Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices

Wen, Jun; Rüegg, Andreas; Wang, C.-C. Joseph; Fiete, Gregory A.

doi:10.1103/physrevb.82.075125

Cited by 221 publications

(232 citation statements)

References 75 publications

(145 reference statements)

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“…However, the vanishing density of states (DOS) renders the Dirac Fermi points robust against weakly repulsive electron-electron interactions. In general, a finite interaction stength is required to open a gap at f = 1/3 and stabilize a topologically nontrivial phase [44,45]. Another topologically nontrivial band-touching occurs at the Γ-point between the upper dispersive and flat bands.…”

Section: After Fourier Transformationmentioning

confidence: 99%

Exotic magnetic orderings in the kagome Kondo-lattice model

et al. 2014

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We consider the Kondo-lattice model on the kagome lattice and study its weak-coupling instabilities at band filling fractions for which the Fermi surface has singularities. These singularites include Dirac points, quadratic Fermi points in contact with a flat band, and Van Hove saddle points. By combining a controlled analytical approach with large-scale numerical simulations, we demonstrate that the weak-coupling instabilities of the Kondo-lattice model lead to exotic magnetic orderings. In particular, some of these magnetic orderings produce a spontaneous quantum anomalous Hall state.

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Section: After Fourier Transformationmentioning

confidence: 99%

Exotic magnetic orderings in the kagome Kondo-lattice model

et al. 2014

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“…19,20 It has also been found that interactions may lead to a topological insulator in a decorated honeycomb and kagome lattices. 21 The main obstacle for realizing an interaction-driven topological insulator is the required interaction profile in real space. In a honeycomb lattice, for example, this amounts to an interaction that is strongest on next-nearest-neighbor bonds.…”

Section: Introductionmentioning

confidence: 99%

Inducing topological order in a honeycomb lattice

Pereg-Barnea

Refael

2012

Phys. Rev. B

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We explore the possibility of inducing a topological insulator phase in a honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi gas) environment. The lattice and the metallic environment interact through a density-density interaction without particle tunneling, and integrating out the metallic environment produces a honeycomb sheet with in-plane oscillating long-ranged interactions. We find the ground state of the interacting system in a variational mean-field method and show that the Fermi wave vector k F of the metal determines which phase occurs in the honeycomb lattice sheet. This is analogous to the Ruderman-KittelKasuya-Yosida (RKKY) mechanism in which the metal's k F determines the interaction profile as a function of the distance. Tuning k F and the interaction strength may lead to a variety of ordered phases, including a topological insulator and anomalous quantum-Hall states with complex next-nearest-neighbor hopping, as in the Haldane and the Kane-Mele model. We estimate the required range of parameters needed for the topological state and find that the Fermi vector of the metallic gate should be of the order of 3π/8a (with a being the graphene lattice constant). The net coupling between the layers, which includes screening in the metal, should be of the order of the honeycomb lattice bandwidth. This configuration should be most easily realized in a cold-atoms setting with two interacting Fermionic species.

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“…Therefore, many-body interaction is expected to enable topological phases in strongly correlated systems by generating circulating currents and spontaneously breaking time-reversal symmetry (TRS), which act as an effective magnetic field or spin-orbit coupling [12,14,15]. This subject has attracted vigorous research due to support from mean-field studies, followed by low-energy renormalization-group analysis [13,16], and the existence of such topological phases has been suggested for the extended Hubbard model on various lattice models [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, unbiased numerical simulations, such as exact diagonalization (ED) and density-matrix renormalization-group (DMRG) studies, found competing states other than topological phases as the true ground states in all previously proposed systems with Dirac points [31][32][33][34] or quadratic band touching points [35,36].…”

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confidence: 99%

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

et al. 2016

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Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band. DOI: 10.1103/PhysRevLett.117.096402 Introduction.-Topological states of matter have led to an ongoing revolution of our fundamental understanding of quantum materials, as exemplified by the discoveries of the integer quantum Hall (IQH) effect [1,2], the quantum anomalous Hall (QAH) effect [3][4][5], and the quantum spin Hall effect [6][7][8]. Crucially, such topological phases emerge from noninteracting electronic structures with nontrivial topology, where a strong magnetic field or a large spin-orbit coupling is typically necessary. Despite great achievements, most of the materials that have exhibited unique topological properties to date can be understood based on noninteracting physics originating from nontrivial band physics. This limitation has inspired recent enthusiasm in exploring topological phases in "trivial" materials [9][10][11][12][13], without the requirement of a nontrivial invariant encoded in a single-particle wave function or band structure. Finding such novel phases can significantly enrich the class of topological materials and thus is of great importance.The strong correlation between electrons can dramatically change the noninteracting physics and induce spontaneous symmetry breakings. Therefore, many-body interaction is expected to enable topological phases in strongly correlated systems by generating circulating currents and spontaneously breaking time-reversal symmetry (TRS), which act as an effective magnetic field or spin-orbit coupling [12,14,15]. This subject has attracted vigorous research due to support from mean-field studies, followed by low-energy renormalization-group analysis [13,16], and the existence of such topological phases has been suggested for the extended Hubbard model on various lattice models [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, unbiased numerical simulations, such as

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Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices

Cited by 221 publications

References 75 publications

Exotic magnetic orderings in the kagome Kondo-lattice model

Exotic magnetic orderings in the kagome Kondo-lattice model

Inducing topological order in a honeycomb lattice

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

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