Topological Charges, Fermi Arcs, and Surface States of $K_4$ Crystal

TL;DR

This paper explores the topological electronic features of the $K_4$ crystal, revealing Weyl nodes with various chiralities and surface Fermi arcs, establishing it as a spinless Weyl semimetal with protected surface states.

Contribution

It constructs a tight-binding model for $K_4$ crystal, identifying multiple Weyl nodes and their associated Fermi arcs, highlighting novel topological properties.

Findings

Presence of Weyl nodes with chiralities $ ext{±}2$ and $ ext{±}1$

Fermi arcs connect Weyl nodes of opposite chirality

$K_4$ crystal is a spinless Weyl semimetal with topologically protected surface states

Abstract

We investigate the topological electronic properties of the $K_4$ crystal by constructing a tight-binding model. The bulk band structure hosts Weyl nodes with higher and conventional chiralities ($\chi = \pm 2$ and $\chi = \pm 1$) located at high-symmetry points in the Brillouin zone. Through analytical evaluation of the Berry curvature, we identify the positions and chiralities of these Weyl nodes. Furthermore, slab calculations for the (001) surface reveal Fermi arcs that connect Weyl nodes of opposite chirality, including those linking $\chi = \pm 2$ nodes with pairs of $\chi = \mp 1$ nodes. These results demonstrate that the $K_4$ crystal is a spinless Weyl semimetal featuring topologically protected surface states originating from multiple types of Weyl nodes.