Majorana zero modes in gate-defined germanium hole nanowires

We theoretically study gate-defined one-dimensional channels in planar Ge hole gases as a potential platform for Majorana zero modes. Assuming that the Ge is proximitized by an s-wave superconductor, we calculate the topological phase diagrams for channels of different geometries, showing that sufficiently narrow Ge hole channels can indeed enter a topological superconducting phase with Majorana zero modes at the channel ends. We estimate the size of the topological gap and its dependence on various system parameters such as channel width, strain, and out-of-plane electric field, allowing us to critically discuss under which conditions Ge hole channels may manifest Majorana zero modes. One of the main advantages of the Ge-based platform is that ultra-clean planar Ge quantum wells with hole mobilities exceeding one million and mean-free paths on the order of tens of microns already exist, such that gate-defined Ge hole channels may be able to overcome some of the problems caused by the presence of substantial disorder in more conventional Majorana platforms.