Nexus and Dirac lines in topological materials

Heikkilä, Tero T.; Volovik, G. E.

doi:10.1088/1367-2630/17/9/093019

Cited by 120 publications

(134 citation statements)

References 27 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: 50%

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

et al. 2016

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“…We find real materials that possess such hybrid loops, e.g., in the ScCdtype transition-metal intermetallic materials [55]. Hybrid nodal lines connecting nexus points have also been predicted in Bernal stacked graphite [56][57][58]. Finally, for K 4 P 3 , the direction of tilt vector is pinned onto the glide mirror plane, but for systems with reduced symmetry, the tilt vector may wind around when going along the loop.…”

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confidence: 77%

Type-II nodal loops: Theory and material realization

et al. 2017

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Nodal loop appears when two bands, typically one electron-like and one hole-like, are crossing each other linearly along a one-dimensional manifold in the reciprocal space. Here we propose a new type of nodal loop which emerges from crossing between two bands which are both electron-like (or hole-like) along certain direction. Close to any point on such loop (dubbed as a type-II nodal loop), the linear spectrum is strongly tilted and tipped over along one transverse direction, leading to marked differences in magnetic, optical, and transport responses compared with the conventional (type-I) nodal loops. We show that the compound K4P3 is an example that hosts a pair of type-II nodal loops close to the Fermi level. Each loop traverses the whole Brillouin zone, hence can only be annihilated in pair when symmetry is preserved. The symmetry and topological protections of the loops as well as the associated surface states are discussed.Topological metals and semimetals have become a focus of current physics research [1,2]. These materials feature nontrivial band-crossings in their low-energy band structures, around which the quasiparticles behave drastically different from the usual Schrödinger-type fermions. Depending on its dimensionality, the crossing manifold may take zero-dimensional (nodal point), onedimensional (nodal loop), or two-dimensional (nodal surface) form [3]. There has already been extensive studies on nodal points, especially on so-called Weyl and Dirac semimetal materials [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, nodal loops begin to attract considerable interest: several nodal-loop materials have been proposed, with interesting physical consequences revealed [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].Consider the generic case of a nodal loop formed by the linear crossing between two bands in a three-dimensional system. Close to any point P on the loop, the dispersion is linear along the two transverse directions of the loop, and is at least quadratic along the tangential direction. The low-energy effective model near P can be expressed as (set = 1)up to first order in the wave-vector q measured from P . Here q i 's (i = 1, 2) are the components of q along two orthogonal transverse directions [see Fig. 1(a)], v i 's are

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“…B. Roy has discussed effects of Coulomb interactions in the bulk of nodal-loop semimetals. B. Pamuk et al has performed first-principles calculations on slabs of rhombohedral graphite (which has been proposed to be a bulk nodal-loop metal [70]), and found interesting ferrimagnetic spin order localized at the surface.…”

Section: Discussionmentioning

confidence: 99%

Correlation effects and quantum oscillations in topological nodal-loop semimetals

Liu

Balents

2017

Phys. Rev. B

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We study the unique physical properties of topological nodal-loop semimetals protected by the coexistence of time-reversal and inversion symmetries with negligible spin-orbit coupling. We argue that strong correlation effects occur at the surface of such systems for relatively small Hubbard interaction U , due to the narrow bandwidth of the "drumhead" surface states. In the Hartree-Fock approximation, at small U we obtain a surface ferromagnetic phase through a continuous quantum phase transition characterized by the surface-mode divergence of the spin susceptibility, while the bulk states remain very robust against local interactions and remain non-ordered. At slightly increased interaction strength, the system quickly changes from a surface ferromagnetic phase to a surface charge-ordered phase through a first-order transition. When Rashba-type spin-orbit coupling is applied to the surface states, a canted ferromagnetic phase occurs at the surface for intermediate values of U . The quantum critical behavior of the surface ferromagnetic transition is nontrivial in the sense that the surface spin order parameter couple to Fermi-surface excitations from both surface and bulk states. This leads to unconventional Landau damping and consequently a naïve dynamical critical exponent z ≈ 1 when the Fermi level is close to the bulk nodal energy. We also show that, already without interactions, quantum oscillations arise due to bulk states, despite the absence of a Fermi surface when the chemical potential is tuned to the energy of the nodal loop. The bulk magnetic susceptibility diverges logarithmically whenever the nodal loop exactly overlaps with a quantized magnetic orbit in the bulk Brillouin zone. These correlation and transport phenomena are unique signatures of nodal loop states. 73.20.Mf, 75.30.Fv, 64.60.Ht The theoretical proposal and experimental verification of Weyl and Dirac semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] has shown that topological electronic structure is not restricted to gapped systems [19][20][21][22][23], but also occurs in gapless systems such as nodal metals [24]. Recently, the interest in topological semimetals has been extended from systems with point nodes to those with a 3D nodal loop, "nodal-chain" [25], "nodal-arc" [26], and even "nodal surfaces" [27], in which there are bulk band touchings along isolated or connected 1D lines, or even at 2D surfaces in the 3D Brillouin zone (BZ) instead of at isolated points.A growing number of material systems have been theoretically proposed to realize nodal-loop semimetals (NLSMs) [28][29][30][31][32][33][34][35][36][37]. In particular, ZrSiS and PbTaSe 2 have been experimentally confirmed by angle-resolved photoemission spectroscopy (ARPES) measurements [31,32,34], and the bulk nodal loops in the ZrSiS-family compounds were further investigated by de Haas-van Alphen (dHvA) quantum oscillations [38,39] and magneto-transport measurements [40].In this paper, we discuss some fundamental physics of NLSMs which is dis...

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Nexus and Dirac lines in topological materials

Cited by 120 publications

References 27 publications

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

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

Type-II nodal loops: Theory and material realization

Correlation effects and quantum oscillations in topological nodal-loop semimetals

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