Abstract
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications. Interplay between topology and strong electron-electron interactions leads to lots of fascinating effects since the discovery of the fractional quantum Hall effect. Here, we theoretically study the Rashba-type spin-orbit coupling effect on a fractional quantum spin Hall system by means of finite size exact diagonalization. Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling. Furthermore, the experimental realization of the Tao-Thouless-like state as well as its evolution in optical lattices are also proposed. The importance of this prediction provides significant insight into the realization of exotic topological quantum states in optical lattice, and also opens a route for exploring the exotic quantum states in condensed matters in future.
Highlights
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications
Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling
In this Letter, we propose a theoretical realization of fractionalized topological Tao-Thouless-like quantum state in a fractional quantum spin Hall system with a thin torus geometric structure by tuning the strength of Rashba-type spin-orbit coupling based on the framework of finite size exact diagonalization method
Summary
The single-particle band dispersion of the Hamiltonian H 0 + Hsoc (see model Hamiltonian in Methods) on the system with torus and cylinder structures are shown, which have a large bulk energy gap with the amplitude of 2t1 well separating the two spin-mixed flatbands and conduction bands. The ground state spectra of the effect of the Rashba spin-orbit coupling αR (see model Hamiltonian in Methods) on a fractional quantum spin Hall state are displayed in the top row of Fig. 2, where the parameters are chosen as αR = 0 and αR = 0.08 for (a1) and (b1), respectively, and shown that the ground state manifold is defined as a set of lowest states [nine-fold degeneracies in (a1) and three-fold degeneracies in (b1)] well separated from other excited states by a clear energy gap.
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