Revealing Topological Superconductivity in Extended Quantum Spin Hall Josephson Junctions

Abstract

Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting "fractional Josephson currents." Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity-even when noise spoils parity conservation. In light of these developments, the following question becomes paramount: How can one compellingly reveal topological superconductivity in these QSH setups? Most detection protocols to date focus on tunneling [23][24][25] and Josephson [7,[26][27][28][29][30][31][32][33][34][35][36] anomalies. The latter originate from the fractional Josephson effect [1] wherein a phase twist δϕ across a topological superconductor yields a supercurrent with 4π periodicity in δϕ-twice that of conventional junctions. One can view the doubled periodicity as arising from a pair of hybridized Majorana modes at the junction, which form an unusual Andreev bound state that mediates supercurrent via single electron (rather than Cooper pair) tunneling. In the simplest case this anomalous current takes the form I 4π ∝ ð−1Þ p sinðδϕ=2Þ, where the parity p ¼ 0; 1 denotes the Andreev bound state's occupation number. Directly observing this spectacular effect is, however, nontrivial. Parity switching processes-which send p → 1 − p and can arise, e.g., from quasiparticle poisoningrestore 2π periodicity to the current unless measurements occur on a time scale short compared to the typical parityflip time. (Long-time-scale measurements may still reveal subtler signatures of topological superconductivity [27,31,32,36], for instance through noise.) Inspired by recent experiments by Hart et al.[18], we study transport in an extended Josephson junction bridged

Effect of magnetic field and Rashba spin-orbit interaction on the Josephson tunneling between superconducting nanowires

“…with The current-phase relation at magnetic field h = 0.1 calculated by using expressions (24), (25) and (26) is presented in Fig. 6.…”

Current-phase relation andh/e-periodic critical current of a chiral Josephson contact between one-dimensional Majorana modes

“…It follows that the critical current has a fractional 2Φ 0 -periodicity rather than the conventional Φ 0 one. The realization of the normal region by two separated chiral channels in the present setup is one of the most relevant distinctions from the junctions with 2D topological insulator where Andreev pairs exist on the same edge 20,21 . The paper is organized as follows.…”

Even-odd flux quanta effect in the Fraunhofer oscillations of an edge-channel Josephson junction

“…An explanation in terms of a Lorentz-force induced asymmetry in the current distribution is therefore unlikely [19][20][21][22][23]. The h/e-periodic Josephson effect of Majorana zero modes [24] is spoiled, on the time scale of the experiment, by any small amount of quasiparticle poisoning [6], so an explanation along these lines is not viable. A conducting pathway through the bulk, parallel to the edges, can explain the data [4]-but only if it is located within 10% of the device center (the flux needs to be accurately partitioned into twice /2).…”

“…We are motivated by recent work on proximity induced superconductivity in quantum spin-Hall (QSH) insulators [2][3][4][5][6][7][8], which in one series of experiments [4] showed Fraunhofer oscillations with an even-odd effect: Large peaks in the critical current at even multiples of h/2e alternate with smaller peaks at odd multiples.…”

“…Following Ref. [6] we assume that the superconductors dope the contacted QSH insulator, locally pushing the Fermi level in the conduction band. The broad conducting pathway that appears along the NS interface will be gapped by the superconducting proximity effect, but a narrow gapless channel may remain because superconductivity only becomes effective at some penetration length ξ 0 from the NS interface.…”