Nanostructured Carbon Allotropes with Weyl-like Loops and Points

Chen, Yuanping; Xie, Yuee; Yang, Shengyuan A.; Pan, Hui; Zhang, Fan; Cohen, Marvin L.; Zhang, Shou-Cheng

doi:10.1021/acs.nanolett.5b02978

Cited by 349 publications

(279 citation statements)

References 58 publications

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“…The novelty could be either from the dimensionality of the band-crossing, or from its degeneracy. Regarding the former, materials with one-dimensional (1D) bandcrossings-nodal rings-have emerged as an interesting topic [20][21][22][23][24][25][26][27][28][29][30][31] . In the identified nodal ring materials, the ring is formed by the crossing between two bands, with linear dispersions along transverse directions.…”

Section: Introductionmentioning

confidence: 99%

Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

et al. 2017

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Topological metals with protected band-crossing points have been attracting great interest. Here we report novel topological band features in a family of metal diboride materials. Using firstprinciples calculations, we show that these materials are metallic, and close to Fermi level, there appears coexistence of one pair of nodal rings and one pair of triply-degenerate nodal points (TNPs). The nodal ring here is distinct from the previously studied ones in that its formation requires four entangled bands, not just two as in previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably, we show that FNR features Dirac-cone-like surface states, in contrast to the usual drumhead surface states for two-band nodal rings. Due to the presence of inversion symmetry, the TNP here is also different from those discussed previously in inversion-asymmetric systems. Especially, when spin-orbit coupling is included, the TNP here transforms into a novel Dirac point that is close to the borderline between the type-I and type-II Dirac point categories. We discuss their respective symmetry protections, and construct effective models for their characterization. The large linear energy range (> 2 eV) in these materials should facilitate the experimental detection of the signatures of these nontrivial band crossings.

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Section: Introductionmentioning

confidence: 99%

Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

et al. 2017

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“…Up to now, three kinds of topological semimetals have been discovered, i.e., 3D Dirac semimetal (DSM), 12,[17][18][19][20][21] Weyl semimetal (WSM), 8,9,22,23 and node-line semimetal (NLS). [24][25][26][27][28][29] The 3D DSM has four-fold degeneracy point, which can be viewed as the kiss of two Weyl fermions with opposite chiralities in the Brillouin zone (BZ). Protected by the crystal symmetry and time reversal symmetry, 3D DSMs can be robust against external perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…[25][26][27]37,45,46 Same with TI and WSM, NLS also has a characteristic surface state, namely, drumhead-like state. [24][25][26][27][28][29] Such a 2D flat band surface state may become a route to achieve high temperature superconductivity. 47,48 As a result, it is of great impetus to search new NLS.…”

Section: Introductionmentioning

confidence: 99%

CaTe: a new topological node-line and Dirac semimetal

Du¹,

Tang²,

Wang³

et al. 2017

npj Quant Mater

115

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Combining first-principles calculations and effective model analysis, we predict that CaTe is a topological node-line semimetal in the absence of the spin-orbit coupling. Using a slab model, we obtain the nearly flat drumhead surface state near the Fermi level. When the spin-orbit coupling is included, three node lines will evolve into a pair of Dirac points along the M−R line. These Dirac points are robust and protected by the C 4 rotation symmetry. Once this crystal symmetry is broken, the Dirac points will be eliminated, and the system becomes a strong topological insulator.npj Quantum Materials (2017) 2:3 ; doi:10.1038/s41535-016-0005-4 INTRODUCTIONTopological insulator (TI) has attracted broad interest in the past 10 years. [1][2][3][4][5][6][7] The unique property of TI is that it is an insulator in the bulk but has exotic metallic surface states due to the topological order. More recently, the research on topological states has been extended to three-dimensional (3D) semimetal systems. [8][9][10][11][12] These systems could demonstrate many fascinating phenomena, such as Weyl fermion quantum transport and various Hall effects, [13][14][15][16] consequently become the rising stars of the field. Up to now, three kinds of topological semimetals have been discovered, i.e., 3D Dirac semimetal (DSM), 12,[17][18][19][20][21] Weyl semimetal (WSM), 8,9,22,23 and node-line semimetal (NLS). [24][25][26][27][28][29] The 3D DSM has four-fold degeneracy point, which can be viewed as the kiss of two Weyl fermions with opposite chiralities in the Brillouin zone (BZ). Protected by the crystal symmetry and time reversal symmetry, 3D DSMs can be robust against external perturbations. Several materials have been theoretically predicted to be 3D DSMs 12,17-21 and some of them have already been confirmed by experiments. [30][31][32][33] If one breaks the time reversal symmetry 8,22,23,34 or the inversion symmetry, 35-38 the 3D DSM will evolve into WSM. Very recently, the predictions about WSM state in TaAs family 37,38 have been confirmed experimentally. [39][40][41][42] Unlike DSM and WSM whose band crossing points distribute at separate k points in the BZ, for a NLS the crossing points around the Fermi level form a closed loop. Several compounds have been proposed as NLSs, including Mackay-Terrones crystals, 25 Bernal graphite, 43 hyperhoneycomb lattices, 44 and antiperovskite Cu 3 PdN 26,27 and Cu 3 NZn. 27 In the absence of spin-orbit coupling (SOC), time reversal symmetry together with inversion or mirror symmetry will guarantee the occurrence of node line in 3D BZ for systems with band inversion. [25][26][27]37,45,46 Same with TI and WSM, NLS also has a characteristic surface state, namely, drumhead-like state. 24-29 Such a 2D flat band surface state may become a route to achieve high temperature superconductivity. 47,48 As a result, it is of great impetus to search new NLS.In this study, based on first-principles calculations and effective model analysis, we propose that CaTe in CsCl-type structure is a NLS with drumhea...

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“…The arguments apply equally well for pseudospins, as long as they are coupled with the orbital motion and change in the scattering. Particularly, the results for the Weyl model here directly applies for those spin-orbit-free Weyl semimetals [38,39].…”

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confidence: 97%

Transverse shift in Andreev reflection

Liu

Yang

2017

Phys. Rev. B

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An incoming electron is reflected back as a hole at a normal-metal-superconductor interface, a process known as Andreev reflection. We predict that there exists a universal transverse shift in this process due to the effect of spin-orbit coupling in the normal metal. Particularly, using both the scattering approach and the argument of angular momentum conservation, we demonstrate that the shifts are pronounced for lightly-doped Weyl semimetals, and are opposite for incoming electrons with different chirality, generating a chirality-dependent Hall effect for the reflected holes. The predicted shift is not limited to Weyl systems, but exists for a general three-dimensional spin-orbitcoupled metal interfaced with a superconductor.Spin-orbit coupling (SOC) underlies many topics that are at the frontier of current research. Intuitively, under SOC, the change of a particle's spin polarization will tend to alter its orbital motion. The effect is particularly pronounced when particles are scattered at certain interfaces. For example, when reflected at an interface, a circularly-polarized light beam acquires a transverse shift normal to its plane of incidence, known as ImbertFedorov shift [1][2][3][4][5][6], due to the intrinsic SOC of light [7]. Recently, an analogous transverse shift is predicted for Weyl electrons [8,9], the fermionic cousin of photons with strong SOC in so-called Weyl semimetals [10][11][12][13][14][15][16][17][18][19], when they are scattered by electrostatic potentials or velocity gradients. This discovery has generated great interest [20,21], and hints at possible universality of such effect in spin-orbit-coupled systems.There is an intriguing scattering process unique for the normal-metal-superconductor (NS) interface-Andreev reflection [22], in which an incoming electron excitation from the normal metal at energy ε above the Fermi level E F is reflected back as a hole excitation with energy ε below E F [23]. The process conserves energy and momentum but not charge: the missing charge of (−2e) is absorbed as a Cooper pair at Fermi level into the superconductor. For excitation energies below the superconducting gap, electrons cannot penetrate into the superconudctor, and Andreev reflection becomes the dominating mechanism for transport through the NS interface. A natural question arises: Is there a transverse shift associated with Andreev reflection? This question is not trivial, since the incoming and outgoing particles possess distinct identities with opposite charges. To our knowledge, it has not been posed or studied before.In this work, we answer the above question in the affirmative. We predict that a transverse shift generally exists in Andreev reflection between a three-dimensional spin-orbit-coupled metal and a conventional superconductor. We explicitly demonstrate the effect for two examples: a lightly-doped Weyl semimetal and a spin-orbitcoupled metal without any band-crossing. The result is derived via the quantum mechanical scattering approach, and in special cases can be exactly veri...

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Nanostructured Carbon Allotropes with Weyl-like Loops and Points

Cited by 349 publications

References 58 publications

Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

CaTe: a new topological node-line and Dirac semimetal

Transverse shift in Andreev reflection

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