Vortices and Chirality in Multi-Band Superconductors

Abstract

We investigate some significant properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken timereversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-π kink solutions exist with the topological charge Q. This yields multi-vortex bound states in three-band superconductors.

Vortex in holographic two-band superfluid/superconductor

“…It would also be very useful to generalize to a JHEP05(2016)011 three-band model. There one can study the existence of chiral and time-reversal symmetry breaking state, interband phase difference induced domain walls, fractional quantum flux vortices [46][47][48] and frustrated superconductors [49]. Lastly, it would be interesting to clarify issues surrounding hidden criticality [50] using a holographic model of multiband superconductivity.…”

Renormalization Group Theory of Effective Field Theory Models in Low Dimensions

“…The Hubbard model is an important model of strongly correlated electrons [60][61][62][63][64][65]. The Nambu-Goldstone (NG) modes in a multi-gap superconductor become massive due to the cosine potential, and thus the dynamical property of the NG mode can be understood by using the sine-Gordon model [66][67][68][69][70][71]. The sine-Gordon model will play an important role in layered high-temperature superconductors because the Josephson plasma oscillation is analysed on the basis of this model [72][73][74][75].…”

Vortices with Fractional Flux Quanta in Multi-Band Superconductors

“…In a two-band superconductor, two order parameters have the same and opposite phases for the attractive and repulsive coupling respectively. When there are three or more bands with interband repulsions, it is interesting that a frustrated state where phase differences among order parameters are neither 0 nor π appears, where time-reversal symmetry (TRS) is broken [6][7][8][9][10][11][12][13][14][15][16] , leading to interesting phase sensitive phenomena such as massless Leggett mode 17 and asymmetric critical current 18 .…”