Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.

Abstract: In this paper, we propose and present data from a fast THz detector based on the repurpose of hot electron bolometer mixers (HEB) fabricated from superconducting NbN thinfilm. This detector is essentially a traditional NbN bolometer element that operates under the influence of a microwave pump. The in-jected microwave power serves the dual purpose of enhancing the detector sensitivity and reading out the impedance changes of the device in response to incidentTHz radiation. We have measured an optical Noise Equivalent Power of 4 pW/ Hz for our detector at a bath temperature of 4.2 K. The measurement frequency was 0.83 THz and the modulation frequency was 1.48 kHz. The readout
scheme is versatile and facilitates both high-speed operation as well as multi-pixel applications.

Abstract: We characterize superconducting antenna-coupled hot-electron bolometers for direct detection of terahertz radiation operating at a temperature of 9.0 K. The estimated value of responsivity obtained from lumped-element theory is strongly different from the measured one. A numerical calculation of the detector responsivity is developed, using the Euler method, applied to the system of heat balance equations written in recurrent form. This distributed element model takes into account the effect of nonuniform heating of the detector along its length and provides results that are in better agreement with the experiment. At a signal frequency of 2.5 THz, the measured value of the optical detector noise equivalent power is 2.0 × 10-13 W · Hz-0.5. The value of the bolometer time constant is 35 ps. The corresponding energy resolution is about 3 aJ. This detector has a sensitivity similar to that of the state-of-the-art sub-millimeter detectors operating at accessible cryogenic temperatures, but with a response time several orders of magnitude shorter.

Abstract: Hot-electron bolometer devices, used successfully in low noise heterodyne mixing at frequencies up to 2.5 THz, have been analyzed. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, is used to model pumped IV curves and understand the physical conditions during the mixing process. We argue that the mixing is predominantly due to the strongly temperature dependent local resistivity of the NbN. Experimentally we identify the origins of different transition temperatures in a real HEB device, suggesting the importance of the intrinsic resistive transition of the superconducting bridge in the modeling.

Abstract: The research by the group of Moscow State Pedagogical University into the hot-electron phenomena in thin superconducting films has led to the development of new types of detectors and their use both in fundamental and applied studies. In this paper, we present the results of testing the terahertz HEB receiver systems based on ultrathin (∼ 4 nm) NbN and MoRe detectors with a response time of 50 ps and 1 ns, respectively. We have developed three types of devices which differ in the way a terahertz signal is coupled to the detector and cover the following ranges: 0.3–3 THz, 0.1–30 THz and 25–70 THz. In the case of the receiving system optimized for 0.3–3 THz, the sensitive element (a strip of asuperconductor with planar dimensions of 0.2μm (length) by 1.7μm (width)) was integrated witha planar broadband log-spiral antenna. For additional focusing ofthe incident radiation a silicon hyperhemispherical lens was used. For the 0.1–30 THz receivingsystem, the sensitive element was patterned as parallel strips(2μm wide each) filling an area of 500×500μm2with a filling factor of 0.5. In the receivingsystem of this type we used direct coupling of the incident radiation to the sensitive element. Inthe 25–70 THz range (detector type 2/2a in Table 1) we used a square-shaped superconductingdetector with planar dimensions of 10×10μm2. Incident radiation was coupled to the detectorwith the use of a germanium hyperhemispherical lens.The response time of the above receiving systems is determined by the cooling rate of the hotelectrons in the film. That depends on the electron-phonon interaction time, which is less forultrathin NbN than in MoRe.

Abstract: We present a new generation of superconducting single-photon detectors (SSPDs) and hot-electron superconducting sensors with record characteristic for many terahertz and optical applications.

Abstract: Diffusion-cooled aluminum hot-electron bolometer (HEB) mixers are of interest for low-noise high resolution THz-frequency spectroscopy within astrophysics. Al HEB mixers offer operation with an order of magnitude less local oscillator power, higher intermediate frequency bandwidth and potentially lower noise than competing devices made from other materials. We report on mixer experiments at 618 GHz with devices fabricated from films with sheet resistances in the range from about 55 Ω down to about 9 Ω per square. Intermediate frequency bandwidths of up to 3 GHz were measured (1 μm long device), with absorbed local oscillator power levels of 0.5 to 6 nW and mixer conversion up to -21.5 dB. High input coupling efficiency implies that the electrons in the device are able to thermalize before escaping from the device. It was found that the long coherence length complicates mixer operations due to the proximity of the contact pads. Also, saturation at the IF frequency may be a concern for this type of device, and warrants further studies.

Abstract: Recently, a next-generation heterodyne mixer detector – a hot electron bolometer (HEB) mixer employing a superconducting microbridge – has gradually opened up terahertz-band astronomy. The surrounding state-of-the-art technologies including fabrication processes, 4 K cryostats, cryogenic low-noise amplifiers, local oscillator sources, micromachining techniques, and spectrometers, as well as the HEB mixers, have played a valuable role in the development of super-low-noise heterodyne spectroscopy systems for the terahertz band. The current developmental status of terahertz-band HEB mixer receivers and their applications for spectroscopy and astronomy with ground-based, airborne, and satellite telescopes are presented.