Bipolar thermoelectric Josephson engine.

Thermoelectric effects in metals are typically small due to the nearly perfect particle-hole symmetry around their Fermi surface. Furthermore, thermo-phase effects and linear thermoelectricity in superconducting systems have been identified only when particle-hole symmetry is explicitly broken, since thermoelectric effects were considered impossible in pristine superconductors. Here, we experimentally demonstrate that superconducting tunnel junctions develop a very large bipolar thermoelectricity in the presence of a sizable thermal gradient thanks to spontaneous particle-hole symmetry breaking. Our junctions show Seebeck coefficients of up to ±300 µV K-1, which is comparable with quantum dots and roughly 105 times larger than the value expected for normal metals at subkelvin temperatures. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine generating phase-tunable electric powers of up to ~140 nW mm-2. Notably, our device implements also the prototype for a persistent thermoelectric memory cell, written or erased by current injection. We expect that our findings will lead to applications in superconducting quantum technologies.

A Josephson phase battery.

A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.

Nonlocal Thermoelectricity in a Superconductor-Topological-Insulator-Superconductor Junction in Contact with a Normal-Metal Probe: Evidence for Helical Edge States.

We consider a Josephson junction hosting a Kramers pair of helical edge states of a quantum spin Hall bar in contact with a normal-metal probe. In this hybrid system, the orbital phase, induced by a small magnetic field threading the junction known as a Doppler shift, combines with the conventional Josephson phase difference and originates an effect akin to a Zeeman field in the spectrum. As a consequence, when a temperature bias is applied to the superconducting terminals, a thermoelectric current is established in the normal probe. We argue that this purely nonlocal thermoelectric effect is a unique signature of the helical nature of the edge states coupled to superconducting leads and it can constitute a useful tool for probing the helical nature of the edge states in systems where the Hall bar configuration is difficult to achieve. We fully characterize thermoelectric response and performance of this hybrid junction in a wide range of parameters, demonstrating that the external magnetic flux inducing the Doppler shift can be used as a knob to control the thermoelectric response and the heat flow in a novel device based on topological junctions.

Thermodynamic cycles in Josephson junctions.

A superconductor/normal metal/superconductor Josephson junction is a coherent electron system where the thermodynamic entropy depends on temperature and difference of phase across the weak-link. Here, exploiting the phase-temperature thermodynamic diagram of a thermally isolated system, we argue that a cooling effect can be achieved when the phase drop across the junction is brought from 0 to π in a iso-entropic process. We show that iso-entropic cooling can be enhanced with proper choice of geometrical and electrical parameters of the junction, i.e. by increasing the ratio between supercurrent and total junction volume. We present extensive numerical calculations using quasi-classical Green function methods for a short junction and we compare them with analytical results. Interestingly, we demonstrate that phase-coherent thermodynamic cycles can be implemented by combining iso-entropic and iso-phasic processes acting on the weak-link, thereby engineering the coherent version of thermal machines such as engines and cooling systems. We therefore evaluate their performances and the minimum temperature achievable in a cooling cycle.

Phase-coherent solitonic Josephson heat oscillator.

Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explored, little is known about soliton-sustained coherent thermal transport. We demonstrate that the soliton configuration determines the temperature profile in the junction, so that, in correspondence of each magnetically induced soliton, both the flowing thermal power and the temperature significantly enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat oscillator, whose frequency is in tune with the oscillation frequency of the magnetic drive. Notably, the proposed heat oscillator can effectively find application as a tunable thermal source for nanoscale heat engines and coherent thermal machines.

A zero-dimensional topologically nontrivial state in a superconducting quantum dot.

The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current-phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.

Counting statistics of non-Markovian quantum stochastic processes.

We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.

Full counting statistics in strongly interacting systems: non-Markovian effects.

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel coupling, and discuss under which circumstances non-Markovian effects appear in the transport properties.