Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative ...Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_(-)≡θ_(1)-θ_(2))exhibits an Ising-type Z_(2) symmetry due to the second order Josephson coupling,where θ_(1,2) are the phases of two gap functions.In contrast,the U(1) symmetry in the channel of θ_(+)≡(θ_(1)+θ_(2))/2 is 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 timereversal 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 Z_(2)-breaking charge-2e superconducting phase.Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.展开更多
基金supported by a startup funding of UCSD and the National Science Foundation (Grant No. DMR-2238360)supported by the National Natural Science Foundation of China (Grant Nos. 12234016, and 12174317)supported by the New Cornerstone Science Foundation。
文摘Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors.When two superconducting gap functions with different symmetries compete,the relative phase channel(θ_(-)≡θ_(1)-θ_(2))exhibits an Ising-type Z_(2) symmetry due to the second order Josephson coupling,where θ_(1,2) are the phases of two gap functions.In contrast,the U(1) symmetry in the channel of θ_(+)≡(θ_(1)+θ_(2))/2 is 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 timereversal 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 Z_(2)-breaking charge-2e superconducting phase.Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors.
