From an array of quantum wires to three-dimensional fractional topological insulators

Article

关键词: PARTICLE STATISTICS;    LOCAL OBSERVABLES;    WELLS;    PHASE;    STATE;   

DOI  :  10.1103/PhysRevB.92.195137

来源: SCIE

【 摘 要 】

The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript, we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in noninteracting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form sigma(xy) = 1/2 e(2)/mh if the filling is nu = 1/m. On the other hand, if the surface is gapped by proximity coupling to an s-wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to omega m(-1), in analogy to the edge of the corresponding Laughlin state.

【 授权许可】

Free