespectively, electron and phonon energies, and f_k,λAnd n_q,νAre their distribution functions. In the equilibrium state, f_k,λ(n_q,ν) Is a fermi-dirac (bose-einstein) distribution.

Let f_k,λAnd n_q,νRespectively is the temperature T_eAnd T_LOfFermi-dirac distribution and bose-einstein distribution, each of the two subsystems (electronic and lattice vibrations) is therefore in thermal equilibrium, but not the whole system. To determine the thermal conductivity between them, equation (1) is multiplied by ε_k,λμ, where μ is the chemical potential, and we integrate it over k and sum over λ. Extended to T_e→T_LWe getWherein

Is a heat capacity, and

in the case of the equation (4),

by assuming density and T_eIndependent (and fixed by an external gate, for example). In the case of the equation (5),

thus, the cooling time is defined by τ^-1Is defined as Σ/C.

An estimate of the cooling time is now provided. The goal is to approximate Im [ χ (q, ω) in equation (7)_q,v)]. For this reason, it is noted that at T1K, only about 4K of energy is present_BThe phonons of T-0.3 meV participate in the integration, since the derivative of the Bose-Einstein distribution strongly suppresses the higher energy excitation. These energies correspond to q to 0.05nm^-1Phonon momentum (using phonon velocity C)_ph＝10⁴m/s). Typical electron momentum is about 2 pi/L_moire～0.1-0.4nm^-1I.e. much larger than the phonon momentum. Therefore, we can estimate Im [ χ (q, ω) in the zero temperature and limit of q → 0_q,v)]. Constrained to two flat bands and approximating the matrix elements as D_{k,λ；k′,λ′}1 (this is τ)^-1Providing an upper limit) and assuming that the band is almost particle pore symmetric, we get after some operations:

wherein f (x) ═ (e)^x+1)^-1Is a fermi-dirac distribution and N (epsilon) is the density of states at energy epsilon. N (ε) was calculated according to the following continuous model: koshino, M. et al, Maximally Localized Wannier Orbituals and the Extended Hubbard Model for a two layer graphene. Phys. Rev. X8, 031087 (2018). Equation (5) is then easily evaluated by (Das Sarma, s., Adam, s., Hwang, E.H) as follows.&Rossi,E.Electronic transport in two-dimensional graphene.Rev.Mod.Phys.83,407–470(2011)：

Wherein (see also Ni, G.X., et al, Fundamental limits to graphene plasmonics. Nature 557, 530-533 (2018)), g is 3.6eV, and ρ is 7.6 × 10^-7kg/m²Andis the reduced planck constant. Note that by knowing the expression for the density of states N (epsilon), the integral over momentum in equations (4) and (6) can be easily recombined into an integral over the band energy.

Calculation of detector response and energy resolution:

calculating the electron heat capacity C to MATBG according to the temperature change_eAfter (T), by converting the absorbed photonsEnergy E_photonCalculating photon-induced temperature increase equal to the temperature-induced increase in internal energy

Where h is the Planck constant, f_photonIs the frequency of the absorbed photon, T₀Is the temperature of MATBG before photon absorption, and T_maxIs the temperature of MATBG upon absorption of a photon. Solution according to f_photonAnd T₀Varying T_maxAnd T is₀We were allowed to calculate the photon energy dependent thermal response of the MATBG sheet.

Using experimentally obtained R (T) and the calculated temperature rise Δ T (T)₀,f_photon)＝T_max(f_photon,T₀)-T₀And calculating the change of the MATBG resistance during photon absorption. Using a current just below the experimentally obtained critical current I_cCalculating the voltage drop DeltaV (T)₀,f_Photon)＝I·ΔR(T₀,f_photon)。

Due to the fast thermalization time of 100-fs (Tielroij, K.J. et al, Photoexitation cascade and multiple hot-carrier generation in graph. Nat. Phys.9, 248-252 (2013)), upon photon absorption, the rise time of the temperature transient is assumed to be instantaneous compared to the subsequent thermal relaxation, which is modeled by the exponential decay of the time constant τ obtained from the above calculation of the heat capacity and cooling time. The corresponding transient voltage response is then calculated according to R (t)).

On the time scale of the thermal time constant of the system, the amount of internal energy fluctuation of the calorimeter in thermal equilibrium with the bath is < Δ E²〉＝k_BT²C(Chui,T.C.P.,Swanson,D.R.,Adriaans,M.J.,Nissen,J.A.&Lipa, J.A. temperature fluctuations in the metabolic syndrome. Phys.Rev.Lett.69, 3005-3008 (1992)). The energy scale determines the uncertainty of any given energy measurement in the calorimeter and is considered as such at the energy of the calorimeterThermodynamic limit in resolution. The full width at the maximum half of the distribution in E is used as an energy discrimination threshold to distinguish between two incident photon energies.

The sensor object of the present invention, analyzed experimentally and theoretically as described above, has the following characteristics:

-implementing a superconducting nano-calorimeter for sensitive energy-resolved broadband photodetection from visible to terahertz frequencies.

Single photon sensitivity for the entire spectrum from visible to terahertz frequencies.

Sensitive energy resolution of-0.2 THz

-high quantum efficiency QE > 90%

Low dark count rate <1Hz

High detector speed 4ns

Fig. 6 shows a different possible alternative arrangement of the sensor of the invention for which the MATBG superconducting film is the active region SC of the nano-calorimeter. For the illustrated embodiment, the active region SC of the nano-calorimeter is patterned into a rectangular shape including a width B of 250nm and a length a of 250nm using a dedicated nano-fabrication technique. Depending on the type of application, the width a and length B may be in the range of 100nm for low energy detection and up to 100 μm for applications requiring large detector areas. The active area may be further shaped to form a nanowire having a width a of about 100nm and a length B of about 100 μm up to 1mm to increase the resistance of the active area and the effective detector area. The active area SC is electrically contacted by two metal electrodes E1 and E1. Electrodes E1 and E2 provide electrical contact of active area SC with dedicated reading electronics.

For certain applications at low photon energies, as depicted in fig. 6(C), (D), (E), (f), the shape of electrodes E1 and E2 may form an antenna having a width C, a length D, which is capable of coupling radiation to active area SC with nearly 100% efficiency. The width C and length D may be between 10 μm and 1mm depending on the application requirements. For mid-to near-infrared applications, the active region of electrical contact may further be embedded in a ring resonator, fabry-perot cavity, or photonic crystal cavity. The shape and size of the active area SC may be adjusted to allow easy integration with different antenna and cavity designs to match the desired detection wavelength. Electrical contact of the active area to dedicated reading electronics can be provided by coupled THz antennas or, in the case of cavity coupling for visible and infrared radiation, by nanofabrication electrodes.

Although the above embodiments relate to calorimeters, as mentioned in the previous section, a bolometer (such as a thermionic bolometer) is also a possible implementation of the sensor of the present invention.

Furthermore, it has to be noted that some well known components of superconducting calorimeters/bolometers (thermal storage, thermal links, reading electronics, coolers, etc.) are not only not described herein, but are also not depicted in the schematic diagrams of fig. 1 and 6, in order to avoid obscuring the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details.

Variations and modifications in the described embodiments may be effected by those skilled in the art without departing from the scope of the invention as defined by the appended claims.