Higher-order topological insulators on porous network models

Han, Ying; He, Ai‐Lei

doi:10.1103/physrevb.104.165416

Cited by 5 publications

(4 citation statements)

References 53 publications

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“…This model belongs to one of islamic pattern which we name the islamic lattice [54]. Islamic lattice consists of 12 deformations, triangles and square and hosts 'holes' which can open the bulk gap easily similar to porus graphene model ( graphene with nanoholes) [47]. Our discussion is based on the tight-binding model of fermions hopping along the nearest-neighbor (NN) and the NNN bonds, and the staggered magnetic fluxes are introduced along the intracellular NN hoppings with a phase factor ϕ.…”

Section: Model and Formulationmentioning

confidence: 99%

“…The hallmarks of CIs are the presence of nonzero Chern numbers and gapless edge states which have one dimension lower than the insulating bulk states, implying the bulk-edge correspondence. Different from CIs, higher-order topological insulators (HOTIs) meet anomalous bulk-boundary correspondence, namely, HOTIs hosting (d-f )-dimensional boundary states where d labels the dimension of bulk states and f is the order of the HOTIs [36][37][38][39][40][41][42][43][44][45][46][47]. For instance, zerodimensional corner states appear in two-dimensional (2D) HOTIs.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, zerodimensional corner states appear in two-dimensional (2D) HOTIs. In previous works, 2D HOTIs have been proposed in models with lattice dimerization [36,37], topological insulators with in-plane magnetic field [44], porous systems [47], etc. Besides the models mentioned above, staggered magnetic fluxes can also give rise to HOTIs [48].…”

Section: Introductionmentioning

confidence: 99%

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Topological phase transitions and flat bands on an islamic lattice

Yan,

Qi,

Zhang

et al. 2023

J. Phys.: Condens. Matter

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We construct an islamic lattice by considering the nearest-neighbor hoppings with staggered magnetic fluxes and the next-nearest-neighbor hoppings. This model supports abundant quantum phases for various values of filling fractions. At $1/4$ filling, there exist Chern insulator (CI) phases with Chern numbers $C=\pm 1,~-2$ and a zero-Chern-number topological insulator (ZCNTI) phase. At $3/8$ filling, several CI phases with Chern numbers $C= \pm1,~3$ and the ZCNTI phase are obtained. For the filling fraction 3/4, CI phases with Chern numbers $C=\pm 1,~2$ and two ZCNTI phase areas appear. Interestingly, these ZCNTI phases host both robust corner states and gapless edge states which can be characterized by the quantized polarization and quadrupole moment. We further find that staggered magnetic fluxes can give rise to the ZCNTI state at $1/4$ and $3/4$ fillings. Phase diagrams for filling fractions $1/8$, $1/2$, $5/8$ and $7/8$ are presented as well. In addition, flat bands are obtained for various filling fractions by tuning the hopping parameters. At 1/8 filling, a best topological flat band (TFB) with flatness ratio about 12 appears. Several trivial flat bands but with total Chern number $|C|=1$ emerge in this model and exactly flat band is found at 3/8 filling. We further investigate $\nu=1/2$ fractional Chern insulate state when hard-core bosons fill into this TFB model.

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Section: Model and Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topological phase transitions and flat bands on an islamic lattice

Yan,

Qi,

Zhang

et al. 2023

J. Phys.: Condens. Matter

Self Cite

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“…Compared with normal insulators, topological insulators (TIs) have the characteristics of being insulated internally and conducting on the surface. As an extension of TIs, high-order topological insulators (HOTIs) have attracted extensive attention of many researchers since they were revealed [1][2][3][4][5], which host topologically protected corner states and have strong stability and robustness [6]. More recently, many models have been intensively explored in photonics [7][8][9][10][11][12][13], acoustics [14][15][16][17][18][19][20], and electric circuits [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Zero-admittance states in honeycomb topological circuits

Huang,

Guo,

Qiu

et al. 2023

Phys. Scr.

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Topological circuits play an important role in exploring high-order topological insulators. In this work, we demonstrate that defects in the bulk without changing the parameters can increase zero-admittance states. Furthermore, the coupling parameters affect the distribution of the zero-admittance states are demonstrated. The impedance is measured to verify the existence of these states. The experimental results agree well with the theoretical results, both showing the strong resonance peak, as well as the impedance distribution of different parameters is mainly concentrated at the 2π/3 corner, 2π/6 corner, or edge. Our work paves the way for the research and experimentation of honeycomb topological circuits.

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