Corner flat bands induced by d density wave and partial corner state modification due to competition with d-wave superconductivity

Abstract

In the realm of condensed matter physics, higher-order topological insulators (TIs) and superconductors have become a focal point of research due to their unique gapless boundary states at lower-dimensional boundaries such as corners and edges. This paper delves into the effects of a d-density wave (DDW) on first-order TIs and the competitive dynamics between DDW and d-wave superconductivity (DSC) within these systems. We demonstrate that a pure DDW state can instigate a transition to a higher-order topological phase, distinct from DSC behavior, as it is influenced by boundary shape and can generate a zero energy corner flat band without additional potentials. However, the introduction of the additional DSC order disrupts this corner flat band, leading to the formation of corner states. Furthermore, we investigate the competitive effects between DSC and DDW, which lead to the transfer of partial corner states. The interplay between these states results by the generation of partial Majorana corner states with different symmetries by proximity-induced DSC, while DDW disrupts these states and creates new corner states at alternative locations. This study provides valuable insights into the manipulation of topological states by competing different order parameters, which could be pivotal for future research and applications in the field.

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