Session B18: Spin-orbit and Superconductivity: Majorana Modes

Quantized Conductance in InSb nanowires at zero magnetic field

We present measurements of InSb nanowires in the ballistic transport regime. In 1D materials such as nanowires, electron scattering has an increased chance of back-reflection, obscuring the observation of quantized conductance at low magnetic fields. By improving the contacts to the nanowire as well as its dielectric environment backscattering events are minimized and conductance quantization is observable at zero magnetic field with high device yield. We study the evolution of individual sub-bands in an external magnetic field, observing a degeneracy between the 2\textsuperscript{nd} and 3\textsuperscript{rd} sub-band when the magnetic field is orientated perpendicular to the nanowire axis.   

Majorana fermions in charge carrier hole quantum wires

In order to realize Majorana fermions in a hybrid semiconductor- superconductor structure, spin helical order is needed, which prevents “fermion doubling”. A natural proposal for Majarana fermion setting is to utilize charge carrier hole systems, which have strong spin orbit couplings that can result in a spin helix. In this work, we demonstrate that transformation of heavy holes into light holes and vice versa upon reflection from the heterostructure boundaries crucially affects Luttinger hole spectrum in low dimensions, and most importantly, spin-orbit interactions in the ground sub-band of a hole quantum wire. Spin orbit interactions are dominated by several terms linear in the hole momentum. We show that the criterion for realizing proximity-induced topologically non-trivial superconducting phase and zero Majorana modes in a hole wire is similar to that for electrons, but an extra constraint should be satisfied. Due to their stronger spin-orbit coupling, the hole systems can be promising settings to study Majorana fermions experimentally.   

Majorana modes in InSb nanowires (II): resolving the topological phase diagram

Majorana modes in hybrid superconductor-semiconductor nanowire devices can be probed via tunnelling spectroscopy which shows a zero bias peak (ZBP) in differential conductance (1). Majoranas are formed when the Zeeman energy $E_Z$ and the chemical potential $\mu$ satisfy the condition $E_Z>\sqrt{\Delta^2+\mu^2}$, with $\Delta$ the superconducting gap. This Majorana condition outlines the topologically non-trivial phase and predicts a particular dependence of ZBPs on the gate voltage and the external magnetic field. In this talk we show that the magnetic field range of ZBPs can be tuned by gate voltage and vice versa, consistent with these Majorana predictions. Supported by measurements in different external magnetic field orientations, these observations pave the way for exploring the topological phase diagram of spin-orbit coupled semiconductor nanowires with induced superconductivity. \\ (1) V. Mourik, K. Zuo et al, \emph{Science} \textbf{336}, 1003 (2012)   

Majorana modes in InSb nanowires (I): zero bias peaks in hybrid devices with low-disorder and hard induced superconducting gap

Majorana modes in hybrid superconductor-semiconductor nanowire devices can be probed via tunnelling spectroscopy which shows a zero bias peak (ZBP) in differential conductance (1). However, alternative mechanisms such as disorder or formation of quantum dots can also give rise to ZBPs, and obscure experimental studies of Majoranas. Further, a soft induced superconducting gap commonly observed in experiments presents an outstanding challenge for the demonstration of their topological protection. In this talk we show that with device improvements, we reach low-disorder transport regime with clear quantized conductance plateaus and Andreev enhancement approaching the theoretical limit. Tunnelling spectroscopy shows a hard induced superconducting gap and no formation of quantum dots. Together with extremely stable ZBPs observed in large gate voltage and magnetic field ranges, we exclude various alternative theories besides the formation of localized Majorana modes for our observations. \\ (1) V. Mourik, K. Zuo et al, \emph{Science} \textbf{336}, 1003 (2012)   

Investigation of semiconductor nanowires with shadow-evaporated epitaxial superconducting shells

We report progress on epitaxially grown InAs/Al core/shell nanowire heterostructures by molecular beam epitaxy with junctions in the Al shells formed in-situ by a crossed wire shadowing method during growth. Such wires allow the creation of superconductor-normal-superconductor (SNS) junctions with high quality superconductor-semiconductor interfaces without introducing damage in the junction by etching the Al. Shadowing is accomplished by a two-step growth process in which the nanowire growth direction is changed resulting in crossed networks of nanowires which shadow one another from the Al flux. We observe hard superconducting gaps and supercurrents in excess of 50 nA with in-plane critical fields above 1 T. We compare our results with shadowed devices to previous data from SNS junctions with wet-etched shells. Our experiments indicate that this crossed wire shadowing technique provides an interesting route to investigating induced superconductivity in semiconductor nanowires.   

Wireless Majorana Fermions: From Magnetic Tunability to Braiding

We propose a versatile platform to investigate the existence of zero-energy Majorana fermions (MFs) and their non-Abelian statistics through braiding [1]. This implementation combines a two-dimensional electron gas formed in a semiconductor quantum well grown on the surface of an $s$-wave superconductor, with a nearby array of magnetic tunnel junctions (MTJs). The underlying magnetic textures produced by MTJs provide highly-controllable topological phase transitions to confine and transport MFs in two dimensions, overcoming the requirement for a network of wires.\\ &[1&] G. Fatin, A. Matos-Abiague, B. Scharf, and I. \v{Z}uti\'c, arXiv e-prints (2015), arXiv:1510.08182v1.   

Spin-Orbit Coupling in Hybrid Semiconductor Structures: From Majorana Fermions to Topological Insulators

Hybrid semiconductor structures with strong spin-orbit coupling are responsible for many fascinating phenomena. Topological states in systems of reduced dimensionality, in particular, offer many intriguing possibilities, both for fundamental research as well as for potential applications. In this talk, we describe the importance of the interplay of spin-orbit coupling (SOC) and the sample geometry in realizing exotic Majorana fermions (MFs) in quantum dots and rings and discuss several schemes to detect MFs [1]. An effective SOC from the magnetic textures provided by magnetic tunnel junctions could enable a versatile control of MFs and their adiabatic exchange [2]. We show that in 2D topological insulators (TIs), such as inverted HgTe/CdTe QWs, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field above which only quantum Hall (QH) states can be found [3]. We propose magneto-optical absorption measurements to probe the magnetic-field induced transition between the QSH and QH regimes. This measurement scheme is robust against perturbations such as additional SOC due to bulk or structure-inversion asymmetry [4]. Finally, tunnel junctions based on the surfaces of 3D TIs are presented. These junctions can exhibit giant tunneling anomalous Hall (TAH) currents and negative differential TAH conductance, which makes them an attractive and versatile system for spintronic applications [5]. [1] B. Scharf and I. Zutic, PRB \textbf{91}, 144505 (2015). [2] G. L. Fatin et al., arXiv:1510.08182. [3] B. Scharf et al., PRB \textbf{86}, 075418 (2012). [4] B. Scharf, et al., PRB \textbf{91}, 235433 (2015). [5] B. Scharf et al, preprint.   

Wavefunction oscillations and fermion parity crossings in disordered Majorana wire

We study aspects of decay and oscillations of Majorana wavefunctions in one dimensional topological superconducting chains, by employing Majorana transfer matrix technique. The phase transition separating the trivial phase and the topological phase associated with the Majorana end modes can be traced to the cancellation of the two parts (‘superconducting’ and ‘normal’) of the Lyapunov exponent of the transfer matrix. We find that the Majorana oscillations and related fermion parity flips can be completely determined by an underlying non-superconducting tight-binding model. Using this observation we pinpoint the behavior of Majorana mode oscillations within the topological phase diagram. For a disordered wire, these band oscillations are completely washed out, leading to a second localization length for the Majorana mode. The remnant oscillations are however manifested and completely randomized by disorder effects. As a result, the associated fermion parity flips depend heavily on the average of the disorder distribution and the number of lattice sites of the chain. We show that the transfer matrix technique offers a simple way of understanding the known log-normal distribution of mid-gap Majorana states.   

Interfacial spin-orbit fields in ferromagnet/normal metal (FN) and ferromagnet/superconductor (FS) systems

Breaking of space-inversion symmetry at interfaces induces spin-orbit fields as an emergent phenomenon. Interfacial spin-orbit fields are believed to enable a wealth of new phenomena, not existent or fragile in the bulk, such as the tunneling anisotropic magnetoresistance (TAMR), interfacial spin-orbit torques, Skyrmions, or possible realization of topological superconductors. We theoretically investigate spin-polarized transport in FN and FS junctions in the presence of Rashba and Dresselhaus interfacial spin-orbit fields. The interplay of magnetism and spin-orbit fields leads to a marked magnetoanisotropy of the conductances. Remarkably, the anisotropy in FS systems---magnetoanisotropic Andreev reflection (MAAR)---is giant compared to TAMR, its normal-state counterpart in FN junctions [1]. We further report on the dependence of spin-flip probability currents on characteristic system parameters [2].\newline [1] P. H\"{o}gl, A. Matos-Abiague, I. \v{Z}uti\'c, J. Fabian, Phys. Rev. Lett. \textbf{115}, 116601 (2015)\newline [2] A. M. Kamerbeek, P. H\"{o}gl, J. Fabian, T. Banerjee, Phys. Rev. Lett. \textbf{115}, 136601 (2015)   

An exactly solvable model for a strongly spin-orbit-coupled nanowire quantum dot

In the presence of spin-orbit coupling, quantum models for semiconductor materials are generally not exactly solvable. As a result, understanding of the strong spin-orbit coupling effects in these systems remains incomplete. Here we develop a method to solve exactly the one-dimensional hard-wall quantum dot problem for a single electron in the presence of a strong spin-orbit coupling and a finite magnetic field. This method allows us to obtain the exact eigenenergies and eigenstates for the single electron. With the help of this solution, we demonstrate unique effects from the strong spin-orbit coupling in a semiconductor quantum dot, in particular the anisotropy of the electron g-factor and its tunability.   

Charge instability in double quantum dots in Ge/Si core/shell nanowires

Controlling dephasing times are of great challenge in the studies of spin qubit. Reported long spin coherence time and predicted strong spin-orbit interaction of holes in Ge/Si core/shell nanowires, as well as their weak coupling to very few nuclear spins of these group IV semiconductors, persuade electrical spin control. We have established Pauli spin blockade in gate-tunable quantum dots formed in these nanowires. The g-factor has been measured and evidence of spin-orbit interaction has been observed in the presence of magnetic field. However, electrical control of spins requires considerable stability in the double dot configuration, and imperfectly these dots suffer from poor stability. We report on fabrication modifications on Ge/Si core/shell nanowires, as well as measurement techniques to suppress the charge instabilities and ease the way to study spin-orbit coupling and resolve electric dipole spin resonance.   

Spin transistor based on pure nonlocal Andreev reflection in EuO-graphene/superconductor/EuO-graphene nanostructure

In graphene-magnetic-insulator hybrid structure such as graphene-Europium-oxide, proximity induced exchange interaction opens up a spin-dependent bandgap and spin splitting in the Dirac band. We show that such band topology allows pure crossed Andreev reflection to be generated exclusively without the parasitic local Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi levels. We model the charge transport in an EuO-graphene/superconductor/EuO-graphene three-terminal device and found that the pure non-local conductance exhibits rapid on/off switching characteristic with a minimal subthreshold swing of $\sim 20$ mV. Non-local conductance oscillation is observed when the Fermi levels in the superconducting lead is varied. The oscillatory behavior is directly related to the quasiparticle propagation in the superconducting lead and hence can be used as a tool to probe the subgap quasiparticle mode in superconducting graphene. The non-local current is 100\% spin-polarized and is highly tunable in our proposed device. This opens up the possibility of highly tunable graphene-based spin transistor that operates purely in the non-local transport regime.