High-order Time-Reversal Symmetry Breaking Normal State

11 Feb 2021  ·  Meng Zeng, Lun-Hui Hu, Hong-Ye Hu, Yi-Zhuang You, Congjun Wu ·

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 ($\theta_-\equiv \theta_1-\theta_2$) exhibits an Ising-type $Z_2$ symmetry due to the second order Josephson coupling, where $\theta_{1,2}$ are the phases of two gap functions respectively. In contrast, the $U(1)$ symmetry in the channel of $\theta_+\equiv \frac{\theta_1+\theta_2}{2}$ is intact. The phase locking, i.e., ordering of $\theta_-$, can take place in the phase fluctuation regime before the onset of superconductivity, i.e. when $\theta_+$ is disordered. If $\theta_-$ is pinned at $\pm\frac{\pi}{2}$, then time-reversal symmetry is broken in the normal state, otherwise, if $\theta_-=0$, or, $\pi$, 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 $\theta_+$ but with $\theta_-$ 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.

PDF Abstract
No code implementations yet. Submit your code now

Categories


Superconductivity Strongly Correlated Electrons