Massless collective excitations in frustrated multiband superconductors

Abstract

We study collective excitations in three-and four-band superconductors with inter-band frustration, which causes neither 0 nor π inter-band phases in the superconducting state. Using a low-energy spin-Hamiltonian originating from a multi-band tight-binding model, we find that mass reduction of a Leggett mode occurs in a wide parameter region of this four-band system. As a limitting case, we have a massless Leggett mode. This massless mode is related to the fact that the mean-field energy does not depend on a relative phase of superconducting order parameters. In other words, we find a link of the massless mode with a degeneracy between a time-reversalsymmetry-breaking state (neither 0 nor π phases) and a time-reversal-symmetric state (either 0 or π phases). Therefore, the mass of collective modes characterizes well the time-reversal symmetry in frustrated multi-band superconductors.

Fluctuation-induced Nambu–Goldstone bosons in a Higgs–Josephson model

“…The model presented in the paper appears as an effective free energy in multi-band superconductors [13][14][15][19][20][21][22][23]. Low energy excitation states are important in superconductors, and the existence of massless modes have been pointed out [18,21,24,25]. In this paper we have presented a new mechanism of the emergence of Nambu-Goldstone bosons.…”

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

“…A multi-band superconductivity has been investigated as a generalization of the BCS theory since early works on the two-band superconductivity. [86][87][88][89] There will appear many interesting properties in superconductors with multiple gaps such as time-reversal symmetry breaking, [90][91][92][93][94][95][96][97][98][99][100][101][102][103] the existence of massless modes, [104][105][106][107][108][109] unusual isotope effect [110][111][112][113][114] and fractional-flux quantum vortices. [115][116][117][118][119] When we have multiple order parameters, there appear multiple Nambu-Goldstone bosons and Higgs bosons.…”

Nambu-Goldstone-Leggett modes in multi-condensate superconductors

“…3(a) and 3(b)). The existence of massless modes was examined numerically for the multi-gap BCS model [33]. , where time-reversal symmetry is broken and a massless mode exists.…”

“…There is, however, a possibility that some of these modes become massless Nambu-Goldstone modes when the Josephson couplings are frustrated. The Josephson couplings between different bands will bring about attractive phenomena; they are (a) time-reversal symmetry breaking (TRSB) [18][19][20][21][22][23][24][25][26][27][28][29][30], (b) the existence of massless (gapless) modes [31][32][33][34][35][36][37] and low-lying excited states, and (c) the existence of kinks and fractionally-quantizedflux vortices [38][39][40][41][42]. The phase-difference mode between two gaps is sometimes called the Leggett mode [43].…”