Many-Body Invariants for Chern and Chiral Hinge Insulators

Kang, Bongsoon; Lee, Wonjun; Cho, Gil Young

doi:10.1103/physrevlett.126.016402

Cited by 21 publications

(8 citation statements)

References 34 publications

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“…The C 4 T symmetric SOTIs with chiral hinge modes can be characterized by the Chern-Simons invariant [38]. Later, it was found that these chiral hinge modes can be also characterized by the winding number of the quadrupole moment [136,137]. For the SOTIs with TRS, the helical hinge states can be characterized by the mirror Chern number in the presence of mirror symmetries [38].…”

Section: Introductionmentioning

confidence: 99%

Higher-order topological phases in crystalline and non-crystalline systems: a review

Yang,

Wang,

et al. 2024

J. Phys.: Condens. Matter

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In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

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Section: Introductionmentioning

confidence: 99%

Higher-order topological phases in crystalline and non-crystalline systems: a review

Yang,

Wang,

et al. 2024

J. Phys.: Condens. Matter

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“…Secondly, topological indices in non-interacting electronic systems are usually defined in terms of Bloch wave functions, which can only capture information in the single-particle Hamiltonian and cannot describe correlation effects. Therefore, in the presence of interaction it is desirable to find an alternative approach that can take into account the many-body physics and characterize the topological properties of the interacting system [49][50][51][52][53][54] .…”

Section: Introductionmentioning

confidence: 99%

Green's Function Approach to Interacting Higher-order Topological Insulators

Li¹,

Kim²

2022

Preprint

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The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in noninteracting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-order topological insulators protected by 𝐶 4 𝑇 symmetry and show that the topological index can be computed through eigenstates of inverse Green's function at zero frequency. If there is an additional 𝑆 4 rotoinversion symmetry, the topological index 𝑃 3 can be determined by eigenvalues of 𝑆 4 at high symmetry momenta, similar to the Fu-Kane parity criterion. We also discuss the robustness of the hinge states under deformation of boundary and show that these hinge states exist even when boundary is smooth and without a sharp hinge. Finally, we discuss the realization of this higher-order topological phase, which includes the higherorder topological insulators in tetragonal lattice structure with 𝐶 4 𝑇-preserving magnetic order, and higher-order topological superconductors with 𝑝 + 𝑖𝑑-wave pairing.

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“…With the recent discovery of higher-order topological insulators (HOTIs) [7,8], efforts were made to generalize these concepts to describe electrical multi-pole moments [7][8][9][10][11][12][13][14] and higher-order Thouless pumps [8,9,[14][15][16]. A n-dimensional bulk with topology of order m can exhibit (n − m)-dimensional corner or hinge states, when open boundary conditions (OBC) are applied.…”

mentioning

confidence: 99%

“…Higher-order topological invariants have been proposed for both band insulators in a single-particle picture (HOTIs) and interacting quantum many-body systems (HOSPTs) protected by crystalline symmetries [8,9,13,14,16,[26][27][28][29][30][31][32]]. Yet, there is an ongoing debate on which of the proposed quantities constitute true bulk invariants and how exactly the multipole polarization can be calculated in extended systems with periodic boundary conditions [11,13].…”

mentioning

confidence: 99%

Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases

Wienand,

Horn,

Aidelsburger

et al. 2021

Preprint

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The bulk-boundary correspondence relates quantized edge states to bulk topological invariants in topological phases of matter. In one-dimensional symmetry-protected topological systems (SPTs), quantized topological Thouless pumps directly reveal this principle and provide a sound mathematical foundation. Symmetry-protected higher-order topological phases of matter (HOSPTs) also feature a bulk-boundary correspondence, but its connection to quantized charge transport remains elusive. Here we show that quantized Thouless pumps connecting C4-symmetric HOSPTs can be described by a tuple of four Chern numbers that measure quantized bulk charge transport in a direction-dependent fashion. Moreover, this tuple of Chern numbers allows to predict the sign and value of fractional corner charges in the HOSPTs. We show that the topologically non-trivial phase can be characterized by both quadrupole and dipole configurations, shedding new light on current debates about the multi-pole nature of the HOSPT bulk. By employing corner-periodic boundary conditions, we generalize Restas's theory to HOSPTs. Our approach provides a simple framework for understanding topological invariants of general HOSPTs and paves the way for an in-depth description of future dynamical experiments.

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Many-Body Invariants for Chern and Chiral Hinge Insulators

Cited by 21 publications

References 34 publications

Higher-order topological phases in crystalline and non-crystalline systems: a review

Higher-order topological phases in crystalline and non-crystalline systems: a review

Green's Function Approach to Interacting Higher-order Topological Insulators

Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases

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