Quasiparticles-mediated thermal diode effect in Weyl Josephson junctions

Oh T., Nagaosa N.

Debnath D., Dutta P.

Volkov P.A., Lantagne-Hurtubise É., Tummuru T., Plugge S., Pixley J.H., Franz M.

Recent Josephson tunneling experiments on twisted flakes of high-${T}_{c}$ cuprate superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ revealed a nonreciprocal behavior of the critical interlayer Josephson current, i.e., a Josephson diode effect. Motivated by these findings we study theoretically the emergence of the Josephson diode effect in twisted interfaces between nodal superconductors, and highlight a strong dependence on the twist angle $\ensuremath{\theta}$ and damping of the junction. In all cases, the theory predicts diode efficiency that vanishes exactly at $\ensuremath{\theta}={45}^{\ensuremath{\circ}}$ and has a strong peak at a twist angle close to $\ensuremath{\theta}={45}^{\ensuremath{\circ}}$, consistent with experimental observations. Near ${45}^{\ensuremath{\circ}}$, the junction breaks time-reversal symmetry $\mathcal{T}$ spontaneously. We find that for underdamped junctions showing hysteretic behavior, this results in a dynamical Josephson diode effect in a part of the $\mathcal{T}$-broken phase. The direction of the diode is trainable in this case by sweeping the external current bias. This effect provides a sensitive probe of spontaneous $\mathcal{T}$ breaking. We then show that explicit $\mathcal{T}$-breaking perturbations with the symmetry of a magnetic field perpendicular to the junction plane lead to a thermodynamic diode effect that survives even in the overdamped limit. We discuss an experimental protocol to probe the double-well structure in the Josephson free energy that underlies the tendency towards spontaneous $\mathcal{T}$ breaking even if $\mathcal{T}$ is broken explicitly. Finally, we show that in-plane magnetic fields can control the diode effect in the short junction limit, and predict the signatures of explicit $\mathcal{T}$ breaking in Shapiro steps.

Tjernshaugen J.B., Amundsen M., Linder J.

Spin-split superconductors offer new functionality compared to conventional superconductors such as diode effects and efficient thermoelectricity. The superconducting state can nevertheless only withstand a small amount of spin splitting. Here, we self-consistently determine the spin transport properties and the phase diagram of a spin-split superconductor in the presence of an injected spin accumulation. Energy and spin relaxation are accounted for in the relaxation time approximation via a single effective inelastic scattering parameter. We find that the spin-splitting field in the superconductor enables a spin diode effect. Moreover, we consider the superconducting phase diagram of a system in contact with a spin accumulation and in the presence of spin relaxation, and find that the inclusion of energy and spin relaxation alters the phase diagram qualitatively. In particular, these mechanisms turn out to induce a superconducting state in large parts of the phase diagram where a normal state would otherwise be the ground state. We identify an Fulde--Ferrel--Larkin--Ovchinnikkov-like state even in the presence of impurity scattering, which can be controllably turned on and off via the electrically induced spin accumulation. We explain the underlying physics from how the superconducting order parameter depends on the nonequilibrium modes in the system as well as the behavior of these modes in the presence of energy and spin relaxation when a spin-splitting field is present.

Cayao J., Nagaosa N., Tanaka Y.

We consider phase-biased Josephson junctions with spin-orbit coupling under external magnetic fields and study the emergence of the Josephson diode effect in the presence of Majorana bound states. We show that junctions having middle regions with Zeeman fields along the spin-orbit axis develop a low-energy Andreev spectrum that is asymmetric with respect to the superconducting phase difference $\ensuremath{\phi}=\ensuremath{\pi}$, which is strongly influenced by Majorana bound states in the topological phase. This asymmetric Andreev spectrum gives rise to anomalous current-phase curves and critical currents that are different for positive and negative supercurrents, thus signaling the emergence of the Josephson diode effect. While this effect exists even in the trivial phase, it gets enhanced in the topological phase due to the spatial nonlocality of Majorana bound states. Our paper thus establishes the utilization of topological superconductivity for enhancing the functionalities of Josephson diodes.

Chen K., Karki B., Hosur P.

We explore Weyl and Dirac semimetals with tilted nodes as platforms for realizing an intrinsic superconducting diode effect. Although tilting breaks sufficient spatial and time-reversal symmetries, we prove that --- at least for conventional $s$-wave singlet pairing --- the effect is forbidden by an emergent particle-hole symmetry at low energies if the Fermi level is tuned to the nodes. Then, as a stepping stone to the three-dimensional semimetals, we analyze a minimal one-dimensional model with a tilted helical node using Ginzburg-Landau theory. While one might expect a drastic enhancement of the effect when the node turns from type-I to type-II, we find that the presence of multiple Fermi pockets is more important as it enables multiple pairing amplitudes with independent contributions to supercurrents in opposite directions. Equipped with this insight, we construct minimal lattice models of Weyl and Dirac semimetals and study the superconducting diode effect in them. Once again, we see a enhancement when the normal state has multiple Fermi pockets per node that can accommodate more than one pairing channel. In summary, this study sheds light on the key factors governing the intrinsic superconducting diode effect in systems with asymmetric band structures and paves the way for realizing it in topological semimetals.

Ghosh S., Patil V., Basu A., Kuldeep, Dutta A., Jangade D.A., Kulkarni R., Thamizhavel A., Steiner J.F., von Oppen F., Deshmukh M.M.

Many superconducting systems with broken time-reversal and inversion symmetry show a superconducting diode effect, a non-reciprocal phenomenon analogous to semiconducting p–n-junction diodes. While the superconducting diode effect lays the foundation for realizing ultralow dissipative circuits, Josephson-phenomena-based diode effect (JDE) can enable the realization of protected qubits. The superconducting diode effect and JDE reported thus far are at low temperatures (~4 K), limiting their applications. Here we demonstrate JDE persisting up to 77 K using an artificial Josephson junction of twisted layers of Bi2Sr2CaCu2O8+δ. JDE manifests as an asymmetry in the magnitude and distributions of switching currents, attaining the maximum at 45° twist. The asymmetry is induced by and tunable with a very small magnetic field applied perpendicular to the junction and arises due to interaction between Josephson and Abrikosov vortices. We report a large asymmetry of 60% at 20 K. Our results provide a path towards realizing superconducting Josephson circuits at liquid-nitrogen temperature. A large Josephson diode effect has been reported at liquid-nitrogen temperatures in twisted flakes of Bi2Sr2CaCu2O8+δ.

Zazunov A., Rech J., Jonckheere T., Grémaud B., Martin T., Egger R.

We study charge transport in voltage-biased single-channel junctions involving helical superconductors with finite Cooper pair momentum. For a Josephson junction, the equilibrium current-phase relation shows a superconducting diode effect: the critical current depends on the propagation direction. We formulate a scattering theory for voltage-biased Josephson diodes and show that multiple Andreev reflection processes cause a rich subharmonic structure in the dc current-voltage curve at low temperatures and small voltages due to Doppler shifts of the spectral gap. In the current-biased case, the diode efficiency has maximal rectification efficiency ${\ensuremath{\eta}}_{0}\ensuremath{\approx}0.4$ for this model. In the voltage-biased case, however, the rectification efficiency can reach the ideal value $\ensuremath{\eta}=1$. We also discuss charge transport for normal-superconducting junctions between a normal metal and a helical superconductor and comment on related models with spin-orbit interactions and magnetic Zeeman fields.

Legg H.F., Laubscher K., Loss D., Klinovaja J.

In bulk superconductors or Josephson junctions formed in materials with spin-orbit interaction, the critical current can depend on the direction of current flow or of applied magnetic field, an effect known as the superconducting (SC) diode effect. Here, we consider the SC diode effect in Josephson junctions in nanowire devices. We find that the $4\ensuremath{\pi}$-periodic contribution of Majorana bound states (MBSs) to the current phase relation (CPR) of single junctions results in a significant enhancement of the SC diode effect when the device enters the topological phase and can therefore be used as an indicator of the phase transition. Crucially, this enhancement of the SC diode effect is independent of the parity of the junction and therefore protected from parity-altering events, such as quasiparticle poisoning, which have hampered efforts to directly observe the $4\ensuremath{\pi}$-periodic CPR of MBSs. We show that this effect can be generalized to SQUIDs and that, in such devices, the parity-protected SC diode effect can provide a highly controllable probe of the topology in a Josephson junction.

Anwar M.S., Nakamura T., Ishiguro R., Arif S., Robinson J.W., Yonezawa S., Sigrist M., Maeno Y.

AbstractNon-reciprocal electronic transport in a material occurs if both time reversal and inversion symmetries are broken. The superconducting diode effect (SDE) is an exotic manifestation of this type of behavior where the critical current for positive and negative currents are mismatched, as recently observed in some non-centrosymmetric superconductors with a magnetic field. Here, we demonstrate a SDE in non-magnetic Nb/Ru/Sr2RuO4 Josephson junctions without applying an external magnetic field. The cooling history dependence of the SDE suggests that time-reversal symmetry is intrinsically broken by the superconducting phase of Sr2RuO4. Applied magnetic fields modify the SDE dynamically by randomly changing the sign of the non-reciprocity. We propose a model for such a topological junction with a conventional superconductor surrounded by a chiral superconductor with broken time reversal symmetry.

Nadeem M., Fuhrer M.S., Wang X.

A superconducting diode enables supercurrent to flow in only one direction, providing new functionalities for superconducting circuits. In recent years, there has been experimental progress towards realizing such behaviour in both Josephson junctions and in junction-free superconductors. In this Review, we discuss experimental work and theoretical developments of the superconducting diode effect (SDE). We present the observation of the SDE including material realization, underlying symmetries, nature of spin–orbit interaction, band topology, device geometry and experimentally measured parameters, reflecting that nonreciprocity is presented. The theoretical work and fundamental mechanisms that lead to nonreciprocal current are discussed through the lens of symmetry breaking. The impact of the interplay between various system parameters on the efficiency or the SDE is highlighted. Finally, we provide our perspective towards the future directions in this active research field through an analysis of electric field tunability and the intertwining between band topology and superconductivity and how this could be useful to steer the engineering of emergent topological superconducting technologies. The superconducting diode effect, in which a nonreciprocal supercurrent is generated, enables new superconducting circuit functionalities. In this Review, we present the recent experimental results in the context of theoretical work and provide an analysis of the intertwining parameters that contribute to this effect.

Lu B., Ikegaya S., Burset P., Tanaka Y., Nagaosa N.

The Josephson rectification effect, where the resistance is finite in one direction while zero in the other, has been recently realized experimentally. The resulting Josephson diode has many potential applications on superconducting devices, including quantum computers. Here, we theoretically show that a superconductor-normal metal-superconductor Josephson junction diode on the two-dimensional surface of a topological insulator has large tunability. The magnitude and sign of the diode quality factor strongly depend on the external magnetic field, gate voltage, and the length of the junction. Such rich properties stem from the interplay between different current-phase relations for the multiple transverse transport channels, and can be used for designing realistic superconducting diode devices.

Dutta P.

Abstract We explore the phase-dependent charge and heat current in short Josephson junctions (JJs) with two normal metal regions attached at opposite ends, formed at helical edge states of two-dimensional topological insulators. For all finite phases, an asymmetry appears around the zero energy in the transmission spectra except for ϕ = n ϕ 0 , where n is a half-integer and φ 0 ( = 2 π ) is the flux quantum. The phase-induced asymmetry plays a key role in inducing charge and heat current through the thermally biased junction. However, the current amplitudes are sensitive to the size of the junction. We show that in the short JJ when subject to a temperature gradient, the charge current shows an odd symmetry in phase. It indicates that the phase-tunable asymmetry around the zero energy is not sufficient to induce a dissipative thermoelectric current in the junction. This is in contrast to the behavior of long JJ, as shown in the literature. The phase-tunable heat currents are obtained with amplitudes set by the phase difference, base temperature, and system size.

Hou Y., Nichele F., Chi H., Lodesani A., Wu Y., Ritter M.F., Haxell D., Davydova M., Ilić S., Glezakou-Elbert O., Varambally A., Bergeret F.S., Kamra A., Fu L., Lee P.A., et. al.

A superconducting strip allows more superconducting current to flow in one direction than in the other---achieving a stronger diode effect than previous devices.

Costa A., Baumgartner C., Reinhardt S., Berger J., Gronin S., Gardner G.C., Lindemann T., Manfra M.J., Fabian J., Kochan D., Paradiso N., Strunk C.

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current–phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0−π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions. A sudden inversion of the supercurrent diode effect is revealed in both inductance and critical current measurements in ballistic Josephson junctions. A simple analytical model shows that the inversion is associated with a ground state jump, the elusive 0−π-like transition.

Debnath D., Dutta P.

Abstract We investigate chiral quantum dot (QD)-based Josephson junction and show the correlation-induced Josephson diode effect (JDE) in it. The presence of electron-electron interaction spontaneously creates an imbalance between up- and down-spin electrons during the non-equilibrium transport making the QD effectively magnetic. The simultaneous presence of the chirality and the interaction eventually results in the field-free JDE in our chiral QD junction. We employ the Keldysh non-equilibrium Green’s function technique to study the behavior of the Josephson current and the rectification coefficient (RC) of our Josephson diode (JD). We show a sign-changing behavior of the RC with the Coulomb correlation and the lead-to-dot coupling strength and find the maximum magnitude of the RC ∼ 72 % for moderate interaction strength. Our proposed field-free JD based on interacting chiral QD may be a potential switching component in superconductor based devices.

Antola F., Braggio A., De Simoni G., Giazotto F.

Abstract Efficient heat management at cryogenic temperatures is crucial for superconducting quantum technologies. This study demonstrates the controlled manipulation of the heat flow and heat rectification through an asymmetric superconducting tunnel junction. The system exhibits a non-reciprocal behavior, developing a thermoelectric regime exclusively when the electrode with the larger gap is heated. This feature significantly boosts thermal rectification effectively classifying the device as a heat diode. At the same time when operating as a thermoelectric engine, the same device also functions as a heat pipe, expelling heat from the cryogenic environment, minimizing losses at the cold terminal. This dual functionality is inherently passive, and the performance of the heat pipe and the heat diode can be finely adjusted by modifying the external electrical load.

Seleznev G.S., Fominov Y.V.