Topological nodal semimetals

Abstract

We present a study of "nodal semimetal" phases, in which non-degenerate conduction and valence bands touch at points (the "Weyl semimetal") or lines (the "line node semimetal") in threedimensional momentum space. We discuss a general approach to such states by perturbation of the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time reversal (TR) or inversion symmetry. We give an explicit model realization of both types of states in a NI-TI superlattice structure with broken TR symmetry. Both the Weyl and the line-node semimetals are characterized by topologically-protected surface states, although in the line-node case some additional symmetries must be imposed to retain this topological protection. The edge states have the form of "Fermi arcs" in the case of the Weyl semimetal: these are chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. The chiral character of the edge states leads to a finite Hall conductivity. In contrast, the edge states of the line-node semimetal are "flat bands": these states are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone, given by the projection of the line node onto the plane of the edge. We discuss unusual transport properties of the nodal semimetals, and in particular point out quantum critical-like scaling of the DC and optical conductivity of the Weyl semimetal, and similarities to the conductivity of graphene in the line node case.

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

“…56. The simple model of Weyl semimetal described in the previous paragraph by H ± (k) breaks TR, however it is also possible to realize a Weyl system when TR is intact but inversion symmetry is broken 14,64,65 . This implies that the system must host more than one flavor of pairs of Weyl fermions for the vector sum of k 0 to vanish.…”

“…Usually the robust topological protection is associated with a non-zero spectral gap in the bulk of the system, and the presence of protected zero energy surface states is regarded as the hallmark of a non-trivial topological phase of matter. However, recently it has been proposed that systems in three spatial dimensions, in the presence of broken time-reversal (TR) and/or spaceinversion (SI) symmetry, can also be topologically protected even without a bulk energy gap [10][11][12][13][14][15][16][17][18][19][20][21] . These are Weyl semimetals (WSM) -the nomenclature based on the Dirac/Weyl equation which is used to describe their low energy excitations 22 .…”

CaTe: a new topological node-line and Dirac semimetal

“…[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.…”

“…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.…”

Topological semimetals with helicoid surface states

“…The nontrivial topology gives rise to anomalous bulk properties of topological semimetals such as the chiral anomaly [3][4][5]. Several classes of topological semimetals have been theoretically proposed so far, including Weyl, [2,[6][7][8][9][10][11][12][13], Dirac [14][15][16][17] and nodal line semimetals [7,[17][18][19][20][21][22][23][24][25][26][27][28][29][30], some among which have been experimentally observed [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”