Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems

Karmela Padavić, Suraj S. Hegde, Wade Degottardi, Smitha Vishveshwara

Research output: Contribution to journalArticle

Abstract

Motivated by recent experimental realizations of topological edge states in Su-Schrieffer-Heeger (SSH) chains, we theoretically study a ladder system whose legs are comprised of two such chains. We show that the ladder hosts a rich phase diagram and related edge-mode structure dictated by choice of interchain and intrachain couplings. Namely, we exhibit three distinct physical regimes: a topological hosting localized zero-energy edge modes, a topologically trivial phase having no edge-mode structure, and a regime reminiscent of a weak topological insulator having unprotected edge modes resembling a twin-SSH construction. In the topological phase, the SSH ladder system acts as an analog of the Kitaev chain, which is known to support localized Majorana fermion end modes, with the difference that bound states of the SSH ladder having the same spatial wave-function profiles correspond to Dirac fermion modes. Further, inhomogeneity in the couplings can have a drastic effect on the topological phase diagram of the ladder system. In particular for quasiperiodic variations of the interchain coupling, the phase diagram reproduces Hofstadter's butterfly pattern. We thus identify the SSH ladder system as a potential candidate for experimental observation of such fractal structure.

Original languageEnglish (US)
Article number024205
JournalPhysical Review B
Volume98
Issue number2
DOIs
StatePublished - Jul 27 2018

Fingerprint

Ladders
ladders
Phase diagrams
Fermions
phase diagrams
fermions
Wave functions
Fractals
fractals
inhomogeneity
insulators
wave functions
analogs
profiles

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems. / Padavić, Karmela; Hegde, Suraj S.; Degottardi, Wade; Vishveshwara, Smitha.

In: Physical Review B, Vol. 98, No. 2, 024205, 27.07.2018.

Research output: Contribution to journalArticle

@article{f1f907c7c2ab4a81a8a5b3e56fb76b67,
title = "Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems",
abstract = "Motivated by recent experimental realizations of topological edge states in Su-Schrieffer-Heeger (SSH) chains, we theoretically study a ladder system whose legs are comprised of two such chains. We show that the ladder hosts a rich phase diagram and related edge-mode structure dictated by choice of interchain and intrachain couplings. Namely, we exhibit three distinct physical regimes: a topological hosting localized zero-energy edge modes, a topologically trivial phase having no edge-mode structure, and a regime reminiscent of a weak topological insulator having unprotected edge modes resembling a twin-SSH construction. In the topological phase, the SSH ladder system acts as an analog of the Kitaev chain, which is known to support localized Majorana fermion end modes, with the difference that bound states of the SSH ladder having the same spatial wave-function profiles correspond to Dirac fermion modes. Further, inhomogeneity in the couplings can have a drastic effect on the topological phase diagram of the ladder system. In particular for quasiperiodic variations of the interchain coupling, the phase diagram reproduces Hofstadter's butterfly pattern. We thus identify the SSH ladder system as a potential candidate for experimental observation of such fractal structure.",
author = "Karmela Padavić and Hegde, {Suraj S.} and Wade Degottardi and Smitha Vishveshwara",
year = "2018",
month = "7",
day = "27",
doi = "10.1103/PhysRevB.98.024205",
language = "English (US)",
volume = "98",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "2",

}

TY - JOUR

T1 - Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems

AU - Padavić, Karmela

AU - Hegde, Suraj S.

AU - Degottardi, Wade

AU - Vishveshwara, Smitha

PY - 2018/7/27

Y1 - 2018/7/27

N2 - Motivated by recent experimental realizations of topological edge states in Su-Schrieffer-Heeger (SSH) chains, we theoretically study a ladder system whose legs are comprised of two such chains. We show that the ladder hosts a rich phase diagram and related edge-mode structure dictated by choice of interchain and intrachain couplings. Namely, we exhibit three distinct physical regimes: a topological hosting localized zero-energy edge modes, a topologically trivial phase having no edge-mode structure, and a regime reminiscent of a weak topological insulator having unprotected edge modes resembling a twin-SSH construction. In the topological phase, the SSH ladder system acts as an analog of the Kitaev chain, which is known to support localized Majorana fermion end modes, with the difference that bound states of the SSH ladder having the same spatial wave-function profiles correspond to Dirac fermion modes. Further, inhomogeneity in the couplings can have a drastic effect on the topological phase diagram of the ladder system. In particular for quasiperiodic variations of the interchain coupling, the phase diagram reproduces Hofstadter's butterfly pattern. We thus identify the SSH ladder system as a potential candidate for experimental observation of such fractal structure.

AB - Motivated by recent experimental realizations of topological edge states in Su-Schrieffer-Heeger (SSH) chains, we theoretically study a ladder system whose legs are comprised of two such chains. We show that the ladder hosts a rich phase diagram and related edge-mode structure dictated by choice of interchain and intrachain couplings. Namely, we exhibit three distinct physical regimes: a topological hosting localized zero-energy edge modes, a topologically trivial phase having no edge-mode structure, and a regime reminiscent of a weak topological insulator having unprotected edge modes resembling a twin-SSH construction. In the topological phase, the SSH ladder system acts as an analog of the Kitaev chain, which is known to support localized Majorana fermion end modes, with the difference that bound states of the SSH ladder having the same spatial wave-function profiles correspond to Dirac fermion modes. Further, inhomogeneity in the couplings can have a drastic effect on the topological phase diagram of the ladder system. In particular for quasiperiodic variations of the interchain coupling, the phase diagram reproduces Hofstadter's butterfly pattern. We thus identify the SSH ladder system as a potential candidate for experimental observation of such fractal structure.

UR - http://www.scopus.com/inward/record.url?scp=85051421292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051421292&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.98.024205

DO - 10.1103/PhysRevB.98.024205

M3 - Article

AN - SCOPUS:85051421292

VL - 98

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 2

M1 - 024205

ER -