Quasicrystalline Chern insulators

He, Ai‐Lei; Ding, Lu-Rong; Zhou, Yuan; Wang, Yifei; Gong, Chang‐De

doi:10.1103/physrevb.100.214109

Cited by 38 publications

(43 citation statements)

References 54 publications

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“…Such bulk-edge correspondence is universal in all CIs established on various crystal lattice models, such as the checkerboard-lattice model [8,9], the kagome-lattice model [10,11], and other exotic lattice models [12][13][14][15][16][17][18]. Even in aperiodic systems, for example the quasicrystalline CI on the Dürer's tiling proposed recently [19], bulk-edge correspondence remains applicable.…”

mentioning

confidence: 69%

Anomalous bulk-boundary correspondence in dimerized topological insulators

He¹,

Luo²,

Zhou³

et al. 2021

Preprint

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The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional firstorder and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At 1 2 -filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the C = 2 Chern insulator states. At 1 4 -filling, we find a C = 0 topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

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mentioning

confidence: 69%

Anomalous bulk-boundary correspondence in dimerized topological insulators

He¹,

Luo²,

Zhou³

et al. 2021

Preprint

Self Cite

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“…Before evaluating the transmission function (19) from the Hamiltonian (14), two steps are essential: First, solving the self energies [Eq. (17)]; Second, inclusion of them into the conductor's Green's function as Eq.…”

Section: Standard Bath Chebyshev Polynomial Methodsmentioning

confidence: 99%

“…Afterwards, they are inserted into Eqs. (16), (20) and finally (19) for the evaluation of the transmission. In this process, the most time-consuming step will be the calculation of lead self energies, and the matrix inversion (which does not preserve the sparseness of the matrix) in Eq.…”

Section: Electronic Transmission In Terms Of Green's Functionsmentioning

confidence: 99%

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Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

Zhang

Liu

et al. 2020

AIP Advances

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Landauer-Büttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, Chebyshev polynomial method has attracted intense interests in numerical simulations of quantum systems due to the high efficiency in parallelization, because the only matrix operation it involves is just the product of sparse matrices and vectors. Many progresses have been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer-Büttiker formula for the conductance of quantum transports in nanostructures. We first describe the full algorithm based on the standard bath KPM. Then, we present two simple but efficient improvements. One of them has a time consumption remarkably less than the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.

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“…Recent work has reexamined what classes of systems can host topological phenomena, and the catalog has expanded to include amorphous materials (17,18) and light elements (19). Additionally, several theoretical works have examined the influence of aperiodicity and quasicrystallinity on topological phases (20) including pentagonal (21) and octagonal ( 22) quasicrystals and so-called "higher-order topological insulators" (23). Further, topological polarization not possible in periodic crystals has been theoretically proposed to exist in quasicrystals.…”

mentioning

confidence: 99%

Layer-dependent topological phase in a two-dimensional quasicrystal and approximant

Cain

Azizi

Conrad

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing “forbidden” symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta1.6Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta21Te13, reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.

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Quasicrystalline Chern insulators

Cited by 38 publications

References 54 publications

Anomalous bulk-boundary correspondence in dimerized topological insulators

Anomalous bulk-boundary correspondence in dimerized topological insulators

Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

Layer-dependent topological phase in a two-dimensional quasicrystal and approximant

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