Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

Abstract

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $0$ and $-1$ [Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation and fixes the mod(1) ambiguity appearing in the Modern Theory of Polarization. In the present work we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from $-N_c$ to $0$, where $N_c$ is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by W. Kohn [Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models.

arXiv comment20 pages, 6 figures

References in corpus (35)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Maximally localized Wannier functions: Theory and applications
• Spintronics and Pseudospintronics in Graphene and Topological Insulators
• A beginner's guide to the modern theory of polarization
• Nearsightedness of Electronic Matter
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Single particle Green's functions and interacting topological insulators
• Edge states and the bulk-boundary correspondence in Dirac Hamiltonians
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Boundary Green functions of topological insulators and superconductors
• Quantum computation on the edge of a symmetry-protected topological order
• Edge modes in band topological insulators
• Unified bulk-boundary correspondence for band insulators
• Low-energy theory of transport in Majorana wire junctions
• Bulk-edge correspondence for Chern topological phases: A viewpoint from a generalized index theorem
• Quantum computation via Floquet topological edge modes
• Thermal transport in one-dimensional spin heterostructures
• Excess charges as a probe of one-dimensional topological crystalline insulating phases
• Fractional boundary charges in quantum dot arrays with density modulation
• Josephson effect in multiterminal topological junctions
• The interacting Rice-Mele model: bulk and boundaries
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators
• From fractional boundary charges to quantized Hall conductance
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Josephson effect in junctions of conventional and topological superconductors
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Analytical results for Green's functions of lattice fermions
• Universality of Boundary Charge Fluctuations
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Quantitative analysis of interaction effects in generalized Aubry-Andŕe-Harper models

Cited by in corpus (3)

• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators