Open AccessDissertation
Numerical study of fractional topological insulators
Cécile Repellin
- 25 Sep 2015
13
TL;DR: In this article, the conditions of emergence of different types of fractional topological insulators, using numerical simulations, were studied, and the low energy excitations on the torus of two of the most emblematic quantum Hall states, the Laughlin and Moore-Read states, were investigated.
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Abstract: Topological insulators are band insulators which are fundamentally different from atomic insulators. Only a non-local quantity called topological invariant can distinguish these two phases. The quantum Hall effect is the first example of a topological insulator, but the same phase can arise in the absence of a magnetic field, and is called a Chern insulator. In the presence of strong interactions, topological insulators may host exotic excitations called anyons. The fractional quantum Hall effect is the only experimentally realized example of such phase. In this manuscript, we study the conditions of emergence of different types of fractional topological insulators, using numerical simulations. We first look at the fractional quantum Hall effect on the torus. We introduce a new projective construction of exotic quantum Hall states that complements the existing construction. We study the low energy excitations on the torus of two of the most emblematic quantum Hall states, the Laughlin and Moore-Read states. We propose and validate model wave functions to describe them. We apply this knowledge to characterize the excitations of the Laughlin state in Chern insulators. We show the stability of other fractional quantum Hall states in Chern insulators, the composite fermion, Halperin and NASS states. We explore the physics of fractional phases with no equivalent in a quantum Hall system, using two different strategies: first by choosing a model with a higher value of the topological invariant, second by adding time-reversal symmetry, which changes the nature of the topological invariant.
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Citations
Paired Hall States
Martin Greiter
- 01 Jan 1992
TL;DR: In this paper, the authors consider the question of perturbation around free fermions and show that very near this point the statistical interactions are weak and their effects calculable; nevertheless they have the important qualitative consequence that a p-wave BCS pairing instability is triggered.
158
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Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
TL;DR: This work provides the first explicit wave-function description of fractional topological insulators in the absence of spin conservation, and demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure.
Direct Observation of a Fractional Charge
TL;DR: In this paper, the authors performed measurements of shot noise in order to determine the quasiparticle charge in the Fractional Quantum Hall regime and found that the charge is e/3.
60
•Journal Article
Zoology of Fractional Chern Insulators
TL;DR: In this article, the authors studied four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings and observed that all cases exhibit a Laughlin-like phase at filling fraction $1/3.
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Spin-orbit gap of graphene: First-principles calculationsYugui Yao
Abstract: Even though graphene is a low-energy system consisting of a two-dimensional honeycomb lattice of carbon atoms, its quasiparticle excitations are fully described by the (2+1)-dimensional relativistic Dirac equation. In this paper we show that, while the spin-orbit interaction in graphene is of the order of 4 meV, it opens up a gap of the order of 10(-3) meV at the Dirac points. We present a first-principles calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can occur only at unrealistically low temperature.
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