Proposed Model of the Giant Thermal Hall Effect in Two-Dimensional Superconductors: An Extension to the Superconducting Fluctuation Regime.

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)NATUAS0028-083610.1038/s41586-019-1375-0]. 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.

Influence of measurement error on Maxwell's demon.

In any general cycle of measurement, feedback, and erasure, the measurement will reduce the entropy of the system when information about the state is obtained, while erasure, according to Landauer's principle, is accompanied by a corresponding increase in entropy due to the compression of logical and physical phase space. The total process can in principle be fully reversible. A measurement error reduces the information obtained and the entropy decrease in the system. The erasure still gives the same increase in entropy, and the total process is irreversible. Another consequence of measurement error is that a bad feedback is applied, which further increases the entropy production if the proper protocol adapted to the expected error rate is not applied. We consider the effect of measurement error on a realistic single-electron box Szilard engine, and we find the optimal protocol for the cycle as a function of the desired power P and error ɛ.

Cooling by heating: Restoration of the third law of thermodynamics.

We have made a simple and natural modification of a recent quantum refrigerator model presented by Cleuren et al. [Phys. Rev. Lett. 108, 120603 (2012)]. The original model consist of two metal leads acting as heat baths and a set of quantum dots that allow for electron transport between the baths. It was shown to violate the dynamic third law of thermodynamics (the unattainability principle, which states that cooling to absolute zero in finite time is impossible). By taking into consideration the finite energy level spacing Δ, in metals we restore the third law while keeping all of the original model's thermodynamic properties intact down to the limit of k(B)T ∼ Δ, where the cooling rate is quenched. The spacing Δ depends on the confinement of the electrons in the lead and therefore, according to our result larger samples (with smaller level spacing), could be cooled efficiently to lower absolute temperatures than smaller ones. However, a large lead makes the assumption of instant equilibration of electrons implausible; in reality one would only cool a small part of the sample and we would have a nonequilibrium situation. This property is expected to be model independent and raises the question whether we can find an optimal size for the lead that is to be cooled.

Dephasing and dissipation in qubit thermodynamics.

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctuation relations (FRs) of nonequilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy U, leads to deviations in FRs under the same conditions. We relate the average 〈e(-ßU)〉 (where ß is the inverse temperature) with the qubit's relaxation and dephasing rates in the weak dissipation limit and discuss this relationship for different mechanisms of decoherence.

Universal behavior of magnetoresistance in quantum dot arrays with different degrees of disorder.

The magnetoresistance in a two-dimensional array of Ge/Si quantum dots was studied in a wide range of zero magnetic field conductances, where the transport regime changes from a hopping to a diffusive one. The behavior of the magnetoresistance is found to be similar for all samples--it is negative in weak fields and becomes positive with increasing magnetic field. The result apparently contradicts existing theories. To explain experimental data we suggest that clusters of overlapping quantum dots are formed. These clusters are assumed to have metal-like conductance, the charge transfer taking place via hopping between the clusters. Relatively strong magnetic field shrinks electron wavefunctions, decreasing inter-cluster hopping and, therefore, leading to a positive magnetoresistance. Weak magnetic field acts on 'metallic' clusters, destroying the interference of the electron wavefunctions corresponding to different paths (weak localization) inside clusters. The interference may be restricted either by inelastic processes, or by the cluster size. Taking into account weak localization inside clusters and hopping between them within the effective medium approximation, we extract effective parameters characterizing charge (magneto-) transport.

Information flow and optimal protocol for a Maxwell-demon single-electron pump.

We study the entropy and information flow in a Maxwell-demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages, which minimizes irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems in which barriers between different regions can be manipulated.

Lightning in superconductors.

Crucially important for application of type-II superconductor films is the stability of the vortex matter--magnetic flux lines penetrating the material. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger a massive electromagnetic breakdown. Up to now, the time-resolved behaviour of these ultra-fast events was essentially unknown. We report numerical simulation results revealing the detailed dynamics during breakdown as within nanoseconds it develops branching structures in the electromagnetic fields and temperature, with striking resemblance of atmospheric lightning. During a dendritic avalanche the superconductor is locally heated above its critical temperature, while electrical fields rise to several kV/m as the front propagates at instant speeds near up to 100 km/s. The numerical approach provides an efficient framework for understanding the ultra-fast coupled non-local dynamics of electromagnetic fields and dissipation in superconductor films.

Slow relaxation of magnetoresistance in AlGaAs-GaAs quantum well structures quenched in a magnetic field.

We observed a slow relaxation of the magnetoresistance in response to an applied magnetic field in selectively doped p-GaAs-AlGaAs structures with a partially filled upper Hubbard band. We have paid special attention to excluding the effects related to temperature fluctuations. Although these effects are important, we have found that the general features of slow relaxation persist. This behavior is interpreted as related to the properties of the Coulomb glass formed by charged centers with account taken of spin correlations, which are sensitive to an external magnetic field. Variation of the magnetic field changes the numbers of the impurity complexes of different types. As a result, it affects the shape and depth of the polaron gap formed at the states belonging to the percolation cluster responsible for the conductance. The suggested model explains both the qualitative behavior and the order of magnitude of the slowly relaxing magnetoresistance.

Statistics of deep energy states in Coulomb glasses.

We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential, which is in agreement with extreme value statistics considerations. The relaxation of the system energy shows logarithmic time dependence reflecting the ultrametric structure of the system.

Dramatic role of critical current anisotropy on flux avalanches in MgB2 films.

Anisotropic penetration of magnetic flux in MgB(2) films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, the anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate perpendicular to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.

Interaction between superconducting vortices and a Bloch wall in ferrite garnet films.

A theoretical model for how Bloch walls occurring in in-plane magnetized ferrite garnet films can serve as efficient magnetic micromanipulators is presented. As an example, the walls' interaction with Abrikosov vortices in a superconductor in close contact with a garnet film is analyzed within the London approximation. The model explains how vortices are attracted to such walls, and excellent quantitative agreement is obtained for the resulting peaked flux profile determined experimentally in NbSe(2) using high-resolution magneto-optical imaging of vortices. In particular, this model, when generalized to include charged magnetic walls, explains the counterintuitive attraction observed between vortices and a Bloch wall of opposite polarity.

Onset of dendritic flux avalanches in superconducting films.

We report a detailed comparison of experimental data and theoretical predictions for the dendritic flux instability, believed to be a generic behavior of type-II superconducting films. It is shown that a thermomagnetic model published very recently [Phys. Rev. B 73, 014512 (2006)10.1103/PhysRevB.73.014512] gives an excellent quantitative description of key features like the stability onset (first dendrite appearance) magnetic field, and how the onset field depends on both temperature and sample size. The measurements were made using magneto-optical imaging on a series of different strip-shaped samples of MgB2. Excellent agreement is also obtained by reanalyzing data previously published for Nb.

Charge transfer between a superconductor and a hopping insulator.

We develop a theory of the low-temperature charge transfer between a superconductor and a hopping insulator. We show that the charge transfer is governed by the coherent two-electron-Cooper pair conversion process time-reversal reflection, where electrons tunnel into a superconductor from the localized states in the hopping insulator located near the interface, and calculate the corresponding interface resistance. A specific feature of this problem is the interplay between the time-reversal reflection at the interface and transport through the percolation cluster. To allow for this interplay, we have generalized the connectivity criterion of the percolation theory to include surface effects. We show that the time-reversal interface resistance is accessible experimentally, and that in mesoscopic structures it can exceed the bulk hopping resistance.

Non-Gaussian low-frequency noise as a source of qubit decoherence.

We study decoherence in a qubit with the distance between the two levels affected by random flips of bistable fluctuators. For the case of a single fluctuator we evaluate explicitly an exact expression for the phase-memory decay in the echo experiment with a resonant ac excitation. The echo signal as a function of time shows a sequence of plateaus. The position and the height of the plateaus can be used to extract the fluctuator switching rate gamma and its coupling strength v. At small times the logarithm of the echo signal is proportional to t3. The plateaus disappear when the decoherence is induced by many fluctuators. In this case the echo signal depends on the distribution of the fluctuators parameters. According to our analysis, the results significantly deviate from those obtained in the Gaussian model as soon as v greater than or approximately equal gamma.

Orbital ac spin-Hall effect in the hopping regime.

The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field E(omega) generates a spin-polarization current, normal to E, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to omega2. At nonzero temperatures the coupling to the phonons yields an imaginary term proportional to omega. The interference also yields persistent spin currents at thermal equilibrium, at E=0. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other.

Models of environment and T1 relaxation in Josephson charge qubits.

A theoretical interpretation of the recent experiments of Astafiev et al. on the T1-relaxation rate in Josephson charge qubits is proposed. The experimentally observed reproducible nonmonotonic dependence of T1 on the splitting E(J) of the qubit levels suggests further specification of the previously proposed models of the background charge noise. From our point of view the most promising is the "Andreev fluctuator" model of the noise. In this model the fluctuator is a Cooper pair that tunnels from a superconductor and occupies a pair of localized electronic states. Within this model one can naturally explain both the average linear T1(E(J)) dependence and the irregular fluctuations.

Mechanical Cooper pair transportation as a source of long-distance superconducting phase coherence.

Transportation of Cooper pairs by a movable single Cooper-pair box placed between two remote superconductors is shown to establish coherent coupling between them. This coupling is due to entanglement of the movable box with the leads and is manifested in the suppression of quantum fluctuations of the relative phase of the order parameters of the leads. It can be probed by attaching a high resistance Josephson junction between the leads and measuring the current through this junction. The current is suppressed with increasing temperature.

Coherent transfer of Cooper pairs by a movable grain.

Superconducting circuits that incorporate Josephson junctions are of considerable experimental and theoretical interest, particularly in the context of quantum computing. A nanometre-sized superconducting grain (commonly referred to as a Cooper-pair box) connected to a reservoir by a Josephson junction is an important example of such a system. Although the grain contains a large number of electrons, it has been experimentally demonstrated that its states are given by a superposition of only two charge states (differing by 2e, where e is the electronic charge). Coupling between charge transfer and mechanical motion in nanometre-sized structures has also received considerable attention. Here we demonstrate theoretically that a movable Cooper-pair box oscillating periodically between two remote superconducting electrodes can serve as a mediator of Josephson coupling, leading to coherent transfer of Cooper pairs between the electrodes. Both the magnitude and the direction of the resulting Josephson current can be controlled by externally applied electrostatic fields.

Kondo temperature for the two-channel Kondo models of tunneling centers.

A two-channel Kondo (2CK) non-Fermi liquid state in a metal resulting from the interaction between electrons and structural defects modeled by double-well potentials (DWP) is revisited. Account only of the two lowest states in DWP is known to lead to rather low Kondo temperature, T(K). We prove that the contribution of higher excited states reduces T(K), if all of the intermediate states are taken into account. Prefactor in T(K) is shown to be determined by the spacing between the second and the third levels epsilon(3) in DWP rather than by the electron Fermi energy epsilon(F). Since epsilon(3)<