Tunable line node semimetals

Phillips, Michael W.; Aji, Vivek

doi:10.1103/physrevb.90.115111

Phys. Rev. B

2014

DOI: 10.1103/physrevb.90.115111

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Tunable line node semimetals

Michael W. Phillips

Vivek Aji

Abstract: Weyl semimetals are examples of a new class of topological states of matter which are gapless in the bulk with protected surface states. Their low energy sector is characterized by massless chiral fermions which are robust against translationally invariant perturbations. A variant of these systems have two non-degenerate bands touching along lines rather than points. A proposal to realize such a phase involves alternating layers of topological insulators and magnetic insulators, where the magnetization lies pe… Show more

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Cited by 135 publications

(117 citation statements)

References 34 publications

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“…In 3D, the conductivity has units of e 2 /h divided by length (restoring ) [19,20]. When Γ t, the conductivity is independent of the scattering rate, as expected [21], and gives…”

mentioning

confidence: 99%

Line of Dirac Nodes in Hyperhoneycomb Lattices

Mullen¹,

Uchoa²,

Glatzhofer³

2015

Phys. Rev. Lett.

300

140

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We propose a family of structures that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon.Introduction.− In honeycomb lattices, the existence of the Dirac point results from the planar trigonal connectivity of the sites and its sub-lattice symmetry [1]. Less well known are "Dirac loops", three dimensional (3D) closed lines of Dirac nodes in momentum space, on which the energy vanishes linearly with the perpendicular components of momentum [2]. To date there are no experimental observations of Dirac loops, and they were predicted to exist only in topological superconductors [3] and 3D Dirac semimetals [4] in which the parameters such as interactions and magnetic field are finely tuned [2].Theoretically, graphene is not the only possible lattice realization with planar trigonally connected atoms [5]. It is therefore natural to ask if there are variations on the honeycomb geometry that might produce exotic Fermi surfaces with Dirac-like excitations and topologically non-trivial states. In this Letter, we propose a family of trigonally connected 3D lattices that admit simple tight-binding Hamiltonians having Dirac loops, without requiring any tuning or spin-orbit coupling. Some of these structures lie in the family of harmonic honeycomb lattices, which have been studied in the context of the Kitaev model [7][8][9][10][11], and experimentally realized in honeycomb iridates [12]. The simplest example is the hyper-honeycomb lattice, shown in Fig. 1a.We derive the low energy Hamiltonian of this family of systems, and analyze the quantization of the conductivity and possible surface states. Even though these systems are 3D semimetals, their Fermi surface is multiply connected, with the shape of a torus, and highly anisotropic. When a magnetic field with toroidal geometry is applied, we find that the Hall conductivity is quantized in 3D at sufficiently large field. Additional spin-orbit coupling effects can create topologically protected surface states in these crystals. We claim that in the presence of spin-orbit coupling, these structures conceptually correspond to a new family of strong 3D topological insulators [13,14]. We finally discuss the experimental feasibility of realizing those structures as new allotropic forms of carbon.Tight-binding lattice.− Our discussion starts with the simplest structure, the hyper-honeycomb lattice (see Fig.

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“…In 3D, the conductivity has units of e 2 /h divided by length (restoring ) [19,20]. When Γ t, the conductivity is independent of the scattering rate, as expected [21], and gives…”

mentioning

confidence: 99%

Line of Dirac Nodes in Hyperhoneycomb Lattices

Mullen¹,

Uchoa²,

Glatzhofer³

2015

Phys. Rev. Lett.

300

140

View full text Add to dashboard Cite

show abstract

“…It is well known that the Dirac nodes are protected by both timereversal and space inversion symmetry. Since magnetic field breaks the time-reversal symmetry, a Dirac node may be split into a pair of Weyl nodes along the magnetic field direction in the momentum space [16][17][18] or transformed into linenodes [17,19]. Therefore, a Dirac semimetal can be considered as a parent compound to realize other topological variant quantum states.…”

mentioning

confidence: 99%

Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions inZrTe5

et al. 2015

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We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe 5 . We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D massless Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe 5 is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration.PACS numbers: 71.55. Ak, 71.70.Di 3D topological Dirac/Weyl semimetals are new kinds of topological materials that possess linear band dispersion in the bulk along all three momentum directions [1][2][3][4][5][6][7]. Their low-energy quasiparticles are the condensed matter realization of Dirac and Weyl fermions in relativistic high energy physics [8,9]. These materials are expected to host many unusual phenomena [10][11][12], in particular the chiral and axial anomaly associated with Weyl fermions [3,[13][14][15]. It is well known that the Dirac nodes are protected by both timereversal and space inversion symmetry. Since magnetic field breaks the time-reversal symmetry, a Dirac node may be split into a pair of Weyl nodes along the magnetic field direction in the momentum space [16][17][18] or transformed into linenodes [17,19]. Therefore, a Dirac semimetal can be considered as a parent compound to realize other topological variant quantum states. However, past 3D Dirac semimetal materials (e.g. Cd 3 As 2 ) suffer from the problem of large residual carrier density which requires very high magnetic field (e.g. above 60 Tesla) to drive them to their quantum limit [20,21]. This makes it extremely difficult to explore the transformation from Dirac to Weyl or line-node semimetals. Up to now, there are no direct evidences of such transformations.ZrTe 5 appears to be a new topological 3D Dirac material that exhibits novel and interesting properties. The compound crystallizes in the layered orthorhombic crystal structure, with prismatic ZrTe 6 chains running along the crystallographic aaxis and linked along the c-axis via zigzag chains of Te atoms to form two-dimensional (2D) layers. Those layers stack along the b-axis. A recent ab initio calculation suggests that bulk ZrTe 5 locates close to the phase boundary between weak and strong topological insulators [22]. However, more recent transport and ARPES experiments identify it to be a 3D Dirac semimetal with only one Dirac node at the Γ point [23]. Interestingly, a chiral magnetic effect associated with the transform...

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“…Figures 4(b) and 4(c) illustrate the relationship. Recently, the existence of topological nodal ring states has been proposed in various systems, 46,47 including orthorhombic iridates, 48 Cu 3 PdN, 49,50 and the non-centrosymmetric superconductor PbTaSe 2 . 51,52 Ca 3 P 2 is a unique instance of a real bulk material in which continuous Dirac states at E F are predicted, and the effect of SOC on these states is negligible.…”

mentioning

confidence: 99%

A new form of Ca3P2 with a ring of Dirac nodes

et al. 2015

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We report the synthesis and crystal structure of a new high-temperature form of Ca3P2. The crystal structure was determined through Rietveld refinements of synchrotron powder x-ray diffraction data. This form of Ca3P2 has a crystal structure of the hexagonal Mn5Si3 type, with a Ca ion deficiency compared to the ideal 5:3 stoichiometry. This yields a stable, charge-balanced compound of Ca2+ and P3−. We also report the observation of a secondary hydride phase, Ca5P3H, which again is a charge-balanced compound. The calculated band structure of Ca3P2 indicates that it is a three-dimensional Dirac semimetal with a highly unusual ring of Dirac nodes at the Fermi level. The Dirac states are protected against gap opening by a mirror plane in a manner analogous to what is seen for graphene.

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Tunable line node semimetals

Cited by 135 publications

References 34 publications

Line of Dirac Nodes in Hyperhoneycomb Lattices

Line of Dirac Nodes in Hyperhoneycomb Lattices

Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions inZrTe5

A new form of Ca3P2 with a ring of Dirac nodes

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