Realizing topological superconductivity with superlattices

Abstract

The realization of topological superconductors (SCs) in one or two dimensions is a highly pursued goal. Prominent proposed realization schemes include semiconductor/superconductor heterostructures and set stringent constraints on the chemical potential of the system. However, the ability to keep the chemical potential in the required range while in the presence of an adjacent SC and its accompanied screening effects, is a great experimental challenge. In this work, we study a SC lattice structure in which the SC is deposited periodically on a one-or two-dimensional sample. We demonstrate that this realization platform overcomes the challenge of controlling the chemical potential in the presence of the superconductor's electrostatic screening. We show how Majorana bound states emerge at the ends of a one-dimensional system proximity coupled to a one-dimensional SC lattice, and move on to present a SC-lattice-based realization of the two-dimensional px + ipy SC, hosting chiral Majorana modes at its edges. In particular, we establish that even when assuming the worst case of absolute screening, in which the chemical potential under the SC is completely unaffected by the external gate potential, the topological phase can be reached by tuning the chemical potential in the area not covered by the SC. Finally, we briefly discuss possible effects of Coulomb blockade on the properties of the system.

Effects of the electrostatic environment on superlattice Majorana nanowires

“…In this work we have analysed in detail the proposal of Levine et al 36 to look for topological superconductivity in Majorana nanowires in which the induced superconductivity is achieved by proximity to a superlattice of SC fingers (instead of having the SC cover continuously the length of the semiconducting wire). This configuration can have practical benefits to manipulate the Majorana wave function and to measure it.…”

“…However, the top-superlattice setup develops larger topological regions and they are present for the two values For small L cell sizes the topological phase is more stable, meaning that there are no trivial holes. This is so because for small and short potential oscillations the electrons in the wire feel an effective homogeneous potential 36 . Moreover, the performance of both setups (top and bottom) is comparable, although the back gate voltages needed for the bottom one are much larger.…”

“…We exploit the periodic nature of this Hamiltonian to build the infinite 1D Hamiltonian in k-space H(k), as explained in Ref. 36. From there, we can compute the class D topological invariant 36 The calculations shown in the main text have been performed using the Thomas-Fermi approximation for the charge density inside the wire.…”

“…36. From there, we can compute the class D topological invariant 36 The calculations shown in the main text have been performed using the Thomas-Fermi approximation for the charge density inside the wire. However, a more realistic and complete description consists of solving the coupled Schrödinger-Poisson equations, which requires to compute the charge density from the eigenspectrum of the Hamiltonian…”

“…In this case 36 , the topological phase diagram becomes more complex than for the uniformly covered nanowire (due to the presence of longitudinal minibands created by the periodicity of the system), and extends over a wider region in parameter space (to lower Zeeman fields and higher values of the chemical potential). Levine et al 36 considered a minimal 1D model for the nanowire superstructure, in a similar fashion to other previous studies [37][38][39][40] with related periodic structures. However, in the last couple of years it has been shown that the electrostatic environment and the three-dimensionality of these wires play an important role in all aspects concern-ing the trivial/topological phases and the appearance of MBSs.…”