Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study

Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac hamiltonians on the boundary with symmetry protected zero modes. This holographic characterization of topological insulators is studied in two dimensions. Dirac hamiltonians on the one dimensional edge are classified according to the discrete symmetries of time-reversal, particle-hole, and chirality, extending a previous classification in two dimensions. We find 17 inequivalent classes, of which 11 have protected zero modes. Although bulk topological invariants are thus far known for only 5 of these classes, we conjecture that the additional 6 describe edge states of new classes of topological insulators. The effects of interactions in two dimensions are also studied. We show that all interactions that preserve the symmetry are exactly marginal, i.e. preserve the gaplessness. This leads to a description of the distinct variations of Luttinger liquids that can be realized on the edge.

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“…Interestingly such a bulk interaction effect on the edge states has been recently confirmed 28,29,33 .…”

Section: Variations Of Luttinger Liquidsmentioning

confidence: 74%

“…An example of DIII (2) is the Kane-Mele model in the presence of particle hole symmetry 28,29 . This can be viewed aa special case of AII (1) -type TI with additional particle-hole symmetry.…”

mentioning

confidence: 99%

Edge states for topological insulators in two dimensions and their Luttinger-like liquids

2012

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“…3,4 In addition, a recent discovery of a spin-liquid phase on the honeycomb lattice 5 has triggered a number of studies that have investigated the role of correlations and the resulting emergent phases on the KaneMele (KM) model. 6 Both nontrivial hopping terms induced by the strong spin-orbit coupling (SOC) and significant on-site Coulomb correlations make A 2 IrO 3 a possible candidate for the so-called Heisenberg-Kitaev (HK) model 7 and its derivatives, [8][9][10][11] on which theoretical investigations are active because of its possible application to topological quantum computations.…”

Section: Introductionmentioning

confidence: 99%

Strain-induced topological insulator phase and effective magnetic interactions in Li2IrO3

Kim

Jeong

et al. 2013

Phys. Rev. B

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We present an effective tight-binding Hamiltonian for Li 2 IrO 3 based on maximally localized Wannier functions for states near the Fermi level as obtained from first-principles electronic structure calculations. The majority of the Wannier orbitals are positioned on the center site with dominant j eff = 1/2 character, while relatively small j eff = 3/2 tails lie on the three nearest-neighbor sites. Interestingly, the spin quantization axis of the j eff = 1/2 components deviates from the local octahedral axis and points toward the nearest-neighbor Ir direction. In our tight-binding model, there are relatively strong next-nearest-and the third-nearest-neighbor hopping terms within the two-dimensional Ir honeycomb lattice in addition to the relatively small but significant interlayer hopping terms. The ratio between the nearest-neighbor and the third-nearest-neighbor hoppings, which can be controlled by the lattice strain, plays a critical role in determinating the Z 2 -invariant character of Li 2 IrO 3 . From our tight-binding model, we also derive an effective Hamiltonian and its parameters for the magnetic exchange interactions. Due to the complex spin-dependent next-nearest-neighbor hopping terms, our pseudospin Hamiltonian includes significant next-nearest-neighbor antiferromagnetic Kitaev terms as well as DzyaloshinskiiMoriya and Heisenberg interactions. From our model Hamiltonian we estimate classical energies of collinear magnetic configurations as functions of the Hund's coupling of the Ir atom, from which zigzag-type magnetic order gives the lowest energy.

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“…Our work is one of the first two papers using QMC to study the interaction effects in topological insulators (The other one is by Assaad's group [46]. These two works are independent from each other).…”

Section: Sign Problem Free Qmc Simulation To the Kane-mele-hubbard Modelmentioning

confidence: 99%

Novel Quantum States with Exotic Spin Properties - Unconventional Generalization of Magnetism

Li¹,

Hung²,

Cai³

et al. 2011

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. My group has investigated the unconventional meta-magnetic states in the Sr3Ru2O7 system, topological insulators, and superconductivity in iron-based superconductors. First, we constructed the microscopic mechanism of the nematic states in the Sr3Ru2O7 system based on its quasi-one-dimensional band structure. The calculated phase diagram agrees with the experimental observation. We performed the detailed theoretical analysis of the quasi-particle interference (QPI) spectroscopy of the STM measurement, which is in nice agreement with the Novel quantum states with exotic spin properties--Unconventional generalization of magnetism Report Title ABSTRACTMy group has investigated the unconventional meta-magnetic states in the Sr3Ru2O7 system, topological insulators, and superconductivity in iron-based superconductors. First, we constructed the microscopic mechanism of the nematic states in the Sr3Ru2O7 system based on its quasi-one-dimensional band structure. The calculated phase diagram agrees with the experimental observation. We performed the detailed theoretical analysis of the quasi-particle interference (QPI) spectroscopy of the STM measurement, which is in nice agreement with the experimental results. Second, we studied strong correlation effects in the 2D topological insulators by performing the sign-problem-free quantum Monte-Carlo simulations, and obtained the phase diagram. How the edge states are destabilized at an intermediate interaction strength is investigated. We have also constructed models of 3D topological insulators based on the generalization of Landau levels. The elegant analytical properties of Landau level provides a good starting point for the future study of fractional topological insulators in 3D. Third, we have investigated the unconventional superconductivity in iron-based superconductors. Time-reversal symmetry breaking states are proposed and the experimentally testable signatures are presented. We further provided a theory explanation of the anisotropic states observed in FeSe superconductors based on orbital ordering.

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Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study

Cited by 241 publications

References 26 publications

Edge states for topological insulators in two dimensions and their Luttinger-like liquids

Edge states for topological insulators in two dimensions and their Luttinger-like liquids

Strain-induced topological insulator phase and effective magnetic interactions in Li2IrO3

Novel Quantum States with Exotic Spin Properties - Unconventional Generalization of Magnetism

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