Higher order topological state induced by $d$-wave competing orders in high-T$_c$ superconductor based heterostructure

TL;DR

This paper proposes a novel higher order topological state in a heterostructure combining a Chern insulator with a $d$-wave pseudogap, demonstrating gapless corner states and Majorana modes through theoretical calculations.

Contribution

It introduces a new platform for higher order topological states using proximity-induced $d$-density-wave order in a Chern insulator, with detailed topological characterization.

Findings

Gapless corner states due to sign change of DDW order

Higher order topology confirmed by polarization and quadrupole moment calculations

Majorana corner states emerge in the superconducting coexistence phase

Abstract

We introduce a two-dimensional Chern insulator in proximity to a $d$-wave pseudogap state of the high-T$_c$ superconducting material as an effective platform to realize the higher order topological system. The proximity-induced $d$-density-wave (DDW) order in the Chern insulator layer serves as an effective mass. The edge states will be fully gapped by this DDW order. In the real space, the sign of the DDW order parameter changes at the system corners due to the $d$-wave factor, leading to the gapless corner states, indicating that this system may be in a higher order topological state. The higher order topology in this coupled system is confirmed based on the calculation of the edge polarization and the quadrupole moment. In the superconducting state where the superconducting order and the DDW order coexist, the Majorana corner states emerge.