Theory of spin Bott index for quantum spin Hall states in nonperiodic systems

Huang, Huaqing; Liu, Feng

doi:10.1103/physrevb.98.125130

Cited by 100 publications

(99 citation statements)

References 73 publications

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“…These results are in qualitative agreement with other works that study schematic models for amorphous topological insulators. 13,[15][16][17]19 Additionally, to probe the edge conductivity, we calculate the two-terminal electronic transport properties in a nanoribbon geometry, using the Landauer approach. In Fig.…”

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confidence: 99%

Toward Realistic Amorphous Topological Insulators

et al. 2019

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The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models on random lattices have demonstrated that amorphous model systems show a non-trivial topology. Using ab initio calculations we show that two-dimensional amorphous materials can also display topological insulator properties. More specifically, we present a realistic state-of-the-art study of the electronic and transport properties of amorphous bismuthene systems, showing that these materials are topological insulators. These systems are characterized by the topological index Z 2 = 1 and bulk-edge duality, and their linear conductance is quantized, G = 2e 2 /h, for Fermi energies within the topological gap. Our study opens the path to the experimental and theoretical investigation of amorphous topological insulator materials.

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confidence: 99%

Toward Realistic Amorphous Topological Insulators

et al. 2019

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“…Thus, we can deduce that the lattice under amorphous deformation (Rd = L/2-ri) still maintains its topological properties. The PDOS approach is a valid method to detect band gaps of non-periodic structures, such as quasicrystals (31,32,34) and amorphous structures (10,33,35), where thousands of eigen states of a superlattice usually need to be calculated to detect band gaps with enough accuracy. Thus, PDOS can be regarded as a statistic parameter to evaluate the average behavior of the cluster of dielectric rods.…”

Section: Resultsmentioning

confidence: 99%

Topological valley transport under long-range deformations

Kong

Davis

et al. 2020

Phys. Rev. Research

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Edge states protected by bulk topology of photonic crystals offer exciting means to study spintronics, and their robustness to short-range disorder makes robust information transfer possible. Here, we investigate topological transport under long-range amorphous deformation without external magnetic field. Vertices of each regular hexagon in a C3-symmetric crystalline structure are shifted randomly. Despite the existence of unpredictable scattering, topological edge modes are determined by statistic behavior of the whole structure. Photonic density of states as well as the Fourier transform can be used to distinguish the topological properties. We further designed and fabricated samples working in the microwave band. The measured transmission spectrum reveals the existence of robust topological states in the amorphous system. This work proves the robustness of bulk topology, points to the study of topological properties of structures undergoing amorphous deformation, and may open the way for exploiting topological insulators in materials with different phases.

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“…1(b). In the previous works by Huang and Liu [28][29][30] , based on the Penrosetype quasicrystal lattice model described by the Hamiltonian (1), they proposed that the quantum spin Hall effect can be realized in quasicrystal lattices.…”

Section: Model and Methodsmentioning

confidence: 99%

“…However, the quasicrystal tiling approximants provides a systematic approach to construct a periodic lattice which can gradually approximate the aperiodic quasicrystal with increasing the vertex number of the super unit cell 10,11,72,73 . It is noted that the spin Bott index has been proposed to identify the quantum spin Hall state in both crystalline and nonperiodic systems 28,29 . Thus, in the Penrose-type quasicrystal lattice, we will adopt the spin Bott index to identify the topological phase.…”

Section: Model and Methodsmentioning

confidence: 99%

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Topological Anderson insulator phase in a quasicrystal lattice

Chen

Zhou

2019

Phys. Rev. B

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Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index. *

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Theory of spin Bott index for quantum spin Hall states in nonperiodic systems

Cited by 100 publications

References 73 publications

Toward Realistic Amorphous Topological Insulators

Toward Realistic Amorphous Topological Insulators

Topological valley transport under long-range deformations

Topological Anderson insulator phase in a quasicrystal lattice

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