Strong evidence is presented for the localization of low-energy quasiparticle states in disordered $d$ -wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of nonmagnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to 50\ifmmode\times\else\texttimes\fi{}50 sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite-size dependence of inverse participation ratios.Strong evidence is presented for the localization of low-energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of nonmagnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to 50\ifmmode\times\else\texttimes\fi{}50 sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite-size dependence of inverse participation ratios.

arXiv:cond-mat/9604188Physical review. B, Condensed matterSep 1, 1996100 citations

Bogoliubov–de Gennes soliton dynamics in unconventional Fermi superfluids

Daisuke A. Takahashi

Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $\text{SU}(d)$ -symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the $d=2$ systems, which describe the mixture of singlet $s$ -wave and triplet $p$ -wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and $N$ -flavor generalization are discussed.Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $\text{SU}(d)$-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the $d=2$ systems, which describe the mixture of singlet $s$-wave and triplet $p$-wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and $N$-flavor generalization are discussed.

arXiv:1509.04242Physical review. B./Physical review. BJan 19, 201613 citations

Disordered d-wave superconductors with interactions

Luca Dell’Anna

arXiv:cond-mat/0607635Nuclear Physics BOct 24, 200622 citations

Strong evidence is presented for the localization of low-energy quasiparticle states in disordered

d

-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of nonmagnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to 50\ifmmode\times\else\texttimes\fi{}50 sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite-size dependence of inverse participation ratios.

Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an

\text{SU}(d)

-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the

d=2

systems, which describe the mixture of singlet

s

-wave and triplet

p

-wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and

N

-flavor generalization are discussed.