Emergence of surface superconductivity through interference in proximitized topological insulators

Proximitized topological insulators (PTIs) have received significant research attention over the past two decades. In this paper, we demonstrate that a low-dimensional PTI in the topologically nontrivial phase (TP) exhibits interference-induced surface superconductivity (SSC) at the system ends/edges with the critical temperature ${T}_cs$ significantly higher than ${T}_cb$ deep inside the system (low-dimensional bulk). Such an SSC is built due to the interference of the scattering quasiparticle states, rather than the presence of the topological bound states (TBSs). As the system delves deeper into the TP, a nontrivial competition between the scattering quasiparticles and TBSs at the surface leads to a crossover from the interference- to TBS-induced phase, where the SSC is governed by the TBSs. Our paper unveils a substantial variation in the maximal ${T}_cs$ along this crossover, attaining values being twice the maximal ${T}_cb$ of the PTI. Beyond shedding light on the nature of the SSC in PTIs, our paper introduces a tangible method for experimentally manipulating their critical superconducting temperatures.