Strong coupling expansion in a correlated three-dimensional topological insulator

Sekine, Akihiko; Nakano, Takashi; Araki, Yasufumi; Nomura, Kentaro

doi:10.1103/physrevb.87.165142

Cited by 15 publications

(26 citation statements)

References 54 publications

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“…The role of Coulomb interaction depends crucially on the fermion dispersion and the dimension. Extensive renormalization group (RG) analysis [53] have revealed that Coulomb interaction is marginally irrelevant in 2D Dirac semimetal [5,36,37], 3D Dirac/Weyl semimetal [38][39][40][41], and also 3D double Weyl semimetal [49,50]. The Fermi liquid (FL) theory is valid in 2D Dirac semimetal [5].…”

Section: Introductionmentioning

confidence: 99%

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Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Wang¹,

Liu²,

Zhang³

2017

Phys. Rev. B

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A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO2/VO2 nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

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Section: Introductionmentioning

confidence: 99%

“…The effects of long-range Coulomb interaction have been studied in various types of semimetals [5,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. The role of Coulomb interaction depends crucially on the fermion dispersion and the dimension.…”

Section: Introductionmentioning

confidence: 99%

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Wang¹,

Liu²,

Zhang³

2017

Phys. Rev. B

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“…In this paper we follow [17,[43][44][45][46][47][48][49] and use the WilsonDirac Hamiltonian as the simplest realistic lattice model of Dirac semimetals and/or topological insulators, which are then tuned into a Weyl semimetal phase by adding the parity-or time-reversal-breaking terms. In our case, parity is broken by the chiral chemical potential µ A .…”

Section: Introductionmentioning

confidence: 99%

Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal

2015

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We report on the mean-field study of the Chiral Magnetic Effect (CME) in static magnetic fields within a simple model of a parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from re-summed ladder diagrams with arbitrary number of loops. We find that on-site repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. Our results suggest that nontrivial corrections to the chiral magnetic conductivity due to inter-fermion interactions are not relevant in practice, since they only become important when the CME response is strongly suppressed by the large gap in the energy spectrum.

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“…As a result, we find a new phase with an in-plane antiferromagnetism in 2D, which appears by the similar mechanism as that of the pion condensate phase (so-called "Aoki phase") in lattice QCD with Wilson fermion [9]. On the other hand, such a phase does not appear in 3D, and the electron correlation results in the shifting of the topological phase boundary [10].…”

Section: Introductionmentioning

confidence: 77%

“…[10] for the details of calculation). Here we should note that φ π vanishes even in the strong coupling limit β = 0, unlike in the 2D case, since the momentum integral at the one-loop level converges in (3 + 1)-dimensions.…”

Section: Pos(lattice 2013)050mentioning

confidence: 99%

Phase structure of topological insulators by lattice strong-coupling expansion

Araki¹,

Kimura²,

Sekine³

et al. 2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

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The effect of the strong electron correlation on the topological phase structure of 2-dimensional (2D) and 3D topological insulators is investigated, in terms of lattice gauge theory. The effective model for noninteracting system is constructed similarly to the lattice fermions with the Wilson term, corresponding to the spin-orbit coupling. Introducing the electron-electron interaction as the coupling to the gauge field, we analyzed the behavior of emergent orders by the strong coupling expansion methods. We show that there appears a new phase with the in-plane antiferromagnetic order in the 2D topological insulator, which is similar to the so-called "Aoki phase" in lattice QCD with Wilson ferions. In the 3D case, on the other hand, there does not appear such a new phase, and the electron correlation results in the shift of the phase boundary between the topological phase and the normal phase.

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Strong coupling expansion in a correlated three-dimensional topological insulator

Cited by 15 publications

References 54 publications

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal

Phase structure of topological insulators by lattice strong-coupling expansion

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