Orbital-Active Dirac Materials from the Symmetry Principle

TL;DR

This paper explores orbital-active Dirac materials, emphasizing symmetry principles that unify various systems and reveal features like Dirac cones, quadratic band touchings, and flat bands, broadening the scope for discovering exotic quantum states.

Contribution

It introduces the concept of orbital-active Dirac materials based on symmetry, unifying diverse systems and analyzing their band structures and potential for exotic states.

Findings

Dirac cones at K and K' points in orbital-active systems

Quadratic band touching points at Gamma

Flat bands emerge in strong anisotropy limit

Abstract

Dirac materials, starting with graphene, have drawn tremendous research interest in the past decade. Instead of focusing on the $p_z$ orbital as in graphene, we move a step further and study orbital-active Dirac materials, where the orbital degrees of freedom transform as a two-dimensional irreducible representation of the lattice point group. Examples of orbital-active Dirac materials occur in a broad class of systems, including transition-metal-oxide heterostructures, transition-metal dichalcogenide monolayers, germanene, stanene, and optical lattices. Different systems are unified based on symmetry principles. The band structure of orbital-active Dirac materials features Dirac cones at $K(K')$ and quadratic band touching points at $\Gamma$, regardless of the origin of the orbital degrees of freedom. In the strong anisotropy limit, i.e., when the $\pi$-bonding can be neglected, flat bands appear due to the destructive interference. These features make orbital-active Dirac materials an even wider playground for searching for exotic states of matter, such as the Dirac semi-metal, ferromagnetism, Wigner crystallization, quantum spin Hall state, and quantum anomalous Hall state.