Elementary formula for the Hall conductivity of interacting systems

Neupert, Titus; Santos, Luiz; Chamon, Claudio; Mudry, Christopher

doi:10.1103/physrevb.86.165133

Cited by 23 publications

(42 citation statements)

References 28 publications

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“…It is shown in Ref. 31 that σ H converges to the Hall conductivity σ H averaged over the degenerate ground states in the thermodynamic limit, provided no spontaneous symmetry-breaking of translation invariance occurs. Observe that the accuracy of the quantization of σ H is limited by the finite size of the system, as the Berry curvature (3.6b) is only summed over L 1 × L 2 points in the BZ to replace an integral in the thermodynamic limit.…”

Section: ?mentioning

confidence: 99%

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Enhancing the stability of a fractional Chern insulator against competing phases

et al. 2012

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We construct a two-band lattice model whose bands can carry the Chern numbers C = 0, ±1, ±2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number C = 2 instead of C = 1. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.

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Section: ?mentioning

confidence: 99%

“…31 for the quantum Hall conductivity σ H as befits a finite lattice. Here, the singleparticle Berry curvature F k and the many-body occupation numbern k averaged over the five quasidegenerate ground states |Ψ i , i = 1, · · · , 5, are given by…”

Section: ?mentioning

confidence: 99%

Enhancing the stability of a fractional Chern insulator against competing phases

et al. 2012

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“…[21][22][23] Finally, it is interesting to note that our construction provides a nice counterexample to the claims of Ref. 24 In this appendix we will briefly outline the definitions of Berry curvature that we use in the main text. First, we write the single-particle Bloch solution for the ath band as ψ ak (r) = e ik·r u ak (r),…”

Section: Discussionmentioning

confidence: 99%

Fractional Chern insulators in bands with zero Berry curvature

2015

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Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilize a fractional Chern insulator. These interactions necessarily break time-reversal symmetry (either spontaneously or explicitly) and have the effect of altering the underlying band structure. We outline a number of ways in which this may be achieved, and show how similar interactions may also be used to create a (time-reversal symmetric) fractional topological insulator. While our approach is rigorous in the limit of long-range interactions, we show numerically that even for short-range interactions a fractional Chern insulator can be stabilized in a band with zero Berry curvature.

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“…This model has been used to describe the topological phase transition in TlBi(S 1−δ Se δ ) 2 and delivered the spin-polarized surface related states both in the trivial and the nontrivial region in good agreement with recent spin-and angle-resolved photoemission measurements. 42 The Hall conductivity in unit of e 2 h is calculated based on Kubo formalism 21,43 which is an integration of the Berry phase of Bloch wave function. The Hall conductivity is thus:…”

Section: Model and Methodsmentioning

confidence: 99%

Quantum anomalous Hall effect with field-tunable Chern number nearZ2topological critical point

et al. 2015

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We study the practicability of achieving quantum anomalous Hall (QAH) effect with field-tunable Chern number in a magnetically doped, topologically trivial insulating thin film. Specifically in a candidate material, TlBi(S 1−δ Se δ )2, we demonstrate that the QAH phases with different Chern numbers can be achieved by means of tuning the exchange field strength or the sample thickness near the Z2 topological critical point. Our physics scenario successfully reduces the necessary exchange coupling strength for a targeted Chern number. This QAH mechanism differs from the traditional QAH picture with a magnetic topological insulating thin film, where the "surface" states must involve and sometimes complicate the realization issue. Furthermore, we find that a given Chern number can also be tuned by a perpendicular electric field, which naturally occurs when a substrate is present.

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Elementary formula for the Hall conductivity of interacting systems

Abstract: A formula for the Hall conductivity of interacting electrons is given under the assumption that the ground state manifold is N_gs-fold degenerate and discrete translation symmetry is neither explicitly nor spontaneously broken.Comment: 7 page

Cited by 23 publications

References 28 publications

Enhancing the stability of a fractional Chern insulator against competing phases

Enhancing the stability of a fractional Chern insulator against competing phases

Fractional Chern insulators in bands with zero Berry curvature

Quantum anomalous Hall effect with field-tunable Chern number nearZ2topological critical point

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