Weak-pairing higher order topological superconductors

Abstract

Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped, topological surfaces and gapless Majorana modes instead on lower-dimensional boundaries, i.e., corners of a two-dimensional system or hinges for a three-dimensional system. Here we propose two general scenarios in which second-order topological superconductivity can be realized spontaneously with weak-pairing instabilities. First, we show that px + ipy-wave pairing in a (doped) Dirac semimetal in two dimensions with four mirror symmetric Dirac nodes realizes second-order topological superconductivity. Second, we show that p+id pairing on an ordinary spin-degenerate Fermi sruface realizes second-order topological superconductivity as well. In the latter case we find that the topological invariants describing the system can be written using simple formulae involving only the low-energy properties of the Fermi surfaces and superconducting pairing. In both cases we show that these exotic superconducting states can be intrinsically realized in a metallic system with electronic interactions. For the latter case we also show it can be induced by proximity effect in a heterostructure of cuprate and topological superconductors. arXiv:1804.01531v3 [cond-mat.supr-con]

Second-Order Topological Superconductors with Mixed Pairing

“…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.…”

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

“…Excitations in these systems come in the form of MKPs, which are distinct from non-degenerate MZMs [16][17][18][19][20][21][22][23][24][25][26] and are protected by time reversal (TR) symmetry [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Unfortunately, MCMs proposed in the condensed matter systems [13][14][15][47][48][49][50][51] have not been realized to date.…”

Majorana corner flat bands in two-dimensional second-order topological superconductors

“…In second-order TSCs these MZMs have been studied at the corners of a two-dimensional (2D) system and hinges of a three-dimensional (3D) system where neighboring hinges have different chiralities 27,28 . These zero-energy corner modes are known as Majorana corner states (MCSs) which have been studied in various kinds of system such as high-temperature superconductors (SCs) [29][30][31][32][33][34] , s-wave superfluid 28,35 , systems with an external magnetic field [36][37][38] , and 2D and 3D second-order TSCs 39 .…”