Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Abstract

The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with the recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disc where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers II: Zero-field topological superconductivity

“…This exotic TRS broken phase is one of the most prominent candidates for the correlated phases appearing in bandinverted semiconductors due to Coulomb interactions [26][27][28][29][30][31][32][33], and it is consistent with the accumulating experimental evidence of excitonic phenomenology reported in InAs/GaSb quantum wells [34][35][36][37][38] as well as in WTe 2 [39,40]. Moreover, the properties of the TRS broken phase provide a comprehensive explanation [41] of the temperature, voltage and length dependencies of the observed conductance in InAs/GaSb bilayers [7,[42][43][44].…”

“…where τ 's and σ's denote the Pauli matrices in the electron-hole and spin basis, the band-inversion parameter E G is defined so that for E G > 0 (E G < 0) the electron and hole bands are (not) inverted at the Γ point, A describes the tunneling between layers, m is the effective mass, and ∆ z is a spin-orbit coupling term arising due to bulk inversion asymmetry. We have ignored the asymmetry of the masses and the momentum-dependent spin-orbit coupling terms, because they are not essential for understanding the phase diagram of the InAs/GaSb bilayers [26,41]. The main effect of Coulomb interactions is the binding of the electrons and holes into excitons with the characteristic size d 0 and binding energy E 0 determined by the relation E 0 = 2 /(md 2 0 ) = e 2 /(4π 0 d 0 ).…”

“…The main effect of Coulomb interactions is the binding of the electrons and holes into excitons with the characteristic size d 0 and binding energy E 0 determined by the relation E 0 = 2 /(md 2 0 ) = e 2 /(4π 0 d 0 ). This leads to an excitonic mean field [26,41]…”

“…The values of the model parameters for InAs/GaSb can be estimated by combining theoretical calculations [5,26,27,50] and the experimentally observed energy gaps [7,34]. This way, we arrive to parameter values [41]: E 0 /k B = 200 K, d 0 = 10 nm, A/(E 0 d 0 ) = 0.06, ∆ z /E 0 = 0.02, g s /E 0 = 1.0 and g p /E 0 = 0.2. The gate-voltage dependent parameter E G is varied in our calculations to tune the system from trivial insulator to QSH insulator phase.…”

“…The gate-voltage dependent parameter E G is varied in our calculations to tune the system from trivial insulator to QSH insulator phase. For small (large) values of E G the system is in a trivial (QSH) insulator phase, and these two phases are separated from each other by an insulating phase with spontaneously broken TRS, where [∆ 1 ], [∆ 2 ] = 0 [26,41]. The bulk gap ∆ bulk remains open for all values of E G , because the intermediate TRS broken phase enables the connection of the topologically distinct phases without bulk gap closing.…”