Anomalous conductivity of $\mathcal{P}\mathcal{T}$-symmetric Fermi liquids

We consider a non-Hermitian yet $\mathcal{P}\mathcal{T}$-symmetric Fermi liquid ($\mathcal{P}\mathcal{T}$-FL) in external electric fields. Due to $\mathcal{P}\mathcal{T}$-symmetry, the system exhibits real spectrum, Fermi surface and electric conductivity are well-defined through propagators. We find that, in contrast to the conventional Fermi liquids (FL), the $\mathcal{P}\mathcal{T}$-FL can exhibit a zero resistance state in the longitudinal ($xx$) channel. Moreover, the temperature dependence of the resistivity anomaly violates the conventional FL scaling (it is not limited by $T^2$). These findings open route to further exploration of transport anomalies beyond the conventional paradigm.