Topological quantization of boundary forces and the integrated density of states

Abstract

For quantum systems described by Schrödinger operators on the half-space $\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy is topologically quantised provided the Fermi energy lies in a gap of the bulk spectrum. Under this condition it is also equal to the integrated density of states at the Fermi energy.

7 pages

References in corpus (4)

• Equality of bulk and edge Hall conductance revisited
• Boundary maps for $C^{\ast }$-crossed products with R with an application to the quantum Hall effect
• Spaces of tilings, finite telescopic approximations and gap-labelling
• Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard)

Cited by in corpus (6)

• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Virtual Topological Insulators with Real Quantized Physics
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Transverse Laplacians for Substitution Tilings
• Topological quantization of ensemble averages
• Rotation Numbers, Boundary Forces and Gap labelling