Laboratory of Topological Quantum Phenomena in Superconducting Systems

Wu Z., Ridderbos J., Li A., Golubov A.A., Zwanenburg F.A., Bakkers E.P., Brinkman A., Li C.

Anomalous critical current enhancement was observed with increasing magnetic field in Josephson junctions based on Ge–Si core-shell nanowires. Despite the predicted topological properties of these nanowires, which could potentially lead to non-trivial superconducting order parameter symmetries, our investigation unveils a more generalized, non-topological explanation for the observed critical current enhancement in these devices. Our findings suggest that the enhancement arises from a thermalization process induced by the magnetic field, wherein in-gap quasiparticles are generated. These quasiparticles play a crucial role in enhancing the cooling of the device, thereby lowering the effective temperature and resulting in an increased critical current. Furthermore, we elucidate how this thermalization effect varies with device geometry and measurement configuration.

Karabassov T., Bobkova I., Silkin V., Lvov B., Golubov A.A., Vasenko A.

Abstract At present the superconducting diode effect (SDE) attracts a lot of attention due to new possibilities in the superconducting electronics. One of the possible realizations of the SDE is the implementation in superconducting hybrid structures. In this case the SDE is achieved by means of the proximity effect. However, the optimal conditions for the SDE quality factor in hybrid devices remain unclear. In this study we consider the Superconductor/Ferromagnet/Topological insulator (S/F/TI) hybrid device and investigate the diode quality factor at different parameters of the hybrid structure. Consequently, we reveal important parameters that have crucial impact on the magnitude of the SDE quality factor.

Karabassov T., Vasenko A.S., Bayazitov V.M., Golubov A.A., Fedulov I.S., Abramova A.V.

Suzuki S., Asano Y., Golubov A.A.

We theoretically study the current-phase relation in a Josephson junction comprising the Zeeman-split superconductors (ZSs) and a normal metal (N). We show that at low temperatures the Josephson current in the ZS/N/ZS junctions exhibits a supercurrent reversal at a certain phase difference ${\ensuremath{\varphi}}_{c}\ensuremath{\in}(0,\ensuremath{\pi})$. By calculating the spectral Josephson current, we demonstrate that the band splitting due to the Zeeman interaction causes the level crossing in the spectra of the Andreev bound states and the sign reversal of the Josephson current. Additionally, we propose an alternative method to observe the supercurrent reversal. Tuning the Rashba spin-orbit coupling electrically, one can control the critical phase difference ${\ensuremath{\varphi}}_{c}$, eliminating the need for manipulating two magnetizations independently.

Suzuki S., Golubov A.A.

The robustness of the chiral surface current of chiral superconductors against surface roughness is studied utilizing the quasiclassical Eilenberger theory. We consider the general chiral superconductors where the pair potential is given by the spherical harmonics ${Y}_{l}^{m}$ such that the $(l,m)=(1,\ifmmode\pm\else\textpm\fi{}1)$ state corresponds to a $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor. The self-consistent calculations demonstrate that the robustness of the chiral current is determined by whether subdominant $s$-wave Cooper pairs are induced by disorder. The induced $s$-wave pairs act as an effective pair potential. As a result, the spontaneous chiral current of $({p}_{x}+i{p}_{y})$- and $({d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy})$-wave superconductors is robust against the roughness because the subdominant $s$-wave Cooper pairs are present.

Kokkeler T., Golubov A., Bergeret S., Tanaka Y.

In noncentrosymmetric superconductors the pair potential has both even-parity singlet and odd-parity triplet components. If time-reversal symmetry is broken, the superconducting phase of these components is not the same, for example in anapole superconductors. In this paper it is shown that breaking time-reversal symmetry by a phase difference between the two components significantly alters both the density of states and the conductance in $s+\mathrm{helical} p$-wave superconductors. The density of states and conductance in $s+\mathrm{chiral} p$-wave superconductors are less influenced by adding a phase difference because time-reversal symmetry is already broken in the $s+p$-wave superconductor. The Tanaka-Nazarov boundary conditions are extended to 3D superconductors, allowing us to investigate a greater variety of superconductors, such as Balian-Werthamer superconductors, in which the direction of the $d$ vector is parallel to the direction of momentum. The results are important for the determination of pair potentials in potentially time-reversal symmetry broken noncentrosymmetric superconductors.

Bobkov G.A., Bobkova I.V., Golubov A.A.

The influence of Rashba spin-orbit coupling (SOC) on superconducting correlations in thin-film superconductor/antiferromagnet (S/AF) structures with compensated interfaces is studied. A unique effect of anisotropic enhancement of proximity-induced triplet correlations by the SOC is predicted. It manifests itself in the anisotropy of the superconducting critical temperature ${T}_{c}$ with respect to orientation of the N\'eel vector relative to the S/AF interface, which is opposite to the behavior of ${T}_{c}$ in superconductor/ferromagnet structures. We show that the anisotropy is controlled by the chemical potential of the superconductor and, therefore, can be adjusted in (quasi-)2D structures.

Suzuki S., Sato T., Golubov A.A., Asano Y.

We study theoretically the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states appearing locally in a superconducting thin film with a small circular magnetic cluster. By solving the Eilenberger equation in two dimensions, we calculate the pair potential, pairing correlations, free-energy density, and quasiparticle density of states for various cluster sizes and exchange potentials. Increasing the exchange potential and cluster size leads to a higher number of nodes in the pair potential. Although the free-energy density beneath the ferromagnet locally exceeds the normal-state value, the FFLO states are stabilized by the superconducting condensate away from the magnetic cluster. Analyzing the pairing-correlation functions, we show that the spatial variation of the spin-singlet $s$-wave pair potential generates $p$-wave Cooper pairs. These odd-frequency Cooper pairs play a dominant role in governing the inhomogeneous subgap spectra observed in the local density of states. Furthermore, we propose an experimental method for the detection of local FFLO states by analyzing the quasiparticle density of states.

Ruzhickiy V., Bakurskiy S., Kupriyanov M., Klenov N., Soloviev I., Stolyarov V., Golubov A.

In this paper, we present a theoretical study of electronic transport in planar Josephson Superconductor–Normal Metal–Superconductor (SN-N-NS) bridges with arbitrary transparency of the SN interfaces. We formulate and solve the two-dimensional problem of finding the spatial distribution of the supercurrent in the SN electrodes. This allows us to determine the scale of the weak coupling region in the SN-N-NS bridges, i.e., to describe this structure as a serial connection between the Josephson contact and the linear inductance of the current-carrying electrodes. We show that the presence of a two-dimensional spatial current distribution in the SN electrodes leads to a modification of the current–phase relation and the critical current magnitude of the bridges. In particular, the critical current decreases as the overlap area of the SN parts of the electrodes decreases. We show that this is accompanied by a transformation of the SN-N-NS structure from an SNS-type weak link to a double-barrier SINIS contact. In addition, we find the range of interface transparency in order to optimise device performance. The features we have discovered should have a significant impact on the operation of small-scale superconducting electronic devices, and should be taken into account in their design.

Karabassov T., Amirov E.S., Bobkova I.V., Golubov A.A., Kazakova E.A., Vasenko A.S.

Currently, the superconducting diode effect (SDE) is being actively discussed, due to its large application potential in superconducting electronics. In particular, superconducting hybrid structures, based on three-dimensional (3D) topological insulators, are among the best candidates, due to their having the strongest spin–orbit coupling (SOC). Most theoretical studies on the SDE focus either on a full numerical calculation, which is often rather complicated, or on the phenomenological approach. In the present paper, we compare the linearized and nonlinear microscopic approaches in the superconductor/ferromagnet/3D topological insulator (S/F/TI) hybrid structure. Employing the quasiclassical Green’s function formalism we solve the problem self-consistently. We show that the results obtained by the linearized approximation are not qualitatively different from the nonlinear solution. The main distinction in the results between the two methods was quantitative, i.e., they yielded different supercurrent amplitudes. However, when calculating the so-called diode quality factor the quantitative difference is eliminated and both approaches result in good agreement.

Tanaka Y., Kokkeler T., Golubov A.

Phys. Rev. B 107, 139901 (2023)

Gaifullin R.R., Deminov R.G., Kushnir V.N., Kupriyanov M.Y., Golubov A.A., Tagirov L.R.

A matrix solution to Usadel linearized equations is used to obtain the critical temperature and distribution of singlet pairing components of a superconductor/ferromagnetic/superconductor/ferromagnetic structure with nonideal boundaries. There is a transition from the π- to the 0-phase state between the superconductor layers upon varying the angle between the magnetizations of ferromagnetic layers in such a structure.

Golovchanskiy I.A., Abramov N.N., Emelyanova O.V., Shchetinin I.V., Ryazanov V.V., Golubov A.A., Stolyarov V.S.

In this work, we study magnetization dynamics in superconductor-ferromagnet-superconductor thin-film structures. Results of the broad-band ferromagnetic resonance spectroscopy are reported for a large set of samples with varied thickness of both superconducting and ferromagnetic layers in a wide frequency, field, and temperature ranges. Experimentally the one-dimensional anisotropic action of superconducting torque on magnetization dynamics is established; its dependence on thickness of layers is revealed. It is demonstrated that experimental findings support the recently proposed mechanism of the superconducting torque formation via the interplay between the superconducting imaginary conductance and magnetization precession at superconductor-ferromagnet interfaces. Microwave spectroscopy studies in this work are supplemented by investigations of the crystal structure and the microstructure of studied multilayers.

Kokkeler T.H., Tanaka Y., Golubov A.A.

Based on a general theory of the nonequilibrium proximity effect developed for unconventional superconductors, a method to distinguish different types of noncentrosymmetric superconductors is proposed.

Karabassov T., Bobkova I.V., Golubov A.A., Vasenko A.S.

It is well known that the ground state of homogeneous superconducting systems with spin-orbit coupling in the presence of the Zeeman field is the so-called helical state, which is characterized by the phase modulation of the order parameter, but zero supercurrent density. In this paper we investigate the realization of the helical state in a hybrid system with spatially separated superconductivity and exchange field by considering a superconductor/ferromagnet ($S/F$) bilayer on top of a three-dimensional topological insulator. This system is characterized by strong spin-momentum locking and, consequently, provides the most favorable conditions for the helical state generation. The analysis is based on the microscopic theory in terms of the quasiclassical Green's functions. We demonstrate that in the bilayer the helical state survives if the exchange field has a nonzero component perpendicular to the $S/F$ interface even in spite of the fact that the superconducting order parameter and the exchange field are spatially separated. At the same time, in this spatially inhomogeneous situation the helical state is accompanied by the spontaneous currents distributed over the bilayer in such a way that the net current vanishes. Further, we show that this hybrid helical state gives rise to nonreciprocity in the system. We demonstrate the realization of the nonreciprocity in the form of the superconducting diode effect and investigate its dependence on the parameters of the bilayer.