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

Abstract

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.

8 pages, 10 figures, v2: final version

References in corpus (12)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Analogs of quantum Hall effect edge states in photonic crystals
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Photonic crystal nanocavity based on a topological corner state
• Topological properties of linear circuit lattices
• Localized heat diffusion in topological thermal materials
• Bulk-edge correspondence of classical diffusion phenomena
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath

Cited by in corpus (5)

• Topological thermal transport
• Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems
• Selectable diffusion direction with topologically protected edge modes
• Observation of Multiple Topological Corner States in Thermal Diffusion
• Multiple topological corner states in the continuum of extended kagome lattice