Abstract
We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order topological phase but later shown to be trivial for perturbations that were thought to protect them. Using various theoretical and simulation techniques, we confirm that it does not display higher-order topology the corner modes are of trivial nature. Nevertheless, they might be protected. First, we show a set of perturbations within a tight-binding model that can move the corner modes away from zero energy, also repeat some perturbations that were used to show that the modes are trivial. In addition, we analyze the protection of the corner modes in more detail and find that only perturbations respecting the sublattice or generalized chiral and crystalline symmetries, and the lattice connectivity, pin the corner modes to zero energy robustly. A destructive interference model corroborates the results. Finally, we analyze a muffin-tin model for the bulk breathing kagome lattice. Using topological and symmetry markers, such as Wilson loops and Topological Quantum Chemistry, we identify the two breathing phases as adiabatically disconnected different obstructed atomic limits.
| Original language | English |
|---|---|
| Article number | 085411 |
| Journal | Physical Review B |
| Volume | 105 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 11 Feb 2022 |
Bibliographical note
Funding Information:We acknowledge useful discussions with Wouter Beugeling, Barry Bradlyn, Maia Garcia Vergniory, FloreKunst, Mikel Iraola, Titus Neupert, Jette van den Broeke and Robin Verstraten. The work of M.A.J.H. and D.B. is supported by the Ministerio de Ciencia e Innovación (MICINN) through Project No. PID2020-120614GB-I00, and by the Transnational Common Laboratory Quantum-ChemPhys (D.B.). A.G.E. and M.B.P. acknowledge support from the Spanish Ministerio de Ciencia e Innovación (Project No. PID2019-109905GA-C2) and from Eusko Jaurlaritza (Grants No. IT1164-19 and No. KK-2021/00082). A.G.-E. and D.B. acknowledge Programa Red Guipuzcoana de Ciencia, Tecnología e Innovación 2021, Grant No. 2021-CIEN-000070-01, Gipuzkoa Next. A.G.-E., M.B.P., and D.B. acknowledge funding from the Basque Government's IKUR initiative on Quantum technologies (Department of Education). I.S. gratefully acknowledges financial support from the European Research Council (Horizon 2020 “FRACTAL,” Grant No. 865570).
Publisher Copyright:
© 2022 American Physical Society.
Funding
We acknowledge useful discussions with Wouter Beugeling, Barry Bradlyn, Maia Garcia Vergniory, FloreKunst, Mikel Iraola, Titus Neupert, Jette van den Broeke and Robin Verstraten. The work of M.A.J.H. and D.B. is supported by the Ministerio de Ciencia e Innovación (MICINN) through Project No. PID2020-120614GB-I00, and by the Transnational Common Laboratory Quantum-ChemPhys (D.B.). A.G.E. and M.B.P. acknowledge support from the Spanish Ministerio de Ciencia e Innovación (Project No. PID2019-109905GA-C2) and from Eusko Jaurlaritza (Grants No. IT1164-19 and No. KK-2021/00082). A.G.-E. and D.B. acknowledge Programa Red Guipuzcoana de Ciencia, Tecnología e Innovación 2021, Grant No. 2021-CIEN-000070-01, Gipuzkoa Next. A.G.-E., M.B.P., and D.B. acknowledge funding from the Basque Government's IKUR initiative on Quantum technologies (Department of Education). I.S. gratefully acknowledges financial support from the European Research Council (Horizon 2020 “FRACTAL,” Grant No. 865570).