Nodal lines and boundary modes in topological Dirac semimetals with magnetism

TL;DR

This paper investigates how introducing magnetism into topological Dirac semimetals can induce nodal-line states with boundary zero modes, revealing new topological phases and boundary phenomena.

Contribution

It demonstrates that magnetic moments can transform Dirac semimetals into Weyl or nodal-line semimetals, with boundary zero modes characterized by topological invariants.

Findings

Magnetism induces transition from Dirac to Weyl or nodal-line semimetals.

Zero boundary modes with drumhead-like structure are found in magnetic nodal-line states.

Boundary zero modes are demonstrated via magnetic domain wall simulations.

Abstract

Nodal-line semimetals with magnetic orders have been theoretically predicted and experimentally observed in only few compounds. We theoretically explore the electronic structure in bulk and boundary of such a magnetic nodal-line state by introducing magnetism in topological Dirac semimetal (TDSM). TDSMs, such as $\mathrm{Cd_3 As_2}$ and $\mathrm{Na_3 Bi}$, are characterized by a pair of spin-degenerate Dirac points protected by rotational symmetries of crystals. By introducing local magnetic moments coupled to the electron spins in the lattice model of TDSM, we show that the TDSM can turn into either a Weyl semimetal or a nodal-line semimetal, which is determined by the orbital dependence in the exchange coupling and the direction of magnetization formed by the magnetic moments. In this magnetic nodal-line semimetal state, we find zero modes with drumhead-like band structure at the boundary that are characterized by the topological number of $\mathbb{Z}$. Those zero modes are numerically demonstrated by introducing magnetic domain walls in the lattice model.