Second-Order Topological Superconductors with Mixed Pairing

Abstract

We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the secondorder phase is further established, which concerns the relative position between Fermi surfaces and nodal points of the superconducting order parameter. In the end, we propose two setups that may bring this mixed-pairing state into the Rashba semiconductor, followed by a brief discussion on the experimental feasibility of the two platforms.Topological superconductors (TSCs) distinguish themselves from trivial ones in the robust midgap states-Majorana zero modes (MZMs)-that could form either at local defects or boundaries [1-9]. Among the various proposals for TSCs, semiconducting systems with Rashba spin-orbit coupling (RSOC) [10-13] as well as topological insulating systems [14] have attracted the most attention. In both platforms, signatures of MZMs have been observed when conventional s-wave pairing is introduced through proximity effect [15][16][17][18][19][20][21][22][23][24][25].In these conventional, also termed as first-order, TSCs, topologically nontrivial bulk in d dimensions is usually accompanied by MZMs confined at (d − 1)-dimensional boundaries, the so-called bulk-boundary correspondence. Very recently, this correspondence was extended in topological phases of nth order [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], where topologically protected gapless modes emerge at (d − n)-dimensional boundaries. In Refs. [46][47][48][49], the authors demonstrate that a topological insulator could be transformed into a second-order TSC when unconventional pairing with the s ± -or d x 2 −y 2 -wave form is introduced. Looking back at the history of first-order TSCs, one may then ask if it is possible for a Rashba semiconductor (RS), which is itself a trivial system as opposed to topological insulators, to accommodate such a higher-order nontrivial phase as well. In this work, we will show that it is possible, provided a mixed-pairing state that exhibits both extended s-wave and d x 2 −y 2 -wave symmetries could be induced therein.Admixture of the two aforementioned pairing states was envisioned shortly after the discovery of iron-based superconductors (FeSCs) [50][51][52][53]. Since then tremendous efforts have been made to identify this mixed-pairing order [54,55]. In this Letter, we shall consider a general mixed state that could reduce to three intensively studied mixed pairings in FeSCs, that is, s + d [56], s + is [57] and s + id [50,52]. Our main finding is that, such a pairing state alone could possibly drive ...

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