Higher-order topological heat conduction on a lattice for detection of corner states

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing kagome lattice. We show that the temperature measurement at a conner node can detect the corner state which causes rapid heat conduction toward the heat bath, and that several-nodes measurement can determine the precise energy of the corner states.Comment: 8 pages, 10 figures, v2: final versio

Topological Description of (Spin) Hall Conductances on Brillouin Zone Lattices : Quantum Phase Transitions and Topological Changes

It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given by the Berry connections of the ground states. We present a topological description for the (spin) Hall conductances on a discretized Brillouin Zone. At the same time, it is quite efficient in practical numerical calculations for concrete models. We demonstrate its validity in a model with quantum phase transitions. Topological changes supplemented with the transition is also described in the present lattice formulation.Comment: proceeding of EP2DS-1