Enhanced orbital magnetic field effects in Ge hole nanowires

Abstract

Hole semiconductor nanowires (NW) are promising platforms to host spin qubits and Majorana bound states for topological qubits because of their strong spin-orbit interactions (SOI). The properties of these systems depend strongly on the design of the cross section and on strain, as well as on external electric and magnetic fields. In this work, we analyze in detail the dependence of the SOI and $g$ factors on the orbital magnetic field. We focus on magnetic fields aligned along the axis of the NW, where orbital effects are enhanced and result in a renormalization of the effective $g$ factor up to $400\%$, even at small values of magnetic field. We provide an exact analytical solution for holes in Ge NWs and we derive an effective low-energy model that enables us to investigate the effect of electric fields applied perpendicular to the NW. We also discuss in detail the role of strain, growth direction, and high energy valence bands in different architectures, including Ge/Si core/shell NWs, gate-defined one-dimensional channels in planar Ge, and curved Ge quantum wells. In core/shell NWs grown along the $[110]$ direction the $g$ factor can be twice larger than for other growth directions which makes this growth direction advantageous for Majorana bound states. Also curved Ge quantum wells feature large effective $g$ factors and SOI, again ideal for hosting Majorana bound states. Strikingly, because these quantities are independent of the electric field, hole spin qubits encoded in curved quantum wells are to good approximation not susceptible to charge noise, significantly boosting their coherence time.

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• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• High-fidelity spin qubit shuttling via large spin-orbit interaction
• Phase driving hole spin qubits
• Majorana zero modes in gate-defined germanium hole nanowires
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Germanium-based hybrid semiconductor-superconductor topological quantum computing platforms: Disorder effects
• Interband contributions to nonlinear transport in semiconductor nanostructures
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential
• Electrical Interconnects for Silicon Spin Qubits
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Finite Length Effects and Coulomb Interaction in Ge Quantum Well-Based Josephson Junctions Probed with Microwave Spectroscopy
• Rashba spin-orbit coupling and artificially engineered topological superconductors