# CAMP Seminar: Topological Carbon: a New Perspective

## Main Content

Topological physics in solids began with carbon but drifted away due to its exceedingly small spin-orbit coupling (SOC), which is thought to be essential for any observable effect. Here, I will discuss a different topological classification within carbon that is above the spin degree of freedom, has no need for the SOC, and hence can be observed at any reasonable temperature. It is based on the orbital symmetry, namely, that of the orbital of a carbon. Both spin and orbit are angular degrees of freedoms and both effects may be viewed as a result of (spherical)-symmetry breaking – in the former by SOC whereas in the latter by the formation of -bonded carbon network. First-principles calculations reveal similarities in their silent and often exotic physical properties.

The simplest topological carbon is polyacetylene. It is a one-dimensional (1D) -orbital (semimetal) chain with a Dirac point right at the Fermi level. Starting with the polyacetylene, one can construct a whole family of topological matter. Graphene is a celebrated example, where parallel placement of the chains in 2D gives rise to Dirac cones. In 3D carbon, one may have two or three such -chain sets intercepting with each other. Various arrangements of the two -chain sets give rise to highly-stable Weyl semimetals with symmetry-protected loops [1] and surfaces [2] as their Fermi surfaces, which can be reduced to Weyl points with characteristic Fermi arcs for the surface states. Upon breaking the topological protection, e.g., by a biaxial strain, one may also obtain 3D Kagome lattice as a remarkable direct-gap, blue optoelectronic semiconductor [3]. The recent experimentally-realized carbon honeycombs (CHCs) [4] may be the first experimental realization of 3D topological carbon. It belongs to the family of three -chain set. Besides its interesting but “trivial” applications such as gas storage that have excited the condensed matter physics community, CHC processes 3D Dirac cone that intercepts with a third flat band [5]. Such a triple-point topological metal [6] has becoming a forefront in today’s topological physics.

[1] Y.-P. Chen, et al., Nano Lett. **15**, 6974 (2015).

[2] C. Zhong, et al., Nanoscale **8**, 7232 (2016).

[3] Y.-P. Chen Y, et al., Phys. Rev. Lett. **113**, 085501 (2014).

[4] N. V. Krainyukova and E. N. Zubarev, Phys. Rev. Lett. **116**, 055501 (2016).

[5] Y. Gao, et al., Nanoscale **8**, 12863 (2016).

[6] Chang, et al., arXiv:1605.06831v1.