Single Dirac point and helical states in a one-dimensional system

TL;DR

This paper demonstrates that a spatially periodic magnetic field with zero mean can induce a single Dirac point and helical states in a one-dimensional system, revealing new topological phenomena in the bulk of 1D lattices.

Contribution

It introduces a novel method to create a single Dirac point in 1D systems using periodic magnetic fields, challenging the no-go theorem and enabling new topological effects.

Findings

Single Dirac point induced by periodic magnetic field

Quantized conductance near the Dirac point

Presence of 1/2-charge solitons at mass kinks

Abstract

Odd numbers of Dirac points and helical states can exist at edges (surfaces) of two-dimensional (three-dimensional) topological insulators. In the bulk of a one-dimensional lattice (not an edge) with time reversal symmetry, however, a no-go theorem forbids the existence of an odd number of Dirac points or helical states. Introducing a magnetic field can violate the time reversal condition but would usually lift the degeneracy at the Dirac points. We find that a spatially periodic magnetic field with zero mean value can induce a single Dirac point in a one-dimensional system with spin-orbit coupling. A wealth of new physics may emerge due to the existence of a single Dirac point and helical states in the bulk of a one-dimensional lattice (rather than edge states). A series of quantized numbers emerge due to the non-trivial topology of the 1D helical states, including the doubled period of helical Bloch oscillations, quantized conductance near the Dirac point, and 1/2-charge solitons at mass kinks. Such a system can be realized in one-dimensional semiconductor systems or in optical traps of atoms.