Spontaneous supercurrent and φ0 phase shift parallel to magnetized topological insulator interfaces

Abstract

Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a spontaneous supercurrent and the appearance of the ϕ0 phase shift parallel to uniformly in-plane magnetized superconducting interfaces made of the surface states of a three-dimensional topological insulator. We consider two weakly coupled uniformly magnetized superconducting surfaces where a macroscopic phase difference between the s-wave superconductors can be controlled externally. We find that, depending on the magnetization strength and orientation on each side, a spontaneous supercurrent due to the ϕ0-states flows parallel to the interface at the junction location. Our calculations demonstrate that nonsinusoidal phase relations of current components with opposite directions result in maximal spontaneous supercurrent at phase differences close to π. We also study the Andreev subgap channels at the interface and show that the spin-momentum locking phenomenon in the surface states can be uncovered through density of states studies. We finally discuss realistic experimental implications of our findings.

Evolution of pair correlation symmetries and supercurrent reversal in tilted Weyl semimetals

“…Hence, the predicted robust self-biased current should be experimentally accessible over a wide range of parameters. 8,9,[76][77][78][79] It is worth men- tioning that in a recent experiment, 79 this self-biased current was observed using a Bi 2 Se 3 platform, which is in agreement with theoretical predictions for topological insulator Josephson junctions [76][77][78] .…”

Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorder

“…Hence, we now proceed to apply our formulated quasiclassical model to hybrid structures made of disordered Weyl semimetals and superconductors, which are practical platforms that the Eilenberger and Usadel equations are able to describe them properly. We note that the quasiclassical Eilenbeger and Usadel approaches were also generalized for spin-orbit coupled systems [70][71][72][73][74][75] , surface channels of topological insulators [63][64][65] , and black phosphorus monolayer (phosphorene) 27 in the presence of superconductivity and a Zeeman field. A specific configuration is depicted in Fig.…”

“…We consider low transparent interfaces (the so-called tunneling limit) between the superconductors and Weyl semimetal and neglect the inverse proximity effect at the interfaces. We therefore find the following expression to the boundary conditions [63][64][65]76,77 ζn kǧ k p = ǧ s ,ǧ SC ,…”

Transport in two-dimensional topological materials: recent developments in experiment and theory

“…The difficulty is that the equilibrium CPR (67) is 2π periodic, as the two contributions there simply swap upon a 2π phase advance. Although the fractional JE cannot be easily inferred from such equilibrium CPRs, they, nevertheless, diagnose unconventional superconductivity in topological materials which has become a subject of intense effort on its own [443,526,527,500,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,425,458,547,548,549]. In order to trace the fractional JE at equilibrium, one may look at the effect of an external magnetic field.…”

“…Since each spin in a singlet pair can be flipped, both up -and down -spin pairs are induced with no net spin magnetization. This phenomenology is behind many microscopic studies of the proximity effect in systems with broken spin rotation symmetry, such as Rashba systems and TI materials [564,565,566,567,568,569,526,570,571,572,573,574,575,537,576,577,578,538,579,580,581,582,583,584,546,585,586,425,587,549].…”