Roton Superconductivity from Loop-Current Chern Metal on the Kagome Lattice

Motivated by the evidence for time-reversal symmetry (TRS) breaking in nonmagnetic kagome metals AV3Sb5, a novel electronic order of persistent orbital loop-current (LC) has been proposed for the observed charge density wave (CDW) state. The LC order and its impact on the succeeding superconducting (SC) state are central to the new physics of the kagome materials. We show that the LC order fundamentally changes the pairing instability and the SC state, leading to an extraordinary topological superconductor, dubbed as a roton superconductor. In the single-orbital model on the kagome lattice, the LC-CDW state is a Chern metal near van Hove filling with a partially filled Chern band hosting 3 Chern Fermi pockets (CFPs). Cooper pairing of quasiparticles on the CFPs generates 3 SC components coupled by complex Josephson couplings induced by the TRS breaking LC. Due to the discrete quantum geometry associated with the 3-fold rotation and sublattice permutation, a small LC produces a large Josephson phase that drives the leading SC instability to the roton superconductor where the relative phases of the 3 SC components are locked at 120{\deg}, forming an emergent vortex-antivortex lattice with pair density modulations. Properties of the roton superconductor include topological chiral edge states carrying nonzero electric currents, fractional 1/3 vortex excitations and charge-6e Cooper pair triplets that are immune to the internal chiral phase fluctuations. We discuss these SC properties in connection to recent experimental evidence for TRS breaking chiral SC state in kagome superconductors, exhibiting pair density modulations, zero-field SC diode effect, and charge-6e flux quantization. These findings are also relevant for the interplay between the orbital-driven quantum anomalous Hall and SC states in other systems, e.g. the graphene and transition metal dichalcogenide based quantum materials.