Hourglass fermion surface states in stacked topological insulators with nonsymmorphic symmetry

Ezawa, Motohiko

doi:10.1103/physrevb.94.155148

Cited by 52 publications

(73 citation statements)

References 35 publications

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“…This stacking approach provides a unifying description of all previously known topological crystalline insulators 27 , both with 37,38 and without 39,40 interactions. The one-dimensional SPT state serving as the building block of our higher dimensional TCMs apparently looks similar to, but, in fact, is remarkably different from the Affleck, Kennedy, Lieb, and Tasaki (AKLT) state 41,42 .…”

Section: Introductionmentioning

confidence: 98%

Topological crystalline magnets: Symmetry-protected topological phases of fermions

Watanabe

2017

Phys. Rev. B

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We introduce a novel class of interaction-enabled topological crystalline insulators in two-and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal symmetry T and a mirror symmetry or a rotation symmetry R. A topological crystalline magnet exhibits two intriguing features: (i) it cannot be adiabatically connected to any Slater insulator and (ii) the edge state is robust against coupling electrons to the edge. These features are protected by the anomalous symmetry transformation property (RT ) 2 = −1 of the edge state. An anisotropic response to the external magnetic field can be an experimental signature.

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Section: Introductionmentioning

confidence: 98%

Topological crystalline magnets: Symmetry-protected topological phases of fermions

Watanabe

2017

Phys. Rev. B

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“…Previously GSPT phases have been mostly studied in the context of weakly-interacting electrons [21][22][23][24][25][26][27]. In particular the gapless surface states of a 3D glide-protected non-symmorphic TI, coined 'hourglass fermions' [25], has been observed in KHgSb using angle-resolved photoemission spectroscopy [28].…”

Section: Introductionmentioning

confidence: 99%

Classification and surface anomaly of glide symmetry protected topological phases in three dimensions

Shi

2017

New J. Phys.

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We study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions with certain on-site symmetries. They are crystalline SPT phases, which are distinguished from a trivial product state only in the presence of non-symmorphic glide symmetry. We classify these GSPT phases with various on-site symmetries such as U(1) and time reversal, and show that they can all be understood by stacking and coupling two-dimensional (2D) short-rangeentangled phases in a glide-invariant way. Using such a coupled layer construction we study the anomalous surface topological orders of these GSPT phases, which gap out the 2D surface states without breaking any symmetries. While this framework can be applied to any non-symmorphic SPT phase, we demonstrate it in many examples of GSPT phases including the non-symmorphic topological insulator with 'hourglass fermion' surface states.

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“…As a generalization, the spin-1 excitation takes 3 × 3 spin matrices and holds a three-fold degeneracy (see 1(b)), its crossing point carries a topological charge ±2 because of no contribution from the middle band with the helicity 0 [32,33]. Spin-3/2 excitations are named as Rarita-Schwinger-Weyl (RSW) fermions [32,[34][35][36], and S takes 4×4 spin matrices. Its Fermi surface has to cross two bands near the crossing point, for example, the helicity 3/2 band with the Berry phase ±3 and the helicity 1/2 band with the Berry phase ±1 (see Fig.…”

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confidence: 99%

Multiple Types of Topological Fermions in Transition Metal Silicides

Tang¹,

Zhou²,

Zhang³

2017

Phys. Rev. Lett.

418

432

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Exotic massless fermionic excitations with non-zero Berry flux, other than Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with 3-fold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe and CoGe, when the spin-orbit coupling (SOC) is considered. Their non-trivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on side surface, which is confirmed by (010) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.Introduction.-Three types of fermions play fundamental roles in our understanding of nature: Majorana, Dirac and Weyl [1]. Much attention has been paid to looking for these fundamental particles in high energy physics during past few decades, whereas only signature of Dirac fermions is captured. Interestingly, the same movement comes up in the field of condensed matter physics [2], and great achievements have been made in last few years. For example, the Majorana-like excitations are detected in superconducting heterostructures [3][4][5][6]; the Dirac [7][8][9][10][11][12] and Weyl [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] fermions are observed in some compounds. These quasiparticles in solid states are not only important for basic science, but also show great potential for practical applications on new devices [30,31].Because symmetries in condensed matter physics are usually much lower than the Poincaré symmetry in high energy physics, quasiparticles in solid states are less constrained such that various new types of fermionic excitations are predicted to exist in 3D lattices [32]. Among these allowed by space group (SG) symmetries are spin-1 and spin-3/2 massless fermionic excitations, besides the well-known spin-1/2 case, namely the Weyl fermion. All of these massless quasiparticles can be described by the low energy Hamiltonian in a unified manner to the linear order of momentum

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Hourglass fermion surface states in stacked topological insulators with nonsymmorphic symmetry

Cited by 52 publications

References 35 publications

Topological crystalline magnets: Symmetry-protected topological phases of fermions

Topological crystalline magnets: Symmetry-protected topological phases of fermions

Classification and surface anomaly of glide symmetry protected topological phases in three dimensions

Multiple Types of Topological Fermions in Transition Metal Silicides

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