We uncover an edge geometric phase mechanism to realize the second-order topological insulators and topological superconductors (SCs), and predict realistic materials for the realization. The theory is built on a novel result shown here that the nontrivial pseudospin textures of edge states in a class of two-dimensional (2D) topological insulators give rise to the geometric phases defined on the edge, for which the effective edge mass domain walls are obtained across corners when external magnetic field or superconductivity is considered, and the Dirac or Majorana Kramers corner modes are resulted. Remarkably, with this mechanism we predict the Majorana Kramers corner modes by fabricating 2D topological insulator on only a uniform and conventional $s$-wave SC, in sharp contrast to the previous proposals which applies unconventional SC pairing or SC $pi$-junction. We find that Au/GaAs(111) can be a realistic material candidate for realizing such Majorana Kramers corner modes.
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