Hyperbolic band topology with non-trivial second Chern numbers

Zhang, Weixuan; Di, Fengxiao; Zheng, Xingen; Sun, Houjun; Zhang, Xiangdong

doi:10.1038/s41467-023-36767-8

Cited by 47 publications

(32 citation statements)

References 54 publications

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“…Recently, based on the similarity between circuit Laplacian and lattice Hamiltonian, simulating topological states with electric circuits has attracted lots of interest [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Compared with other classical platforms, circuit networks possess remarkable advantages of being versatile and reconfigurable.…”

Section: Based On the Above Results We Can Further Obtain Thatmentioning

confidence: 99%

Three-dimensional non-Abelian Bloch oscillations and novel higher-order topological states

Pan

Chen²,

et al. 2023

Preprint

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Exploring novel topological phases of matter is one of the most fascinating research areas because they support some of the most fascinating properties for robust signal transports and wave propagations. Recently, higher-order topological insulators (HOTIs) have been introduced, and were shown to host topological corner states under the theoretical framework of Benalcazar-Bernevig-Hughes (BBH). Here we unveil some novel topological effects in HOTIs by studying the three-dimensional (3D) non-Abelian Bloch oscillations (BOs). In HOTIs, BOs with a multiplied period occur when a force with a special direction is applied due to the effect of the non-Abelian Berry curvature. Along the direction of the oscillations we find a novel higher-order topological state that goes beyond the theoretical framework of BBH. The emergence of such a higher-order topological state coincides with the appearance of the 3D non-Abelian BOs. That is, the 3D non-Abelian BOs can be used as a tool to probe novel higher-order topological states. The phenomena including the 3D non-Abelian BOs and the novel topological states are observed experimentally with designed electric circuit networks. Our work opens up a new way to detect novel topological phases theoretically and experimentally.

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Section: Based On the Above Results We Can Further Obtain Thatmentioning

confidence: 99%

Three-dimensional non-Abelian Bloch oscillations and novel higher-order topological states

Pan

Chen²,

et al. 2023

Preprint

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“…Hyperbolic lattices are an exotic class of lattices in non-Euclidean space with constant negative curvature, supporting tessellation of any regular p-site polygon with p > 2, which has been recently realized in circuit quantum electrodynamics and electric circuits [90][91][92][93][94]. In [67], it has been shown that HSTE can also emerge in hyperbolic Haldane models with sublattice-dependent gain and loss ±iγ.…”

Section: Hste In Hyperbolic Latticesmentioning

confidence: 99%

A brief review of hybrid skin-topological effect

Zhu,

2024

J. Phys.: Condens. Matter

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The finding of non-Hermitian skin effect has revolutionized our understanding of non-Hermitian topological phases, where the usual bulk-boundary correspondence is broken and new topological phases specific to non-Hermitian system are uncovered. Hybrid skin-topological effect (HSTE) is a class of newly discovered non-Hermitian topological states that simultaneously supports skin-localized topological edge states and extended bulk states. Here we provide a brief review of HSTE, starting from different mechanics that have been used to realize HSTE, including non-reciprocal couplings, onsite gain/loss, and non-Euclidean lattice geometries. We also review some theoretical developments closely related to the HSTE, including the concept of higher-order non-Hermitian skin effect, parity-time symmetry engineering, and non-Hermitian chiral skin effect. Finally, we summarize recent experimental exploration of HSTE, including its realization in electric circuits systems, non-Hermitian photonic crystals, and active matter systems. We hope this review can make the concept of hybrid-skin effect clearer and inspire new finding of non-Hermitian topological states in higher dimensional systems.

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“…At present, the topological properties of topological insulators have been implemented in electrical circuit [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Topological circuits are primarily composed of inductor-capacitor(LC) networks and can be fabricated on printed circuit board (PCB), which offer the advantages of flexible design, inexpensive electronic components, and well-established technology, and are used to experimentally verify the existence of topological states.…”

Section: Introductionmentioning

confidence: 99%

Topological end states in one-dimensional Su–Schrieffer–Heeger-like chain electric circuits

Huang,

Guo,

Qiu

et al. 2024

Phys. Scr.

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Topological circuits provide a convenient experimental platform for observing topological states. In this work, we construct a one-dimensional Su-Schrieffer-Heeger(SSH)-like chain in topological electric circuits and find two types of end states, but only the type-II end states are pinned at zero admittance. The topological properties can be characterized by the sum of Zak phases, which related to the ratio of inter-cell capacitors to intra-cell capacitors. Theoretical and experimental results, which agree well with each other, of these two end states are well demonstrated by impedance peaks. We examine the robustness of these two end states by adding extra capacitors. Our work enriches the study of topological circuits and provides an example for investigating the exotic topological physics.

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Hyperbolic band topology with non-trivial second Chern numbers

Cited by 47 publications

References 54 publications

Three-dimensional non-Abelian Bloch oscillations and novel higher-order topological states

Three-dimensional non-Abelian Bloch oscillations and novel higher-order topological states

A brief review of hybrid skin-topological effect

Topological end states in one-dimensional Su–Schrieffer–Heeger-like chain electric circuits

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