Splitting the Hinge Mode of Higher-Order Topological Insulators

The surface of a higher order topological insulator comprises a two-dimensional topological insulator (TI) with broken inversion symmetry, whose mass is determined by the microscopic details of the surface such as surface potentials and termination. It hosts a helical mode pinned to selected hinges where the surface gap changes its sign. We study the effect of perturbations that break time reversal and particle conservation on this helical mode, such as a Zeeman field and a proximate superconductor. We find that in contrast to the helical modes of inversion symmetric TIs, which are gapped by these couplings, the helical modes at the hinges can remain gapless and spatially split. When this happens, the Zeeman field splits the helical mode into a chiral mode surrounding the magnetized region, and a superconductor results in a helical Majorana mode surrounding the superconducting region. The combination of the two might lead to the gapping of one of the chiral Majorana modes, and leave a single one-dimensional chiral Majorana mode around the superconducting island. We propose that the different topological states can be measured in electrical transport.

Figure 1

(a) A Zeeman field splits the hinge state into two spin-momentum locked chiral modes, forming a quantum anomalous Hall (QAH) region. For a strong enough field, two chiral modes from different hinges overlap, extending the QAH over the entire region in between hinges. (b) Proposed Majorana interferometer, as an extension to Refs. [19, 20]. A magnetic flux ${\mathrm{\Phi }}_0$ is enclosed by a helical Majorana mode. The interference will be evident by an electron current from the superconductor to the ground, that ensures charge conservation. (c) When one chiral mode is gapped, the flux is encircled by a single chiral Majorana mode. It realizes the junction proposed in Refs. [25, 26, 27, 28], where the conductance is quantized to $e^2/2h$.