Detecting competing orders through the edge states in the heterostructures with high-Tc superconductors

Considering a $d$-wave superconductor being in proximity to a two-dimensional Weyl model, a topological superconductor with gapless edge states may be realized. We here demonstrate that the system can become topologically trivial when an additional d-density-wave order is also included. The edge states become gapped and may be detected in experiments. For this, the d-density-wave order can be detected experimentally, so that different scenarios for the pseudogap in high-T$_c$ superconductors may be distinguished. Moreover, this method may be used to detect various hidden orders through putting high-T$_c$ superconductors being in proximity to various topological nontrivial materials.