Ballistic Majorana nanowire devices

Abstract

Majorana modes are zero-energy excitations of a topological superconductor that exhibit non-Abelian statistics. Following proposals for their detection in a semiconductor nanowire coupled to an s-wave superconductor, several tunnelling experiments reported characteristic Majorana signatures. Reducing disorder has been a prime challenge for these experiments because disorder can mimic the zero-energy signatures of Majoranas, and renders the topological properties inaccessible. Here, we show characteristic Majorana signatures in InSb nanowire devices exhibiting clear ballistic transport properties. Application of a magnetic field and spatial control of carrier density using local gates generates a zero bias peak that is rigid over a large region in the parameter space of chemical potential, Zeeman energy and tunnel barrier potential. The reduction of disorder allows us to resolve separate regions in the parameter space with and without a zero bias peak, indicating topologically distinct phases. These observations are consistent with the Majorana theory in a ballistic system , and exclude the known alternative explanations that invoke disorder or a nonuniform chemical potential.

Real-space mapping of topological invariants using artificial neural networks

“…4(b). Such modulation is feasible by means of local gates in the experimental realizations involving semiconducting nanowires [15]. With such modulation, we observe the emergence of zero-energy modes in the local density of states [ Fig.…”

“…In particular, we consider a model Hamiltonian for electrons moving in a honeycomb lattice with Rashba spin-orbit coupling t R and offplane exchange B z , that is known to result in a two-dimensional quantum anomalous Hall state [58]: (15) where t R is the Rashba coupling, σ are the spin Pauli matrices, B z is the external Zeeman field, and τ i = ±1 is the sublattice operator. The first term is the usual tight-binding hopping term, the second one describes the Rashba interaction [58,59], and the third term is the so-called exchange or Zeeman term which couples to the spin degree of freedom.…”

“…We now move to apply our methodology to the system defined by Eq. (15). First, to train the neural network, we generate different spatially uniform Hamiltonians by choosing randomly each of the coupling parameters.…”

“…For every set of parameters, we built the Hamiltonian as in Eq. (15) and calculated the local density matrix for the central atom and its three first neighbors which are used as input of the network, in this case a 128-dimensional array. Again we chose having two hidden layers with 101 and 21 neurons.…”

“…This is the natural scenario in van der Waals heterostructures, where Moire patterns [9][10][11] could coexist with any topological state [12,13]. A more controlled situation is the proposals for topological superconductivity involving nanowires, where the topological state is controlled locally by electric gates [14,15]. Even though real-space formulations for the topological invariant do exist [16][17][18][19][20], their computation requires an integration over the whole space.…”