Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

Abstract

We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_{\phi }\in [0,L]$ is given by a perfectly linear function of $x_{\phi }$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant. For systems with weak potential amplitudes, we additionally develop Green's function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation.

arXiv comment26 pages, 8 figures

References in corpus (49)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Maximally-localized generalized Wannier functions for composite energy bands
• Maximally localized Wannier functions: Theory and applications
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantum Spin Hall Effect
• Synthetic magnetic fields for ultracold neutral atoms
• Spintronics and Pseudospintronics in Graphene and Topological Insulators
• Nearsightedness of Electronic Matter
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Non-Abelian gauge potentials in graphene bilayers
• Composite Majorana Fermion Wavefunctions in Nanowires
• Strong Spin-Orbit Interaction and Helical Hole States in Ge/Si Nanowires
• Strong tuning of Rashba spin orbit interaction in single InAs nanowires
• Transition from fractional to Majorana fermions in Rashba nanowires
• Spin-orbit interaction in InSb nanowires
• Boundary Green functions of topological insulators and superconductors
• Quantum computation on the edge of a symmetry-protected topological order
• Non-Abelian Gauge Fields in Photonic Cavities and Photonic Superfluids
• Low-energy theory of transport in Majorana wire junctions
• Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers
• Majorana Fermions in Ge/Si Hole Nanowires
• Quantum computation via Floquet topological edge modes
• Non-Abelian magnetic monopole in a Bose-Einstein condensate
• Double and negative reflection of cold atoms in non-Abelian gauge potentials
• Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Vectorial control of the spin-orbit interaction in suspended InAs nanowires
• Thermal transport in one-dimensional spin heterostructures
• Fractional boundary charges in quantum dot arrays with density modulation
• Josephson effect in multiterminal topological junctions
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Trapped fermions in a synthetic non-Abelian gauge field
• From fractional boundary charges to quantized Hall conductance
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• 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
• Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators