Inter-Dirac-Cone Coherence Beyond the Valley Framework

Abstract

Although interactions are known to generate exotic phases in pseudospin-1/2 flat-band Dirac materials, it remains an open question whether higher-pseudospin Dirac cones continue to govern low-energy interaction-driven orders even without a well-defined valley degree of freedom. Here, we demonstrate a new form of inter-Dirac-cone coherence beyond the valley framework, which is realized through a staggered virtual-loop-current (SVLC) order in a partially filled pseudospin-1 Dirac flat band. Remarkably, the SVLC order continues to be driven by coherence between the pseudospin-1 Dirac cones even after the conventional valley-based description ceases to apply. The virtual loop currents are shown to originate from interaction-driven quantum fluctuations of charge densities and are found to exhibit an alternating circulation between the neighboring triangular plaquettes. The resulting spontaneous time-reversal symmetry breaking induces finite intrinsic anomalous Hall conductivity and orbital magnetization. The SVLC order is shown to be the lowest-energy solution in restricted real-space Hartree-Fock calculations in the weakly interacting regime. Our study establishes inter-Dirac-cone coherence as the organizing principle for interaction-driven orders in higher-pseudospin Dirac systems and identifies these systems as a new platform for driving exotic emergent phases beyond the valley framework.

16 pages, 10 figures