Quantum anomalous Hall states in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-orbital honeycomb optical lattices

Zhang, MacHi; Hung, Hsiang Hsuan; Zhang, Chuanwei; Wu, Congjun

doi:10.1103/physreva.83.023615

Cited by 60 publications

(43 citation statements)

References 92 publications

(200 reference statements)

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“…Unlike the quantum Hall effect, which arises from Landau-level quantization in a strong magnetic field, QAHE is induced by internal magnetization and SO coupling. Although there have been a number of theoretical studies of this unusual effect, [11][12][13][14][15][16] no experimental observation has been reported so far. In a recent paper, 10 we predicted on the basis of tight-binding lattice models and ab initio calculations that QAHE can occur in single-layer graphene in the presence of both an exchange field and Rashba SO coupling.…”

Section: Introductionmentioning

confidence: 87%

Quantum anomalous Hall effect in single-layer and bilayer graphene

et al. 2011

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The quantum anomalous Hall effect can occur in single-and few-layer graphene systems that have both exchange fields and spin-orbit coupling. In this paper, we present a study of the quantum anomalous Hall effect in single-layer and gated bilayer graphene systems with Rashba spin-orbit coupling. We compute Berry curvatures at each valley point and find that for single-layer graphene the Hall conductivity is quantized at σ xy = 2e 2 /h, with each valley contributing a unit conductance and a corresponding chiral edge state. In bilayer graphene, we find that the quantized anomalous Hall conductivity is twice that of the single-layer case when the gate voltage U is smaller than the exchange field M, and zero otherwise. Although the Chern number vanishes when U > M, the system still exhibits a quantized valley Hall effect, with the edge states in opposite valleys propagating in opposite directions. The possibility of tuning between different topological states with an external gate voltage suggests possible graphene-based spintronics applications.

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Section: Introductionmentioning

confidence: 87%

Quantum anomalous Hall effect in single-layer and bilayer graphene

et al. 2011

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“…But the existence of DPs is particularly appealing and constitutes a qualitative difference with the one-dimensional case. This geometric object, the DP (that takes its name from the diabolo-like shape of the conical intersection), appears in physics in quite different contexts such as, for instance, quantum triangular billiards [17], conical refraction in crystal optics [18], the electronic spectrum of polyatomic molecules [22], or the dispersion relations for massless fermions (Dirac electrons) in QED and for electrons in graphene [23,24] or optical lattices [25]. The diabolo is associated with some remarkable phenomena appearing in those systems.…”

Section: Dispersion Relation For Two-dimensional Alternate Quantumentioning

confidence: 99%

N-dimensional alternate coined quantum walks from a dispersion-relation perspective

et al. 2013

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We suggest an alternative definition of N -dimensional coined quantum walk by generalizing a recent proposal [Di Franco et al., Phys. Rev. Lett. 106, 080502 (2011)]. This N -dimensional alternate quantum walk, AQW (N) , in contrast with the standard definition of the N -dimensional quantum walk, QW (N) , requires only a coin qubit. We discuss the quantum diffusion properties of AQW (2) and AQW (3) by analyzing their dispersion relations that reveal, in particular, the existence of diabolical points. This allows us to highlight interesting similarities with other well-known physical phenomena. We also demonstrate that AQW (3) generates considerable genuine multipartite entanglement. Finally, we discuss the implementability of AQW (N) In both its standard forms, the coined [1] and the continuous one [2], quantum walk is the quantum version of a classical random process, described by the diffusion and the telegrapher's equations, respectively [3]. In the coined quantum walk-the process we consider here-there is a system (the walker) that undergoes a conditional displacement, to the right or the left, depending on the output of a coin throw, as in the random walk. But differently from its classical counterpart, here both coin and walker are quantum in nature. The onedimensional coined quantum walk-QW (1) for short-has been studied from many different perspectives, especially from the quantum computational point of view [4]. In the last few years, quantum walks have also received increasing experimental attention [5][6][7], including cases with more than one particle [8].The situation is quite different when dealing with Ndimensional quantum walks, QW (N) for short. They were first discussed by Mackay et al., who introduced them in complete analogy with QW (1) [9] (see also Ref. [10]). As defined in Ref. [9], QW (N) requires the use of a 2 N -dimensional qudit as coin, as well as a coin operator represented by a 2 N × 2 N unitary matrix. This introduces increasing complexity in the process as N grows, especially from the experimental viewpoint [11,12], but also from the theoretical one [13,14]. However, Di Franco et al. [15] have recently proposed an alternative twodimensional quantum walk, namely, the alternate quantum walk-AQW for short-that is simpler than the standard one. In AQW the coin is a single qubit, as in QW (1) , and each time step is divided into two halves: in the first one the coin is thrown (i.e., a Hadamard transformation is applied on the coin qubit) and the conditional displacement along x is performed; then, in the second half of the time step, the coin is thrown again and the conditional displacement along y is performed. Hence, in AQW, the four-dimensional qudit of QW (2) is replaced by a single qubit, the price paid for that being to double the number of substeps per single time step. Quite unexpectedly, AQW reproduces the same spatial probability distributions of QW (2) when the Grover coin is used -Grover-QW (2) for short -for a set of particular initial conditions, precisely those for ...

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“…Notable quantum phases, such as super-conductivity, quantum hall effect, Mott insulating phase and topological phase, have great significance in theoretical investigations and promising potential in applications. These exotic phases have been found in many quantum systems with quite common structure, such as the honeycomb lattice, the triangular lattice, the decorated honeycomb lattice, the kagomé lattice and so forth16171819202122232425262728293031. Recently a unique quantum many particle lattice system named square-octagon lattice have been investigated in theoretical way intensively and a plenty of meaningful results have been presented.…”

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confidence: 99%

Quantum magnetic phase transition in square-octagon lattice

Bao

Tao

Liu

et al. 2014

Sci Rep

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Quantum magnetic phase transition in square-octagon lattice was investigated by cellular dynamical mean field theory combining with continuous time quantum Monte Carlo algorithm. Based on the systematic calculation on the density of states, the double occupancy and the Fermi surface evolution of square-octagon lattice, we presented the phase diagrams of this splendid many particle system. The competition between the temperature and the on-site repulsive interaction in the isotropic square-octagon lattice has shown that both antiferromagnetic and paramagnetic order can be found not only in the metal phase, but also in the insulating phase. Antiferromagnetic metal phase disappeared in the phase diagram that consists of the anisotropic parameter λ and the on-site repulsive interaction U while the other phases still can be detected at T = 0.17. The results found in this work may contribute to understand well the properties of some consuming systems that have square-octagon structure, quasi square-octagon structure, such as ZnO.

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Quantum anomalous Hall states in thep-orbital honeycomb optical lattices

Cited by 60 publications

References 92 publications

Quantum anomalous Hall effect in single-layer and bilayer graphene

Quantum anomalous Hall effect in single-layer and bilayer graphene

N-dimensional alternate coined quantum walks from a dispersion-relation perspective

Quantum magnetic phase transition in square-octagon lattice

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