Nonperturbative phase diagram of interacting disordered Majorana nanowires

Abstract

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong-coupling regime. This method allows for a nonperturbative treatment in the disorder strength, electron-electron interactions, and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase and a glassy, nontopological localized phase, characterized by replica symmetry breaking.

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

“…Performing a renormalization-group analysis of the corresponding bosonized low-energy theory in replica space, Lobos et al [11] showed that disorder and repulsive interactions reinforce each other in suppressing the topological phase and thus eliminating Majorana edge modes in the wires. Crépin et al [16] corroborated this finding using a Gaussian variational approach.…”

“…Two of the most relevant experimental influences are disorder [10][11][12][13][14][15][16][17] and interactions [11,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Concerning the effects of disorder, it has been observed that moderate disorder supports the topological phase by pinning down quasiparticles associated with the phase transition, which has been investigated in particular for the two-dimensional toric code [34][35][36].…”

Exact zero modes in twisted Kitaev chains

“…Note that Eq. (20) applies to arbitrary boundary conditions, while Eq. (3) is valid only for the PBC and the APBC.…”

“…The existence of Majorana zero modes is of special interest because it can be applied to the physical construction of qubits for topological quantum computing [13][14][15] . From an experimental point of view, it is essential to investigate the effects of disorder [16][17][18][19][20] and interactions [21][22][23][24][25][26][27][28][29][30][31][32] . Furthermore, various theoretical aspects have been revealed, including the connection with supersymmetry 30,31,[33][34][35] , the generalization to parafermion modes [36][37][38][39][40][41][42][43] , and the construction of topologically invariant defects 44 .…”

Density of states at disorder-induced phase transitions in a multichannel Majorana wire

“…Also, when disorder preserves certain symmetries on the average, the disorder itself may drive a topological insulator into a new type of topological phase, the so-called "statistical topological insulator" [6,7]. Topological superconductors, finally, can display thermal metal [8] or glassy phases [9] or enter a topologically nontrivial phase upon increasing disorder strength [10].…”