摘要
We theoretically investigate a one-dimensional Su–Schrieffer–Heeger(SSH)model with spin–orbit coupling(SOC)and sublattice-dependent gain and loss.As the gain and loss increase,the system transitions from a parity-time(PT)symmetric phase to a parity-time and anti-parity-time(PT&APT)symmetry-breaking phase,and finally to an anti-paritytime(APT)symmetric phase.Notably,when the intracell and intercell hopping,intracell and intercell SOC parameters are all equal to half the gain–loss parameter,the model exhibits a doubly degenerate exceptional point(EP).When the SOC is equal for intracell and intercell interactions,a stronger hopping mechanism within cells compared to that between cells results in an increase in SOC that transitions the Zak phase from zero to a non-quantized value,eventually arriving at one.In contrast,a reduction in the strength of intracell hopping leads the Zak phase to transition from two to a non-quantized value,eventually arriving at one.If the intracell and intercell SOC are not aligned,altering these couplings leads to a shift in the Zak phase from two to a non-quantized level,then to one,re-entering the non-quantized region,and eventually arriving at zero.We suggest a practical experimental setup for our model that can be implemented using electrical circuits.
基金
Project supported by the Natural Science Foundation of Chongqing,China(Grant No.CSTB2024NSCQ-MSX0736)
Science and Technology Innovation Key R&D Program of Chongqing(Grant No.CSTB2024TIAD-STX0035)
the Research Foundation of Institute for Advanced Sciences of CQUPT(Grant No.E011A2022328)。
