Detecting topological superconductivity with φ0 Josephson junctions

Abstract

The interplay of superconductivity, magnetic fields, and spin-orbit interaction lies at the heart of topological superconductivity. Remarkably, the recent experimental discovery of ϕ0 Josephson junctions by Szombati et al. [1], characterized by a finite phase offset in the supercurrent, require the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we theoretically show that a quantum dot ϕ0 Josephson junction can serve as a new qualitative indicator for topological superconductivity: Microscopically, we find that the phase shift in a junction of s−wave superconductors is due to the spin-orbit induced mixing of singly occupied states on the qantum dot, while for a topological superconductor junction it is due to singlet-triplet mixing. Because of this important difference, when the spin-orbit vector of the quantum dot and the external Zeeman field are orthogonal, the s-wave superconductors form a π Josephson junction while the topological superconductors have a finite offset ϕ0 by which topological superconductivity can be distinguished from conventional superconductivity. Our prediction can be immediately tested in nanowire systems currently used for Majorana fermion experiments and thus offers a new and realistic approach for detecting topological bound states. Non-abelian anyons are the building blocks of topological quantum computers [2]. The simplest realization of a non-abelian anyon are Majorana bound states (MBSs) in topological superconductors (TSs) [3]. It has been proposed that such a TS can be induced by an s-wave superconductor (SC) in systems of nanowires with spinorbit interaction (SOI) subject to a Zeeman field [4][5][6][7], in chains of magnetic atoms [8][9][10][11] and in topological insulators [12][13][14][15][16][17]. However, providing experimental evidence for the existence of this new phase of matter has remained a major challenge.Here we present a new qualitative indicator of MBS based on ϕ 0 Josephson junctions (ϕ 0 JJs). In ϕ 0 JJs the Josephson current is offset by a finite phase, ϕ 0 , so that a finite supercurrent flows even when the phase difference between the superconducting leads and the magnetic flux enclosed by the Josephson junction (JJ) vanishes. Such ϕ 0 JJs have been discussed in systems based on unconventional superconductors [18][19][20][21][22] [32,33]. Recently, the connection between ϕ 0 JJs based on nanowires and TSs has also been discussed [34]. Most relevant for the present work, the emergence of a ϕ 0 JJ was theoretically predicted [35][36][37] in a system of a quantum dot (QD) with SOI subject to a Zeeman field when coupled to s-wave superconducting leads and observed in recent experiments [1]. Interestingly, the ingredients for observing a ϕ 0 JJ in this type of system largely overlap with those required to generate MBSs. In this work, we focus on two models for ϕ 0 JJs based on QDs which, compared to previous studies [35][36][37], are in the singlet-triplet anticrossing regime. In the...

Anomalous current in diffusive ferromagnetic Josephson junctions

“…A 3 for details) (25) where χ = ( P l × h 1 )h is the chirality and h 1⊥ = h 1 − h(hh 1 )/h 2 is the perpendicular component of the exchange field h 1 . As in our first example, the usual component of the current is proportional to I 0 ∝ γ −4 , and therefore I an I 0 .…”

“…This effect is referred to as the anomalous Josephson effect (AJE) and takes place only in systems with a broken time-reversal symmetry. The AJE has been predicted in junctions which combine conventional superconductors with magnetism and spinorbital interaction [15][16][17][18][19][20][21][22][23], between unconventional superconductors [24], and between topologically nontrivial superconducting leads [25]. In the presence of magnetic flux piercing the normal interlayer superconducting proximity currents are generated, which naturally leads to a phase shift of the CPR [26,27].…”

Spin-dependent coupling between quantum dots and topological quantum wires

“…In this paper we study MBSs formed in a quantum wire with proximity-induced superconductivity near a quantum dot [28][29][30][31][32][33][34][35][36][37], which is also formed inside a quantum wire, all of which are subject to an applied magnetic field perpendicular to the SOI. First calculating the wave functions of the quantum dot and MBSs, which can be done analytically in the strong spin-orbit regime, we are able to find the spin dependence of the quantum dot-MBS coupling which has been largely neglected [21,22,28,29].…”

Josephson effect in junctions of conventional and topological superconductors

“…Once spin mixing is induced by the magnetic impurity and the local magnetic field, we predict that a finite Josephson current flows even in the deep topological limit. In particular, in the cotunneling regime, we find an anomalous Josephson effect with finite supercurrent at vanishing phase difference (ϕ 0 -junction behavior) [45][46][47], see also Refs. [48][49][50][51].…”