Abstract
Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional supercon-ductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_≡ θ1-θ2)exhibits an Ising-type Z2 symmetry due to the second order Josephson coupling,where θ1,2 are the phases of two gap functions.In contrast,the U(1)symmetry in the channel of θ+=θ1+θ2/2is intact.The phase locking,i.e.,ordering of θ_,can take place in the phase fluctuation regime before the onset of superconductivity,i.e.,when θ+is disordered.If θ-is pinned at±π/2,then time-reversal symmetry is broken in the normal state,otherwise,if θ_=0,or,π,rotational symmetry is broken,leading to a nematic normal state.In both cases,the order parameters possess a 4-fermion structure beyond the scope of mean-field theory,which can be viewed as a high order symmetry breaking.We employ an effective two-component XY-model assisted by a renormalization group analysis to address this problem.As a natural by-product,we also find the other interesting intermediate phase corresponds to ordering of θ+but with θ_disordered.This is the quartetting,or,charge-4e,superconductivity,which occurs above the low temperature Z2-breaking charge-2e superconducting phase.Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.
基金项目
startup funding of UCSD()
国家自然科学基金(DMR-2238360)
国家自然科学基金(12234016)
国家自然科学基金(12174317)
New Cornerstone Science Foundation()
维普
万方数据