Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges

TL;DR

This paper theoretically demonstrates the emergence of 1D helical conducting channels at step edges in 3D higher-order topological insulators, revealing how their location depends on electron hopping strength and enabling potential quantum computing applications.

Contribution

It introduces a new understanding of how 1D helical states form at step edges in higher-order topological insulators and explains their dependence on electron hopping parameters.

Findings

1D helical states appear at step edges and opposite surfaces.

Location of states depends on electron hopping strength.

Continuous connection between physical pictures without bulk gap closing.

Abstract

We study theoretically the electronic structure of three-dimensional (3D) higher-order topological insulators in the presence of step edges. We numerically find that a 1D conducting state with a helical spin structure, which also has a linear dispersion near the zero energy, emerges at a step edge and on the opposite surface of the step edge. We also find that the 1D helical conducting state on the opposite surface of a step edge emerges when the electron hopping in the direction perpendicular to the step is weak. In other words, the existence of the 1D helical conducting state on the opposite surface of a step edge can be understood by considering an addition of two different-sized independent blocks of 3D higher-order topological insulators. On the other hand, when the electron hopping in the direction perpendicular to the step is strong, the location of the emergent 1D helical conducting state moves from the opposite surface of a step edge to the dip ($270^{\circ}$ edge) just below the step edge. In this case, the existence at the dip below the step edge can be understood by assigning each surface with a sign ($+$ or $-$) of the mass of the surface Dirac fermions. These two physical pictures are connected continuously without the bulk bandgap closing. Our finding paves the way for on-demand creation of 1D helical conducting states from 3D higher-order topological insulators employing experimental processes commonly used in thin-film devices, which could lead to, e.g., a realization of high-density Majorana qubits.