Excitonic instability of three-dimensional gapless semiconductors: Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>theory

Janssen, Lukas; Herbut, Igor F.

doi:10.1103/physrevb.93.165109

Cited by 43 publications

(49 citation statements)

References 48 publications

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“…To further simplify the problem, we take A 1 = A 2 ≡ 1. Such truncation scheme has previously been adopted to study dynamical gap generation in 2D Dirac semimetal [65,70,73,74], in QED 3 model [125,127], and also in 3D quadratical semimetal [46]. These studies serve as a very useful starting point for further, improved analysis.…”

Section: Dyson-schwinger Equation Of Excitnonic Gapmentioning

confidence: 99%

“…It has been used in such 2D Dirac semimetal as graphene [65, 69-71, 76, 77, 81], 3D semimetal with quadratic touching points [46], and finite temperature QED 3 [131]. A universal feature shared by these systems is that the fermion mass gap depends on energy and momentum separately due to the explicit breaking of Lorentz invariance, which makes it very difficult to solve the self-consistent gap equation numerically.…”

Section: A Instantaneous Approximationmentioning

confidence: 99%

“…Since Nambu and Jona-Lasinio [68], the DS equation approach has been widely applied to study DCSB in QCD [123,124] and QED 3 [125][126][127][128][129][130][131]. It also has been used to examine whether an excitonic gap can be dynamically generated by the Coulomb interaction in graphene [65,[69][70][71][72][73][74][75][76][77][78][79][80][81][82][83] and other closely related materials [41,46,82]. The role played by the DS equation in the studies of excitonic gap generation is similar to that played by the gap equation in the studies of the formation of superconductivity in BCS theory.…”

Section: Dyson-schwinger Equation Of Excitnonic Gapmentioning

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%

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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: Dyson-schwinger Equation Of Excitnonic Gapmentioning

confidence: 99%

Section: A Instantaneous Approximationmentioning

confidence: 99%

Section: Dyson-schwinger Equation Of Excitnonic Gapmentioning

confidence: 99%

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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“…In addition, Weyl SM (WSM), in which the low-energy fermionic excitations display linear dispersion around pairs of nodes with opposite chirality, was observed in TaAs, NbAs, TaP, and NbP by the angle-resolved photoemission spectroscopy (ARPES) [10][11][12][13][14]. There also exist other types of SMs, such as 3D nodal line SM (NLSM) [15][16][17][18], 2D semi-DSM , 3D double-WSM [47][48][49][50][51][52][53][54][55][56][57][58][59], 3D triple-WSM [49,53,[56][57][58][59][60][61][62], 3D anisotropic-WSM [49,[63][64][65], and 3D Luttinger SM [66][67][68][69][70].…”

Section: Introductionmentioning

confidence: 99%

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

2019

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The influence of weak disorder on the superconductivity in ordinary metals can be formally described by the Abrikosov-Gorkov diagrammatic approach. The vertex correction is ignored in this approach because an inequality k F l?1, where k F is the Fermi momentum and l mean free path, is satisfied in ordinary metals with a large Fermi surface. In a Dirac semimetal that has discrete Fermi points, this inequality may break down even for arbitrarily weak disorder since k 0 F  , and thus the vertex correction could be important. We incorporate the vertex correction into the self-consistent equations of the superconducting gap and the disorder scattering rate, and then apply the generalized approach to study how s-wave superconductivity is affected by random chemical potential in two-and threedimensional Dirac semimetals, as well as two-dimensional semi-Dirac semimetal. In the clean limit, superconductivity is formed only when the pairing interaction strength is greater than some critical value in these materials. Adding random chemical potential to the system promotes superconductivity by generating a finite fermionic density of states at the Fermi level. In three-dimensional Dirac semimetal, the critical attraction strength is reduced by weak disorder, but remains finite. In the other two cases, superconductivity is induced by arbitrarily weak attraction. Including the vertex correction does not change these qualitative results, and actually could further promote superconductivity in the weak-attraction regime. Bilayer graphene is quite special in that its zero-energy density of states is nonzero despite the existence of Fermi points. Due to this peculiar property, superconductivity is always slightly suppressed by random chemical potential, and the impact of vertex correction is nearly negligible.

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Random-mass disorder in the critical Gross-Neveu-Yukawa models

Yerzhakov

Maciejko

2021

Nuclear Physics B

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Excitonic instability of three-dimensional gapless semiconductors: Large-Ntheory

Cited by 43 publications

References 48 publications

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

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

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

Random-mass disorder in the critical Gross-Neveu-Yukawa models

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