arXiv:cond-mat/9905388

Disordered d-wave superconductors with chiral symmetry

Takahiro Fukui

Published May 26, 1999• 0 citations

Abstract

A two-dimensional lattice model for d-wave superconductor with chiral symmetry is studied. The field theory at the band center is shown to be in the universality class of U(2n)/O(2n) and U(2n) nonlinear sigma model for the system with broken and unbroken time-reversal symmetry, respectively. Vanishing of the beta function implies extended states at the band center. Density of state vanishes as a cubic function of the energy at the band center for the former case, while linear for the latter.

DOI: 10.48550/arxiv.cond-mat/9905388

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arXiv:cond-mat/9905388

Disordered d-wave superconductors with chiral symmetry

Takahiro Fukui

Published May 26, 1999• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9905388

Related papers

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We study the effects of quenched disorder on the two-dimensional

d

-wave superconductors (SCs) at zero temperature by Monte Carlo simulations. The model is defined on the three-dimensional (3D) lattice and the SC pair field is put on each spatial link as motivated in the resonating-valence-bond theory of the high-

{T}_{c}

SCs. For the nonrandom case, the model exhibits a second-order phase transition to a SC state as density of charge carriers is increased. It belongs to the universality class different from that of the 3D

XY

model. Quenched disorders (impurities) are introduced both in the hopping amplitude and the plaquette term of pair fields. Then the second-order transition disappears at a critical concentration of quenched disorder, ${p}_{c}\ensuremath{\simeq}15%$. Implication of the results to cold atomic systems in optical lattices is also discussed.

(2n)

symmetry, both of which are broken to Sp

(n),

and the fluctuation around a saddle point is described, respectively, by the Sp

{(n)}_{2}

Wess-Zumino-Witten model and U

(2n)

/Sp

(n)

nonlinear sigma model.

d+is

superconducting phase, which is characterized by nonvanishing chirality and density-current correlation. Our results suggest the possibility of a bulk time-reversal symmetry breaking state in overdoped cuprates.

m

) are topologically protected, while others are not and therefore are subject to Anderson localization in the presence of disorder. We study transport properties of such quasi-one-dimensional quantum wires with broken time-reversal and spin-rotational symmetries (class D) and calculate the average conductance, its variance and the third cumulant, as well as the average shot noise power. The results are obtained for arbitrary wire length, tracing a crossover from the diffusive Drude regime to the regime of strong localization where only

m

protected channels conduct. Our approach is based on the nonperturbative treatment of the nonlinear supersymmetric sigma model of symmetry class D with two replicas developed in our recent publication [D. S. Antonenko et al., Phys. Rev. B 102, 195152 (2020)]. The presence of topologically protected modes results in the appearance of a topological Wess-Zumino-Witten term in the sigma-model action, which leads to an additional subsidiary series of eigenstates of the transfer-matrix Hamiltonian. The developed formalism can be applied to study the interplay of Anderson localization and topological protection in quantum wires of other symmetry classes.