Correlation effects in double-Weyl semimetals

Lai, Hsin-Hua

doi:10.1103/physrevb.91.235131

Cited by 65 publications

(69 citation statements)

References 39 publications

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“…It is also interesting to make a RG analysis to study the impact of various types of disorder on the Cooper pairing instability in other semimetal materials, such as 3D Dirac semimetals [10], 2D semi-Dirac semimetals [69][70][71], and double-and triple-Weyl semimetals [72][73][74].…”

Section: Summary and Discussionmentioning

confidence: 99%

Superconductivity in two-dimensional disordered Dirac semimetals

et al. 2017

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In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength |u| is larger than some critical value |uc| because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders, including random mass, random gauge potential, and random chemical potential, and show that the first two suppress superconductivity. In particular, the critical BCS coupling |uc| is increased to certain larger value if the system contains only random mass or random gauge potential, which makes the onset of superconductivity more difficult. In the case of random chemical potential, the effective disorder parameter flows to the strong coupling regime, where the perturbation expansion breaks down and cannot provide a clear answer concerning the fate of superconductivity. When different types of disorder coexist in one system, their strength parameters all flow to strong couplings. In the strong coupling regime, the perturbative renormalization group method becomes invalid, and one needs to employ other methods to treat the disorder effects. We perform a simple gap equation analysis of the impact of random chemical potential on superconductivity by using the AbrikosovGorkov diagrammatic approach, and also briefly discuss the possible generalization of this approach.

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Section: Summary and Discussionmentioning

confidence: 99%

Superconductivity in two-dimensional disordered Dirac semimetals

et al. 2017

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“…In a 3D anisotropic Weyl semimetal where the spectrum displays quadratic dependence on momentum in one direction but linear dependence on other components of momenta, Yang et al supposed a shell of (bΛ, Λ) for the integration over the quadratic component of momenta [48]. Lai [49] used the similar RG scheme to examine the impact of Coulomb interaction in a 3D double Weyl semimetal, in which the dispersion is quadratic in two components of momenta but linear in the third component. Different from Lai [49], Jian and Yao [50] considered the same model but made use of a different RG scheme which defines the momentum shell by…”

Section: B Non-fermi Liquid Behaviors At Semimetal-insulator Qcpmentioning

confidence: 99%

“…RG method has recently been applied to study the influence of Coulomb interaction in several semimetals which are distinguished mainly by the fermion dispersions [34,35,[48][49][50][51]. In a 3D anisotropic Weyl semimetal where the spectrum displays quadratic dependence on momentum in one direction but linear dependence on other components of momenta, Yang et al supposed a shell of (bΛ, Λ) for the integration over the quadratic component of momenta [48].…”

Section: B Non-fermi Liquid Behaviors At Semimetal-insulator Qcpmentioning

confidence: 99%

“…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%

“…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%

See 2 more Smart Citations

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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Topological Phase Transitions: Criticality, Universality, and Renormalization Group Approach

Chen

Sigrist

2019

Advanced Topological Insulators

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Correlation effects in double-Weyl semimetals

Cited by 65 publications

References 39 publications

Superconductivity in two-dimensional disordered Dirac semimetals

Superconductivity in two-dimensional disordered Dirac semimetals

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

Topological Phase Transitions: Criticality, Universality, and Renormalization Group Approach

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