One-dimensional topological metal

Abstract

We propose a type of topological states of matter exhibiting topologically nontrivial edge states (ESs) within gapless bulk states (GBSs) protected by both spin rotational and reflection symmetries. A model presenting such states is simply comprised of a one-dimensional reflection symmetric superlattice in the presence of spin-orbit (SO) coupling containing an odd number of sublattices per unit cell. We show that the system has a rich phase diagram including a topological metal (TM) phase where nontrivial ESs coexist with nontrivial GBSs at Fermi level. Topologically distinct phases can be reached through a subband gap closing-reopening transition depending on the relative strength of inter- and intraunit cell SO couplings. Moreover, the topological class of the system is AI with an integer topological invariant called $\mathbb{Z}$ index. The stability of TM states is also analyzed against Zeeman magnetic fields and on-site potentials resulting in that the spin rotational symmetry around the lattice direction is a key requirement for the appearance of such states. Also, possible experimental realizations are discussed.