Majorana fermions in Ge/Si hole nanowires

Abstract

We consider Ge/Si core/shell nanowires with hole states coupled to an s-wave superconductor in the presence of electric and magnetic fields. We employ a microscopic model that takes into account material-specific details of the band structure such as strong and electrically tunable Rashba-type spin-orbit interaction and g factor anisotropy for the holes. In addition, the proximity-induced superconductivity Hamiltonian is derived starting from a microscopic model. In the topological phase, the nanowires host Majorana fermions with localization lengths that depend strongly on both the magnetic and electric fields. We identify the optimal regime in terms of the directions and magnitudes of the fields in which the Majorana fermions are the most localized at the nanowire ends. In short nanowires, the Majorana fermions hybridize and form a subgap fermion whose energy is split away from zero and oscillates as a function of the applied fields. The period of these oscillations could be used to measure the dependence of the spin-orbit interaction on the applied electric field and the g factor anisotropy.

Spin and charge signatures of topological superconductivity in Rashba nanowires

“…One of the hallmarks of such phases, in particular of topological superconductivity, are zero-energy modes such as Majorana fermions (MF) that emerge at the edges of the system. Various candidate materials can host such topological states [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but one of the most promising platforms are semiconducting nanowires of InAs or InSb material, with strong Rashba spin orbit interaction (SOI), subjected to an external magnetic field and in proximity to an s-wave superconductor [22,23]. Experimental evidence has been reported for topological phases in such wires [24][25][26][27][28][29][30][31] as well as in magnetic atomic chains on superconducting substrates [32][33][34].…”

Magnetic field evolution of spin blockade in Ge/Si nanowire double quantum dots

“…On the other hand, spin-orbit interaction is predicted 13 and suggested by experiments 14-17 to be strong in Ge/Si core/shell nanowires. This offers a path to electrical spin manipulation 18,19 , as well as to realizing Majorana fermions [20][21][22][23] .In this work we perform transport measurements on electrostatically defined double quantum dots 2 made in Ge/Si core/shell nanowires, and detect Pauli spin blockade at several charge degeneracy points. We expand and adapt a previously developed rate equation model to analyze the magnetic-field evolution of the leakage current 24 .…”

“…On the other hand, spin-orbit interaction is predicted 13 and suggested by experiments [14][15][16][17] to be strong in Ge/Si core/shell nanowires. This offers a path to electrical spin manipulation 18,19 , as well as to realizing Majorana fermions [20][21][22][23] .…”

Strong confinement-induced engineering of the g factor and lifetime of conduction electron spins in Ge quantum wells

“…Cubic- k terms have been shown to dominate the k · p SOI Hamiltonian of two-dimensional hole gases33. Electric-field-induced tuning of the hole g factor34 has been reported in hybrid devices made from superconductors and self-assembled nanocrystals35, while core–shell Ge/Si nanowires36 have been envisioned as hosts for Majorana fermions37.…”