Quantum-metric-induced giant and reversible nonreciprocal transport phenomena in chiral loop-current phases of kagome metals

Rich spontaneous symmetry-breaking phenomena with nontrivial quantum geometric properties in metals represent central issues in condensed matter physics. In this context, the emergence of chiral loop-current order, accompanied by time-reversal symmetry-symmetry breaking in various kagome metals, has garnered significant attention. Particularly noteworthy is the giant electrical magnetochiral anisotropy (eMChA) in CsV3Sb5, which provides compelling evidence of time-reversal-symmetry and inversion-symmetry breakings. However, the underlying essence of this observation has remained obscured due to the lack of theoretical understanding. Here, we reveal that the loop-current order causes giant and reversible eMChA coefficient, ${\gamma }_{eM}$, is proportional to the loop-current-induced orbital magnetization $M_{orb}$ times the lifetime of conduction electrons $\tau$. In kagome metals, the derived ${\gamma }_{eM}$ is substantial and reversible by minute magnetic fields, due to the large $\tau (\gg a_0\mathrm{/}{v}_{Fermi})$ and the field-induced reversal of $M_{orb}$. By considering the experimentally observed stripe charge-density wave, the loop-current state becomes non-centrosymmetric, thereby giving rise to the eMChA. Surprisingly, the quantum-metric, which defines a fundamental geometric aspect of Bloch wavefunctions, acquires significant momentum dependence in the loop-current phase, resulting in a dramatic enhancement of eMChA by $\sim 100$ times. This research not only clarifies the fundamental symmetry-breaking states in kagome metals, but also opens a new path for exploring quantum-metric-induced phenomena arising from exotic quantum phase transitions in strongly correlated metals