Tobias Meng

We consider holes confined to Ge/Si core/shell nanowires subject to strong Rashba spin-orbit interaction and screened Coulomb interaction. Such wires can, for instance, serve as host systems for Majorana bound states. Starting from a microscopic model, we find that the Coulomb interaction strongly influences the properties of experimentally realistic wires. To show this, a Luttinger liquid description is derived based on a renormalization group analysis. This description in turn allows to calculate the scaling exponents of various correlation functions as a function of the microscopic system parameters. It furthermore permits to investigate the effect of Coulomb interaction on a small magnetic field, which opens a strongly anisotropic partial gap.

We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin order, for instance for the resistivity of the system at transitions between different quantum Hall plateaus.

We study the nuclear spin relaxation in a ballistic nanowire with hyperfine and Rashba spin-orbit interactions (SOI) and in the presence of magnetic field and electron interactions. The relaxation rate shows pronounced peaks as function of magnetic field and chemical potential due to van Hove singularities in the Rashba bands. As a result, the regimes of weak and strong SOIs can be distinguished by the number of peaks in the rate. The relaxation rate increases with increasing magnetic field if both Rashba subbands are occupied, whereas it decreases if only the lowest one is occupied.

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of e/2, giving rise to a Josephson current with 8π periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as Z₄ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems.

We discuss how electron-electron interactions renormalize the spin-orbit induced anticrossings between different subbands in ballistic quantum wires. Depending on the ratio of spin-orbit coupling and subband spacing, electron-electron interactions can either increase or decrease anticrossing gaps. When the anticrossings are closing due to a special combination of Rashba and Dresselhaus spin-orbit couplings, their gap approaches zero as an interaction dependent power law of the spin-orbit couplings, which is a consequence of Luttinger liquid physics. Monitoring the closing of the anticrossings allows to directly measure the related renormalization group scaling dimension in an experiment. If a magnetic field is applied parallel to the spin-orbit coupling direction, the anticrossings experience different renormalizations. Since this difference is entirely rooted in electron-electron interactions, unequally large anticrossings also serve as a direct signature of Luttinger liquid physics. Electron-electron interactions furthermore increase the sensitivity of conductance measurements to the presence of anticrossing.

We investigate the low-energy properties of (quasi) helical and fractional helical Luttinger liquids. In particular, we calculate the Drude peak of the optical conductivity, the density of states, as well as charge transport properties of the interacting system with and without attached Fermi liquid leads at small and large (compared to the gap) frequencies. For fractional wires, we find that the low energy tunneling density of states vanishes. The conductance of a fractional helical Luttinger liquid is non-integer. It is independent of the Luttinger parameters in the wire, despite the intricate mixing of charge and spin degrees of freedom, and only depends on the relative locking of charge and spin degrees of freedom.

Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, k_F ≈ k_SO. We show that this regime is characterized by a strongly anisotropic electron spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low frequency spin fluctuations along this direction. Since the spin response in the gapless regime k_F not ≈ k_SO has a power law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insensitive conductance measurements.

In quantum wires, the hyperfine coupling between conduction electrons and nuclear spins can lead to a (partial) ordering of both of them at low temperatures. By an interaction-enhanced mechanism, the nuclear spin order, caused by RKKY exchange, acts back onto the electrons and gaps out part of their spectrum. In wires with two subbands characterized by distinct Fermi momenta k_F1 and k_F2, the nuclear spins form a superposition of two helices with pitches π/k_F1 and π/k_F2, thus exhibiting a beating pattern. This order results in a reduction of the electronic conductance in two steps upon lowering the temperature.

Quantum critical systems with multiple dynamics possess not only one but several time scales, tau_i ~ xi^z_i, which diverge with the correlation length xi. We investigate how scaling predictions are modified for the simplest case of multiple dynamics characterized by two dynamical critical exponents, z_> and z_<. We argue that one should distinguish the case of coupled and decoupled multiple dynamic scaling depending on whether there exists a scaling exponent which depends on both z_i or not. As an example, we study generalized Phi^4-theories with multiple dynamics below their upper critical dimension, d+z_<<4. We identify under which condition coupled scaling is generated. In this case the interaction of quantum and classical fluctuations leads to an emergent dynamical exponent, z_e=z_>/(nu (z_>-z_<)+1).

We study the physics of the superconducting variant of Weyl semimetals, which may be realized in multilayer structures comprising topological insulators and superconductors. We show how superconductivity splits each Weyl node into two. The resulting Bogoliubov Weyl nodes can be pairwise independently controlled, allowing to access a set of phases characterized by different numbers of bulk Bogoliubov Weyl nodes and chiral Majorana surface modes. We analyze the physics of vortices in such systems, which trap zero energy Majorana modes only under certain conditions. We finally comment on possible experimental probes, thereby also exploiting the similarities between Weyl superconductors and 2-dimensional p+ip superconductors.

We study a carbon nanotube quantum dot embedded into a SQUID loop in order to investigate the competition of strong electron correlations with proximity effect. Depending whether local pairing or local magnetism prevails, a superconducting quantum dot will respectively exhibit positive or negative supercurrent, referred to as a 0 or $\pi$ Josephson junction. In the regime of strong Coulomb blockade, the 0 to $\pi$ transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at larger tunneling amplitude the Kondo effect develops for an odd charge (magnetic) dot in the normal state, and quenches magnetism. In this situation, we find that a first order 0 to $\pi$ quantum phase transition can be triggered at fixed valence when superconductivity is brought in, due to the competition of the superconducting gap and the Kondo temperature. The SQUID geometry together with the tunability of our device allows the exploration of the associated phase diagram predicted by recent theories. We also report on the observation of anharmonic behavior of the current-phase relation in the transition regime, that we associate with the two different accessible superconducting states. Our results ultimately reveal the spin singlet nature of the Kondo ground state, which is the key process in allowing the stability of the 0-phase far from the mixed valence regime.

We consider electrons in a quantum wire interacting via a long-range Coulomb potential screened by a nearby gate. We focus on the quantum phase transition from a strictly one-dimensional to a quasi-one-dimensional electron liquid, that is controlled by the dimensionless parameter $n x_0$, where $n$ is the electron density and $x_0$ is the characteristic length of the transverse confining potential. If this transition occurs in the low-density limit, it can be understood as the deformation of the one-dimensional Wigner crystal to a zigzag arrangement of the electrons described by an Ising order parameter. The critical properties are governed by the charge degrees of freedom and the spin sector remains essentially decoupled. At large densities, on the other hand, the transition is triggered by the filling of a second one-dimensional subband of transverse quantization. Electrons at the bottom of the second subband interact strongly due to the diverging density of states and become impenetrable. We argue that this stabilizes the electron liquid as it suppresses pair-tunneling processes between the subbands that would otherwise lead to an instability. However, the impenetrable electrons in the second band are screened by the excitations of the first subband, so that the transition is identified as a Lifshitz transition of impenetrable polarons. We discuss the resulting phase diagram as a function of $n x_0$.

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent Numerical Renormalization Group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as STM measurements on carbon nanotubes, or radiative emission in optical quantum dots.

Threshold photoemission excited by polarization-modulated ultraviolet femtosecond laser light is exploited for phase-sensitive detection of magnetic circular dichroism (MCD) for a magnetite thin film. Magnetite (Fe₃O₄) shows a magnetic circular dichroism of approx. (4.5 ± 0.3) x 10^-3 for perpendicularly incident circularly polarized light and a magnetization vector switched parallel and antiparallel to the helicity vector by an external magnetic field. The asymmetry in threshold photoemission is discussed in comparison to the magneto-optical Kerr effect. The optical MCD contrast in threshold photoemission will provide a basis for future laboratory photoemission studies on magnetic surfaces.