Edge Mass-Kink and Fractional Corner Charge in Higher-Order Topological Insulators
Date:
Abstract: Higher-order topological insulators are d-dimensional topological insulators with the absence of (d-1)-dimensional gapless states, of which the bulk-boundary correspondence is manifested as (d-2)-dimensional in-gap states instead. There are various mechanisms that generate such topological phases, still, a unified theory is lacking. A recent theory shows that the 0-dimensional in-gap states emerge at corners where two edges have phase difference between their mass of edge Dirac cones, which explains the origin of the in-gap states in higher-order topological insulators. Yet, the analyses retain in the pen-and-paper level or need the energy spectrum of a nano-disk/nano-ribbons with considerable size, which are both impractical to apply on real materials. I will briefly introduce the concept of mass-kink and demonstrate how to use it to predict the numbers and the distributions of the in-gap states. Then, I will present my recent works on using material specific tight-binding hamiltonians and real-space renormalization group through Green’s function to calculate the phases of mass for edge Dirac cones, which is not only computational cheap but also gives accurate values for fractional corner charges.
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