Topological Classification and Stability of Fermi Surfaces

Zhao, Y. X.; Wang, Z. D.

doi:10.1103/physrevlett.110.240404

Cited by 195 publications

(230 citation statements)

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“…In this sense, these are canonical examples of gapless points whose stability is not captured only by local symmetry (chiral symmetry), but originates from spatial symmetry. For two-fold rotation C 2 , we can also use the Ktheory and the Clifford algebra to classify gapless points: 3,6,[34][35][36][41][42][43] In this case, the symmetry operators C 2 and Γ can be considered as an element of a complex Clifford algebra Cl n = {e 1 , . .…”

Section: A Class Aiii+cn In 2dmentioning

confidence: 99%

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry

2014

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We explore a new class of topologically stable zero energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion and rotation, the Hamiltonian can be separated into independent chiralsymmetric subsystems by the eigenvalue of the space symmetry operator. Each subsystem supports chiral zero energy modes when a topological index assigned to the block is nonzero. By applying the argument to Bloch electron systems, we detect band touching at symmetric points in the Brillouin zone. In particular, we show that Dirac nodes appearing in honeycomb lattice (e.g. graphene) and in half-flux square lattice are protected by three-fold and two-fold rotation symmetry, respectively. We also present several examples of Dirac semimetal with isolated band-touching points in threedimensional k-space, which are protected by combined symmetry of rotation and reflection. The zero mode protection by spatial symmetry is distinct from that by the conventional winding number. We demonstrate that symmetry-protected band touching points emerge even though the winding number is zero. Finally, we identify relevant topological charges assigned to the gapless points.

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Section: A Class Aiii+cn In 2dmentioning

confidence: 99%

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry

2014

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“…An important set of questions concerns the topological properties of gapless Fermi systems (3)(4)(5)(6)(7)(8).…”

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confidence: 99%

Are the surface Fermi arcs in Dirac semimetals topologically protected?

Kargarian

Randeria

Lü

2016

Proc. Natl. Acad. Sci. U.S.A.

167

143

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Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na 3 Bi and Cd 3 As 2 , we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at k = (0,0, ± Q), where gapless states on the side surfaces are protected only near k z = 0. We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na 3 Bi and Cd 3 As 2 . Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments. Of particular interest are 3D semimetals where the bulk electronic dispersion exhibits point nodes at the Fermi level and the low-energy physics are effectively described by a Weyl or Dirac Hamiltonian (9).A striking feature of 3D Weyl semimetals (WSMs), which necessarily break either time-reversal or inversion symmetry, is the existence (5) of topologically protected surface "Fermi arcs." Here the Fermi contour in the surface Brillouin zone breaks up into disconnected pieces, which connect the projection of two Weyl nodes with opposite chirality. The Fermi arcs have been recently observed in angle-resolved photoemission spectroscopy (ARPES) studies of noncentrosymmetric TaAs (10-15).Here we focus on another outstanding example, the Dirac semimetal (DSM), which is the 3D analog of graphene. In the presence of both time-reversal and inversion symmetries, the electronic excitations near each node are described by a four-component Dirac fermion, and a dispersion that is linear in all directions in k space (16)(17)(18). ARPES has clearly observed linearly dispersing bands near Dirac nodes in two DSM materials, Na 3 Bi (19, 20) and Cd 3 As 2 (21-23). The signatures of Fermi arcs by ARPES in Na 3 Bi (24) and by their peculiar quantum oscillations (25) in Cd 3 As 2 (26) have recently been reported. Although DSM can in principle appear in a system with spin rotational symmetry (27), here we focus on DSMs in spinorbit-coupled systems that are more closely related to material realizations.We can understand the Dirac fermions as two degenerate Weyl fermions with opposite chirality, where crystal symmetries forbid the two Weyl nodes from hybridizing and opening up a gap at each Dirac point (16,28). Given this picture of the bulk, it is natural to expect the surface states in a DSM (17, 18) as two copies of the chiral Fermi arc on the WSM surface: i.e., the "double Fermi arcs" shown schematically in Fig. 1A.In thi...

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“…This conclusion was also borne out by detailed microscopic calculations within a renormalization group formalism in [16]. Separately, it has been pointed out that Weyl loop materials host 'drumhead' surface states [17] (see also [18][19][20]) with a large density of states, which could naturally support high temperature surface SC [21]. However, a detailed analysis of the symmetry and topology of surface superconductivity in these materials has never yet been performed [22].…”

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confidence: 99%

Topological surface superconductivity in doped Weyl loop materials

Wang

Nandkishore

2017

Phys. Rev. B

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We study surface superconductivity involving the `drumhead' surface states of (doped) Weyl loop materials. The leading weak coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with $p+ip$ symmetry. We show that the surface SC state is "topological" as long as it is fully gapped, and the system traps Majoarana modes wherever a vortex line enters or exits the bulk. In contrast to true 2D $p+ip$ superconductors, these Majorana zero modes arise even in the "strong pairing" regime where the chemical potential is entirely above/below the drumhead. We also consider conventional $s$-wave pairing, and show that in this case the surface hosts a flat band of charge neutral Majorana fermions, whose momentum range is given by the projection of the bulk Fermi surface. Weyl loop materials thus provide access to new forms of topological superconductivity.Comment: 9 pages, 5 figure

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Topological Classification and Stability of Fermi Surfaces

Cited by 195 publications

References 22 publications

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry

Are the surface Fermi arcs in Dirac semimetals topologically protected?

Topological surface superconductivity in doped Weyl loop materials

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