Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

Abstract

We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmetry arguments which constrain the possible form of the electron-electron interactions in these systems and classify the possible superconducting phases which result. Exact diagonalization of the Bogoliubov-de Gennes Hamiltonian confirms the existence of gapped edge states and Majorana corner states, which strongly depend on the spatial structure of the gap. Possible applications to vanadium-based superconducting kagome metals AV$_3$Sb$_3$ (A=K,Rb,Cs) are discussed.

Topological Phases of an Interacting Majorana Benalcazar–Bernevig–Hughes Model

“…In order to go beyond the mean field treatment, we add repulsive Coulomb interactions to the MBBH model with the aim of gaining insight on how the interactions affect the stability of the topological phases, which is still an open problem despite intense investigations [23,[35][36][37].…”

“…The question was addressed by considering the effect of Coulomb repulsive interactions [19][20][21] and/or by developing a number-conserving theory [22] in order to go beyond the BCS approximation. In particular, some recent studies investigated the physical properties of HOTSCs when Coulomb interactions are taken into account [23,24].…”

Majorana corner states on the dice lattice

“…Higher order topology in quantum matter has recently generated a flurry of activity in several broad areas, including the field of superconductivity [1][2][3][4][5][6][7][8][9][10][11][12] . At the boundaries and vortex cores, a topological superconductor harbors Majorana quasiparticles, with potential value in the long-sought area of decoherence-free quantum computing [13][14][15][16][17][18] .…”

Chiral excitonic order from twofold van Hove singularities in kagome metals

“…Kagome systems have been a major focus of theoretical and experimental investigation; due to their ability to realise Dirac points, flat bands and van Hove singularities, they have been predicted to host a range of novel correlated phases of matter [1][2][3][4][5][6][7][8][9] . Recently, a new class of materials AV 3 Sb 5 (A=K,Rb,Cs) have attracted a great deal of attention due to their demonstration of unconventional superconductivity alongside competing density wave order, spatially modulated superconducting order and possible signatures of Majorana states in superconducting vortices .…”