The stability of the fractional quantum Hall effect in topological insulators

Abstract

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the n = 0 and |n| = 1 Landau levels, it is ruled out in higher |n| Landau levels. Unlike graphene, the fractional quantum Hall effect in topological insulators is predicted to show an interesting asymmetry between n = 1 and n = −1 Landau levels due to spin-orbit coupling.

Strongly correlated states of trapped ultracold fermions in deformed Landau levels

“…In order to see that, let us revise (and specify to our setup) the two main assumptions that are commonly used to study interacting gases within a LL picture: namely, the lowest LL approximation and the formalism of HPs [24]. Such a path has been demonstrated successful in a wealth of physical systems, ranging from usual quantum Hall setups (see, e.g., [25] and references therein) to graphene [26][27][28] and topological insulators [29].…”

“…The LL structure is indeed preserved and simply undergoes a deformation, that splits the degeneracy among internal states and leads to a sequence of different LLs as lowest energy states as a function of the spin-orbit coupling. The effective interaction between atoms in these deformed Landau levels (DLLs) can be described in terms of Haldane pseudopotentials (HPs) [24] (i.e., one coefficient per each relative angular momentum between particles), as proposed in diverse physical systems displaying an effective LL structure [25][26][27][28][29]. In the case of ultracold gases subjected to the considered U (2) gauge potential, it has been shown that even a bare contact interaction between the atoms yields two-particle HPs in the DLLs that dramatically vary with the spin-orbit coupling and introduce effective finite-range interactions [30,31].…”

Signatures of Fractional Quantum Hall States in Topological Insulators

“…The experimental observation of topological surface states (SSs) in three-dimensional bulk solids has allowed the study of a correlated chiral Dirac fermion system, which can host a single Dirac valley without spin degeneracy [3][4][5][6][7][8][9][10]. Recent theoretical studies suggest that the fractional quantum Hall effect (FQHE) might be observable in topological insulators [11,12]. However, due to the dominant bulk conduction it is difficult to probe the strong correlation effect in topological insulators from resistivity measurements [8,9].…”

“…Theoretically, the relativistic nature of Dirac fermions is believed to significantly modify the electron-electron interactions, with the possibility to produce more robust ground states at the n = 1 Landau level (LL) in TIs than in conventional two-dimensional electron systems [20][21][22][23]. The unique spin texture and the coexistence of non-insulating bulk states also raise the intriguing question of whether TIs may host exotic FQH states owing to the non-trivial Berry's phase [16], huge Zeeman energy [24], and the screening effect from bulk carriers [11]. The potential realization of more stable non-Abelian FQH states in TIs is of practical interest for topological quantum computing [12,25].…”

“…Such a property makes the exact origin of these oscillations unclear [9]. On the other hand, the FQHE in TIs is theoretically precluded in the |n| > 1 LLs [11], suggesting the features in Bi 2 Se 2 Te unlikely to be ascribed to the FQHE. So far, transport studies of FQHE in TIs have been limited to samples with * All correspondence should be addressed to D. Qu (qu2@llnl.gov) mobility below 3,000 cm 2 /Vs and the SS conduction is susceptible to conducting bulk states.…”