Jascha Ulrich

Probing variations of the Rashba spin-orbit coupling at the nanometre scale

Scanning tunnelling spectroscopy provides access to the spatial variations in the strength of Rashba spin–orbit coupling in a two-dimensional electron system, with local fluctuations shown to cause spin dephasing. As the Rashba effect is an electrically tunable spin–orbit interaction1, it could form the basis for a multitude of applications2,3,4, such as spin filters3, spin transistors5,6 and quantum computing using Majorana states in nanowires7,8. Moreover, this interaction can determine the spin dephasing9 and antilocalization phenomena in two dimensions10. However, the real space pattern of the Rashba parameter, which critically influences spin transistors using the spin-helix state6,11,12 and the otherwise forbidden electron backscattering in topologically protected channels13,14, is difficult to probe. Here, we map this pattern down to nanometre length scales by measuring the spin splitting of the lowest Landau level using scanning tunnelling spectroscopy. We reveal strong fluctuations correlated with the local electrostatic potential for an InSb inversion layer with a large Rashba coefficient (∼1 eV A). This type of Rashba field mapping enables a more comprehensive understanding of its fluctuations, which might be decisive towards robust semiconductor-based spintronic devices.

Majorana-assisted nonlocal electron transport through a floating topological superconductor

The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies have required the presence of an additional global charging energy. Adding nonlocal terms in the form of a global charging energy to the Hamiltonian when testing the intrinsic nonlocality of the Majorana modes seems to be conceptually troublesome. Here, we show that a floating superconductor allows to observe nonlocal current correlations in the absence of charging energy. We show that the non-interacting and the Coulomb-blockade regime have the same peak conductance

Spectral properties and local density of states of disordered quantum Hall systems with Rashba spin-orbit coupling

e^2/h

Supersymmetry in the Majorana Cooper-pair box

but different shot-noise power; while the shot noise is sub-Poissonian in the Coulomb-blockade regime in the large bias limit, Poissonian shot noise is generically obtained in the non-interacting case.

Dual approach to circuit quantization using loop charges

We theoretically investigate the spectral properties and the spatial dependence of the local density of states (LDoS) in disordered two-dimensional electron gases (2DEG) in the quantum Hall regime, taking into account the combined presence of electrostatic disorder, random Rashba spin-orbit in- teraction, and finite Zeeman coupling. To this purpose, we extend a coherent-state Greens function formalism previously proposed for spinless 2DEG in the presence of smooth arbitrary disorder, that here incorporates the nontrivial coupling between the orbital and spin degrees of freedom into the electronic drift states. The formalism allows us to obtain analytical and controlled nonperturbative expressions of the energy spectrum in arbitrary locally flat disorder potentials with both random electric fields and Rashba coupling. As an illustration of this theory, we derive analytical microscopic expressions for the LDoS in different temperature regimes which can be used as a starting point to interpret scanning tunneling spectroscopy data at high magnetic fields. In this context, we study the spatial dependence and linewidth of the LDoS peaks and explain an experimentally-noticed correlation between the spatial dispersion of the spin-orbit splitting and the local extrema of the potential landscape.

Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high-energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4π-periodic Majorana-Josephson coupling realizes supersymmetry for a certain characteristic ratio of the conventional Josephson to the Majorana-Josephson coupling strength. The supersymmetry we find is a “hidden” minimally bosonized supersymmetry that provides a nontrivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of a Majorana-Josephson coupling of the characteristic strength.

Universal power-law decay of electron-electron interactions due to nonlinear screening in a Josephson junction array

The conventional approach to circuit quantization is based on node fluxes and traces the motion of node charges on the islands of the circuit. However, for some devices, the relevant physics can be best described by the motion of polarization charges over the branches of the circuit that are in general related to the node charges in a highly nonlocal way. Here, we present a method, dual to the conventional approach, for quantizing planar circuits in terms of loop charges. In this way, the polarization charges are directly obtained as the differences of the two loop charges on the neighboring loops. The loop charges trace the motion of fluxes through the circuit loops. We show that loop charges yield a simple description of the flux transport across phase-slip junctions. We outline a concrete construction of circuits based on phase-slip junctions that are electromagnetically dual to arbitrary planar Josephson junction circuits. We argue that loop charges also yield a simple description of the flux transport in conventional Josephson junctions shunted by large impedances. We show that a mixed circuit description in terms of node fluxes and loop charges yields an insight into the flux decompactification of a Josephson junction shunted by an inductor. As an application, we show that the fluxonium qubit is well approximated as a phase-slip junction for the experimentally relevant parameters. Moreover, we argue that the

Changing anyonic ground degeneracy with engineered gauge fields

0\ensuremath{-}\ensuremath{\pi}

Probing the Nodal Structure of Landau Level Wave Functions in Real Space

qubit is effectively the dual of a Majorana Josephson junction.

Large impedances and Majorana bound states in superconducting circuits

Supersymmetries in quantum mechanics offer a way to obtain degeneracies in the excitation spectrum which do not originate from selection rules. The mechanism behind the degeneracies is the same as the one that leads to the miraculous cancellations of divergences in supersymmetric field theories found in the high energy physics context. Even though of importance, there is up to now no realistic proposal of non-integrable systems that show level degeneracies due to a supersymmetric structure. Here, we propose an implementation of a quantum-mechanical supersymmetry in a Cooper-pair box shunted by a Josephson junction rhombus which is effectively