The Berry phase in graphene and graphite multilayers

Mikitik, G. P.; Sharlaı̆, Yu. V.

doi:10.1063/1.2981389

Cited by 45 publications

(52 citation statements)

References 35 publications

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“…3(a)). Previously, TPs have been discussed in the context of Bernal-stacked graphite with neglected SOI [57][58][59], spin-1 quasiparticles in two dimensions [60,61] and strained HgTe [62]. The TP we find is furthermore accompanied by four Weyl nodal lines [63] in the vertical mirror planes, degenerate lines between the second and third band in Fig.…”

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confidence: 80%

Topological Phases inInAs1−xSbx: From Novel Topological Semimetal to Majorana Wire

et al. 2016

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Superconductor proximitized one-dimensional semiconductor nanowires with strong spin-orbit interaction (SOI) are at this time the most promising candidates for the realization of topological quantum information processing. In current experiments the SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence of the topological transition in these devices on microscopic details makes scaling to a large number of devices difficult unless a material with dominant intrinsic bulk SOI is used. Here we show that wires made of certain ordered alloys InAs1−xSbx have spin splittings up to 20 times larger than those reached in pristine InSb wires. In particular, we show this for a stable ordered CuPt-structure at x = 0.5, which has an inverted band ordering and realizes a novel type of a topological semimetal with triple degeneracy points in the bulk spectrum that produce topological surface Fermi arcs. Experimentally achievable strains can drive this compound either into a topological insulator phase, or restore the normal band ordering making the CuPt-ordered InAs0.5Sb0.5 a semiconductor with a large intrinsic linear in k bulk spin splitting.In recent years, a range of topological phases have been realized in materials, ranging from topological insulators [1, 2] (TIs) and semimetals [3][4][5][6] (TSMs) to superconductors [7, 8] (TSCs). The non-trivial topology of the ground state wavefunctions in these phases causes a variety of phenomena in such materials ranging from topologically protected metallic surface or edge states in TIs [1, 2] and Fermi arcs and anomalous magnetotransport in TSMs [4,[9][10][11], to quasiparticles with nonAbelian particle statistics [12][13][14][15][16][17][18][19] in TSCs, which could be used for topological quantum computation [20,21].Arguably the simplest scheme for realizing nonAbelian statistics in a solid-state device is based on manipulating Majorana zero modes (MZMs) in networks of semiconductor wires. MZMs were predicted to appear at the ends of spin-orbit coupled wires subject to a parallel magnetic field, proximity coupled to an s-wave superconductor. Experimental observations, consistent with the theory, were reported for InAs and InSb zincblende nanowires [19,[22][23][24].The stability of MZMs in such a setup depends greatly on the size of the spin-orbit splitting (SOS) of the conduction band. SOS is very small in bulk zincblende semiconductors [25] and the realization of the MZMs thus relies on the externally induced Rashba SOS [26], which is estimated to be of the order of 1 meV [27,28]. This value is very small compared to the bulk splitting in some recently discovered compounds [29][30][31][32]. However, most of these materials are not suitable for realizing MZMs within the above scenario, while for others such experiments appear to be challenging. It is thus desirable to understand if large values of bulk SOS can be achieved within the III-V materials class, used in most experiments at this time. A bulk SOS dom...

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confidence: 80%

Topological Phases inInAs1−xSbx: From Novel Topological Semimetal to Majorana Wire

et al. 2016

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“…[67,[70][71][72]. We identify the key properties of the model that allow stabilizing the nexus in the momentum space: reflection symmetries and the existence of more than one electron-or holelike bands close to the Fermi energy.…”

Section: Introductionmentioning

confidence: 99%

“…Recently the idea that a momentum space nexus may occur in topological semimetals was put forward in Ref. [67] in the context of Bernally (AB) stacked graphite, where the existence and merging of multiple band contact lines is theoretically well established [70][71][72].…”

Section: Introductionmentioning

confidence: 99%

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Hyart

Heikkilä

2016

Phys. Rev. B

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Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for Helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bulk-boundary correspondence of topological media, the presence of Dirac lines lead to the formation of drumhead surface states at the side surfaces of the system. We calculate the surface state spectrum, and especially illustrate the effect of the nexus on these states.

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“…Existence of NLS has been proposed in Bernal graphite [31,32] and other all-carbon allotropes, including hyper-honeycomb lattices [33] and Mackay-Terrones crystal (MTC) [12].…”

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confidence: 99%

Topological Node-Line Semimetal and Dirac Semimetal State in AntiperovskiteCu3PdN

et al. 2015

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Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu 3 PdN can host a three-dimensional (3D) topological nodal line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by coexistence of time-reversal and inversion symmetry. There are three nodal line circles in total due to the cubic symmetry."Drumhead"-like surface flat bands are also derived. When SOC is included, each nodal line evolves into a pair of stable 3D Dirac points as protected by C 4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na 3 Bi and Cd 3 As 2 , both having only one pair of Dirac points. Once C 4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z 2 indices. * Electronic address: hmweng@iphy.ac.cn † Electronic address: Hu.Xiao@nims.go.jp 1 arXiv:1504.04577v2 [cond-mat.mtrl-sci]

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The Berry phase in graphene and graphite multilayers

Cited by 45 publications

References 35 publications

Topological Phases inInAs1−xSbx: From Novel Topological Semimetal to Majorana Wire

Topological Phases inInAs1−xSbx: From Novel Topological Semimetal to Majorana Wire

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Topological Node-Line Semimetal and Dirac Semimetal State in AntiperovskiteCu3PdN

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