Scattering description of edge states in Aharonov-Bohm triangle chains
arXiv:2311.05153 · doi:10.1103/PhysRevB.109.L081408
Abstract
Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a benchmark a one-dimensional triangle chain whose versatility yields a scattering matrix that ``flows" in parameter space among several members of the topology classification scheme. Our results show that the reflection amplitudes (from both ends of a sufficiently long chain) do indicate the appearance of edge states in {\it all} (topological and non-topological) cases. For the topological cases, the transmission has a peak at the topological phase transition, which happens at the Fermi energy. A peak still exists as one moves into the non-topological `trivial' regions, in which another transmission peak may occur at nonzero energy, at which a relevant edge state appears in the isolated chain. For finite chains, the peak in the transmission strongly depends on their coupling of the leads, and {\it not} on the phase transition of the isolated chain. In any case, {\it the appearance of a peak in the transmission is not sufficient to conclude that the system undergoes a topological phase transition.}
References in corpus (23)
- Topological Insulators
- Topological insulators and superconductors
- Classification of topological quantum matter with symmetries
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Colloquium: Topological Band Theory
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Lasing in topological edge states of a 1D lattice
- The Zak phase and the existence of edge states in graphene
- Experimental observation of Aharonov-Bohm cages in photonic lattices
- Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
- Scattering formula for the topological quantum number of a disordered multi-mode wire
- Scattering theory of topological insulators and superconductors
- Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
- Topological Phase Transition without Gap Closing
- Aharonov-Bohm Caging and Inverse Anderson transition in Ultracold Atoms
- Sub-symmetry protected topological states
- Winding numbers of phase transition points for one-dimensional topological systems
- Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
- Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
- Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
- Spectral analysis, chiral disorder and topological edge states manifestation in open non-Hermitian Su-Schrieffer-Heeger chains
- Cataloging topological phases of -stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries