Yuri M. Galperin

The performance of low-temperature detectors utilizing thermal effects is determined by their energy relaxation properties. Usually, heat transport experiments in mesoscopic structures are carried out in the steady state, where temperature gradients do not change in time. Here, we present an experimental study of dynamic thermal relaxation in a mesoscopic system—thin metallic film. We find that thermal relaxation of hot electrons in copper and silver films is characterized by several time constants, and that the annealing of the films changes them. In most cases, two time constants are observed, and we can model the system by introducing an additional thermal reservoir coupled to the film electrons. We determine the specific heat of this reservoir and its coupling to the electrons. We suspect that multiscale thermal relaxation arises from the complicated morphology of the films, in which the electron–phonon coupling strength in grains with different orientations varies.

In this short review we pass through the milestones in the studies of the electronic topological transitions (ETT) and focus on some recent applications of the ideas worked out in their classical theory. These are: two-dimensional electron systems, de Haas-van Alphen effect, classification of ETT in multidimensional systems, superconductivity in systems close to ETT, and thermoelectricity in heavy-fermion systems where the cascades of topological changes of Fermi surface (FS) are generated by magnetic field. The history of studies of ETT is inextricably linked with Kharkov school of condensed matter physics, with such names as I. M. Lifshitz, V. G. Bar’yakhtar, and many other. Among them is Moisey Isaakovich Kaganov, who contributed much in the studies of the role of geometry and topology of FS in physical properties of the metals. Two of the authors (A.V. and Y.G.) had the honor and pleasure to work with M. I. Kaganov — Y. M. Blanter, M. I. Kaganov, A. V. Pantsulaya, and A. A. Varlamov, Phys. Rep. 245, 159 (1994);¹ all of us have been learning the niceties of science from his books. “The Fermi surface is the stage on which the drama of the life of the electron is played out” wrote Kaganov and Lifshitz. We devote this work to their memory.

We extend the thermodynamic approach for the description of the thermal Hall effect in two-dimensional superconductors above the critical temperature, where fluctuation Cooper pairs contribute to the conductivity, as well as in disordered normal metals where the particle-particle channel is important. We express the Hall heat conductivity in terms of the product of temperature derivatives of the chemical potential and of the magnetization of the system. Based on this general expression, we derive the analytical formalism that qualitatively reproduces the superlinear increase of the thermal Hall conductivity with the decrease of temperature observed in a large variety of experimentally studied systems [Grissonnanche et al., Nature (London) 571, 376 (2019)]. We also predict a nonmonotonic behavior of the thermal Hall conductivity in the regime of quantum fluctuations, in the vicinity of the second critical field and at very low temperatures.

We theoretically analyze two setups of low-energy single-photon counters based on Josephson junctions (JJs). For this, we propose two simple and general models based on the macroscopic quantum tunneling formalism (MQT). The first setup is similar to the photon counter based on the “cold-electron bolometer” (CEB), where the JJ replaces the CEB in the center of the superconducting antenna. In the second setup, the JJ is capacitively coupled to the antenna. We derive the Hamiltonians for the two setups, and we write the Schrödinger equations, taking into account both the antenna and the JJ. The quantum particles of the MQT models move in two-dimensional potential landscapes, which are parabolic along one direction and may have the form of a washboard potential along another direction. Such a potential landscape has a series of local minima, separated by saddle points. If the particle is prepared in the initial state in the metastable “ground state” of a local minimum, then the photon absorption causes it to jump into an excited state. If the excitation energy is bigger than the potential barrier seen by the quantum particle (the difference between the ground state and the saddle point), the photon is detected. The models are simple and allow us to do mostly analytical calculations. We show that the two setups are equivalent from the MQT point of view since one Hamiltonian can be transformed into the other by changes in variables. For typical values of the JJ and antenna parameters, the setups may work as counters of photons of wavelengths up to at least 1 cm. Dark count rates due to the phase particle tunneling directly from the ground state into the running state have also been evaluated.

The magnetic anisotropy of superconducting niobium films of different thickness was investigated using magneto-optical imaging. A wide range of anisotropic behaviors was generated by freezing in different in-plane external magnetic fields with magnitude up to 1.12 kOe. The critical fields for the parallel configuration of the different samples were calculated, taking into account the strong deviation of the superconducting properties at small thicknesses. Above their lower in-plane critical field the films are in the mixed state containing coplanar vortices. In structurally isotropic Nb films, when then applying a perpendicular magnetic field, the frozen-in vortices were seen to guide the perpendicular ones. It is shown that the anisotropy increases with both the film thickness and the magnitude of the in-plane field. The results demonstrate that field-induced anisotropy is a highly versatile way to manipulate vortex matter in film superconductors.

Active triggering and manipulation of ultrafast flux dynamics in superconductors are demonstrated in films of Nb. Controlled amounts of magnetic flux were injected from a point along the edge of a square sample, which at 2.5 K responds by nucleation of a thermomagnetic avalanche. Magneto-optical imaging was used to show that when such films are cooled in the presence of in-plane magnetic fields they become anisotropic, and the morphology of the avalanches changes systematically, both with the direction and magnitude of the field. The images reveal that the avalanching dendrites consistently bend towards the direction perpendicular to that of the in-plane field. The effect increases with the field magnitude, and at 1.5 kOe the triggered avalanche becomes quenched at the nucleation stage. The experimental results are explained based on a theoretical model for thermomagnetic avalanche nucleation in superconducting films, and by assuming that the frozen-in flux generates in-plane anisotropy in the film thermal conductance. The results demonstrate that applying in-plane magnetic fields to film superconductors can be a versatile external tool for controlling their ultrafast flux dynamics.

Stability of the vortex matter—magnetic flux lines penetrating into the material—in type-II superconductor films is crucially important for their application. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger an electromagnetic breakdown. In this paper, we review recent theoretical and experimental results on development of the above mentioned thermomagnetic instability. Starting from linear stability analysis for the initial critical-state flux distribution we then discuss a numerical procedure allowing to analyze developed flux avalanches. As an example of this approach we consider ultra-fast dendritic flux avalanches in thin superconducting disks. At the initial stage the flux front corresponding to the dendrite's trunk moves with velocity up to 100 km/s. At later stage the almost constant velocity leads to a specific propagation regime similar to ray optics. We discuss this regime observed in superconducting films coated by normal strips. Finally, we discuss dramatic enhancement of the anisotropy of the flux patterns due to specific dynamics. In this way we demonstrate that the combination of the linear stability analysis with the numerical approach provides an efficient framework for understanding the ultra-fast coupled nonlocal dynamics of electromagnetic fields and dissipation in superconductor films.