Quantized surface magnetism and higher-order topology: Application to the Hopf insulator

Zhu, Penghao; Hughes, Taylor L.; Alexandradinata, A.

doi:10.1103/physrevb.103.014417

Cited by 20 publications

(16 citation statements)

References 53 publications

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“…For N = 2, the correspondence ( 20) is a generalization of recently discussed bulk-boundary correspondence for the Hopf insulator. 28,48 The above procedure divides a finite sample of the Nband Hopf insulator into bulk and surface subsystems. It is important to note that such division is not unique.…”

Section: Bulk-boundary Correspondencementioning

confidence: 99%

N -band Hopf insulator

Lapierre

Neupert

Trifunovic

2021

Phys. Rev. Research

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We study the generalization of the three-dimensional two-band Hopf insulator to the case of many bands, where all the bands are separated from each other by band gaps. The obtained Z classification of such a N -band Hopf insulator and the formulation of its bulk-boundary correspondence are our main results. We find that the quantized boundary effect can only be measured in a non-equilibrium state.

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Section: Bulk-boundary Correspondencementioning

confidence: 99%

N -band Hopf insulator

Lapierre

Neupert

Trifunovic

2021

Phys. Rev. Research

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“…We dub C( n) the surface Chern number, and it is equal to the Hopf invariant χ for any orientation of n. Unlike conventional topological insulators, the Hopf bulk-boundary correspondence indicates that the sum over all boundary-localized bands has non-trivial first Chern number, instead of just the occupied boundary-localized bands. Furthermore, we recently showed that the correspondence between the surface Chern number and the Hopf invariant also implies the existence of chiral hinge states if a spectral gap exists for excitations of surface states [4]. Thus, the topology diagnosed by the Hopf invariant potentially has a higher order character [5,6].…”

Section: Introductionmentioning

confidence: 99%

$\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump

Zhu¹,

Hughes²

2022

Preprint

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We introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator. The spin Hopf insulator harbors nontrivial Kane-Mele Z2 invariants on its surfaces, and is the first example of a nonmagnetic delicate topological insulator with spin-orbit coupling. We show that the Kane-Mele Z2 topology on the surface is generically unstable, but can be stabilized by the addition of a composition of the particle hole and spatial inversion symmetry. Such a symmetry not only protects the surface Z2 invariant, but also protects gapless helical hinge states on the spin Hopf insulator. Furthermore, we show that in the presence of four-fold rotational symmetry, the spin Hopf insulator exhibits a returning Thouless pump, as well as surface states on sharp boundary terminations.

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“…HOTIs are topological crystalline insulators that have protected topological features on the boundaries with co-dimension greater than one. In contrast to (1st order) three-dimensional time-reversal protected topological insulators that show an insulating bulk with conducting surface modes, three-dimensional 2nd order HOTIs show insulating bulk and surfaces, but with one-dimensional conducting channels at hinges (i.e., the intersection of two surface facets) or equivalent crystal defects [1][2][3][4][5][6] . While several groups have recently succeeded in observing HOTI phases in electronic circuit, phononic, and photonic systems [7][8][9][10] , the experimental realization and characterization of HOTIs in solid state materials has proven more challenging.…”

Section: Introductionmentioning

confidence: 99%

Evidence for Higher order topology in Bi and Bi$_{0.92}$Sb$_{0.08}$

Aggarwal,

Zhu,

Hughes

et al. 2021

Preprint

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Higher order topological insulators (HOTIs) are a new class of topological materials which host protected states at the corners or hinges of a crystal. HOTIs provide an intriguing alternative platform for helical and chiral edge states and Majorana modes, but there are very few known materials in this class. Recent studies have proposed Bi as a potential HOTI, however, its topological classification is not yet well accepted. In this work, we show that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems. Bi and Bi0.92Sb0.08 (110) films were grown on silicon substrates using molecular beam epitaxy and studied by scanning tunneling spectroscopy. The surfaces manifest rectangular islands which show localized hinge states on three out of the four edges, consistent with the theory for the HOTI phase. This establishes Bi and Bi0.92Sb0.08 as HOTIs, and raises questions about the topological classification of the full family of BixSb1−x alloys.

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Quantized surface magnetism and higher-order topology: Application to the Hopf insulator

Cited by 20 publications

References 53 publications

N -band Hopf insulator

N -band Hopf insulator

$\mathbb{Z}_{2}$ Spin Hopf Insulator: Helical Hinge States and Returning Thouless Pump

Evidence for Higher order topology in Bi and Bi$_{0.92}$Sb$_{0.08}$

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