Topological node-line semimetal in three-dimensional graphene networks

Abstract

Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, called Mackay-Terrones crystals (MTC), have been proposed and experimentally explored, yet their topological properties remain to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically non-trivial electronic states by exhibiting node-lines in bulk. When the node-lines are projected on to surfaces to form circles, "drumhead"-like flat surface bands nestled inside of the circles are formed. The bulk node-line can evolve into 3D Dirac point in the absence of inversion symmetry, which has shown its plausible existence in recent experiments.

CaTe: a new topological node-line and Dirac semimetal

“…Therefore, the band inversion originates from the crystal field effect. With the time reversal and space inversion symmetry, such band inversion will result in node lines as proved in Weng et al 25 The effective Hamiltonian for the node line around M point can be established by using the k * Á p * method. Considering the crystal symmetry at M point and time reversal symmetry, the effective Hamiltonian can be written as the following form:…”

“…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][25][26][27][28][29] Such a 2D flat band surface state may become a route to achieve high temperature superconductivity.…”

“…[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.…”

“…[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.…”

“…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.…”