Enhanced localization and protection of topological edge states due to geometric frustration

Madail, L.; Flannigan, Stuart; Marques, A. M.; Daley, Andrew J.; Dias, R. G.

doi:10.1103/physrevb.100.125123

Cited by 18 publications

(11 citation statements)

References 36 publications

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“…Similar behavior to that of the extended SSH chain should be present in other bipartite 1D [26,[29][30][31] and 2D [32][33][34][35] topological insulators if long-range hopping terms are introduced. A simple 2D example where the approach of this paper can be applied is that of a plane of parallel extended SSH chains with uniform or staggered hopping terms between them.…”

Section: Discussionsupporting

confidence: 55%

Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

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In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexation must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

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Section: Discussionsupporting

confidence: 55%

Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

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“…Note, here, we do not attempt to load into the BLT states, meaning we loose population into the other states that overlap with the initial state. For experimental scenarios, it would be prudent to instead use state preparation schemes or shortcuts to adiabaticity to load efficiently into the BLT states [88][89][90].…”

Section: Bulk Localised Transportmentioning

confidence: 99%

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

Johnstone,

Colbrook,

Nielsen

et al. 2021

Preprint

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Robust edge transport can occur when charged particles in crystalline lattices interact with an applied external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge states. When the confining lattice geometry is altered to be quasicrystaline, i.e. quasiperiodic, then Bloch's theorem breaks down. However, for the quasicrystalline system, we still expect to observe the basic characteristics of bulk states and current carrying edge states. Here, we show that for quasicrystals in magnetic fields, there is also a third option; the bulk localised transport states. These states share the in-gap nature of the well-known edge states and can support transport along them, but they are fully contained within the bulk of the system, with no support along the edge. This results in transport being possible both along the edge and within distinct regions of the bulk. We consider both finite-size and infinite-size systems, using rigorous error controlled computational techniques that are not prone to finite-size effects. The bulk localised transport states are preserved for infinite-size systems, in stark contrast to the normal edge states. This allows for transport to be observed in infinite-size systems, without any perturbations, defects, or boundaries being introduced. We confirm the ingap topological nature of the bulk localised transport states for finite and infinite-size systems by computing common topological measures; namely the Bott index and local Chern marker. The bulk localised transport states form due to a magnetic aperiodicity arising from the interplay of length scales between the magnetic field and quasiperiodic lattice. Bulk localised transport could have interesting applications similar to those of the edge states on the boundary, but that could now take advantage of the larger bulk of the lattice. The infinite size techniques introduced here, especially the calculation of topological measures, could also be widely applied to other crystalline, quasicrystalline, and disordered models.

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“…We illustrated in Ref. [19] by considering periodic boundary conditions in the y-direction, that these geometrically enhanced edge states exist at the ak y = π point in the Brillouin zone.…”

Section: Geometrically Protected Edge Statesmentioning

confidence: 99%

“…Also, in Ref. [19] we showed that for non-interacting particles, these edge states can be prepared by an adiabatic ramping protocol, where we simulated a time- dependent variation of the value of the tunnelling dimerisation J 1 /J 2 . In Fig.…”

Section: Geometrically Protected Edge Statesmentioning

confidence: 99%

“…We then consider interacting particles in these systems in two example cases of weak and strong interactions. We first probe the robustness of edge and corner states in a Lieb lattice with diagonal boundary conditions [19] when weak interactions are introduced, and then we investigate the many-body phases manifested in a half-filled 1D Lieb ladder for strong attractive interactions. These calculations provide a potential roadmap for experimental investigation of many-body phases for cold atoms in a Lieb lattice.…”

Section: Introductionmentioning

confidence: 99%

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Hubbard models and state preparation in an optical Lieb lattice

Flannigan,

Madail,

Dias

et al. 2021

Preprint

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Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier functions localised at individual sites for a realistic experimental setup, and determining coefficients for a Hubbard-like model. Based on this, we show how experiments could probe the robustness of edge states in a Lieb lattice with diagonal boundary conditions to the effects of interactions and realise strongly correlated many-body phases in this geometry. We then generalise this to interacting particles in a half-filled 1D Lieb ladder, where excitations are dominated by flat band states. We show that for strong attractive interactions, pair correlations are enhanced even when there is strong mixing with the Dirac cone. These findings in 1D raise interesting questions about the phases in the full 2D Lieb lattice which we show can be explored in current experiments.

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Enhanced localization and protection of topological edge states due to geometric frustration

Cited by 18 publications

References 36 publications

Long-range hopping and indexing assumption in one-dimensional topological insulators

Long-range hopping and indexing assumption in one-dimensional topological insulators

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

Hubbard models and state preparation in an optical Lieb lattice

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