Coupled wire model of symmetric Majorana surfaces of topological superconductors

Abstract

Time reversal symmetric topological superconductors in three spatial dimensions carry gapless surface Majorana fermions. They are robust against any time reversal symmetric single-body perturbation weaker than the bulk energy gap. We mimic the massless surface Majorana's by coupled wire models in two spatial dimensions. We introduce explicit many-body interwire interactions that preserve time reversal symmetry and give energy gaps to all low energy degrees of freedom. We show the gapped models generically carry non-trivial topological order and support anyonic excitations.

Classification and surface anomaly of glide symmetry protected topological phases in three dimensions

“…Previously, the STOs of AFM TIs (class A) and superconductors (class D) have been constructed explicitly in [35] and [36]. These AFM topological phases preserves a combination T T x x  õ · of lattice translation T x and time reversal.…”

Topological strings linking with quasiparticle exchange in superconducting Dirac semimetals

“…The fusion content of the condensed theory was presented in Ref. 11. Here we review the relevant features of the condensation following the procedure proposed in Ref.…”

“…In this case, more exotic vortices are shown to be possible, out of phases with longrange topological order allowed in the superconductor Majorana surfaces. Thus, under strong interactions, we also argue in favor of further fractionalizations of quasiparticle exchanges based on identifying vortices whose internal matter is shown to be described by the relative tensor product G = SO(3) 3 SO(4) 1 conformal field theories (CFTs) 10,11 . These consist of CFTs with c = 1/4 central charge, described by counter propagating SO(3) 3 and SO(4) 1 Wess-Zumino-Witten theories under a particular process of condensation 12 , as described in the main text.…”

Three-dimensional fractional topological insulators in coupled Rashba layers

“…We generalize the approach of weakly coupled wires [20] to three dimensions by considering a stack of weakly coupled two-dimensional electron gas (2DEG) layers. Although the coupled wires approach is a very successful method for theoretically constructing two-dimensional (2D) [12,[20][21][22][23][24][25][26][27][28][29][30] and 3D [31][32][33] topological systems, the coupled layers approach [34] is simpler to handle and is physically more transparent when describing 3D systems. We consider a stack of 2D layers with Rashba spin-orbit interaction (SOI) weakly tunnel coupled to each other.…”