Strongly Interacting Holes in Ge/Si Nanowires

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

Quantum criticality with multiple dynamics

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).Comment: 8 pages including supplementary material. Minor changes as compared to the previous versio

Quantum Critical Matter: Quantum Phase Transitions with Multiple Dynamics and Weyl Superconductors

In this PhD thesis, the physics of quantum critical matter and exotic quantum state close to quantum phase transitions is investigated. We will focus on three different examples that highlight some of the interesting phenomena related to quantum phase transitions. Firstly, we discuss the physics of quantum phase transitions in quantum wires as a function of an external gate voltage when new subbands are activated. We find that at these transitions, strong correlations lead to the formation of an impenetrable gas of polarons, and identify criteria for possible instabilities in the spin- and charge sectors of the model. Our analysis is based on the combination of exact resummations, renormalization group techniques and Luttinger liquid approaches. Secondly, we turn to the physics of multiple divergent time scales close to a quantum critical point. Using an appropriately generalized renormalization group approach, we identify that the presence of multiple dynamics at a quantum phase transition can lead to the emergence of new critical scaling exponents and thus to the breakdown of the ususal scaling schemes. We calculate the critical behavior of various thermodynamic properties and detail how unusual physics can arise. It is hoped that these results might be helpful for the interpretation of experimental scaling puzzles close to quantum critical points. Thirdly, we turn to the physics of topological transitions, and more precisely the physics of Weyl superconductors. The latter are the superconducting variant of the topologically non-trivial Weyl semimetals, and emerge at the quantum phase transition between a topological superconductor and a normal insulator upon perturbing the transition with a time reversal symmetry breaking perturbation, such as magnetism. We characterize the topological properties of Weyl superconductors and establish a topological phase diagram for a particular realization in heterostructures. We discuss the physics of vortices in Weyl superconductors, and establish under which conditions they can trap zero energy Majorana modes. Our disucssion ends with some remarks on possible experimental signatures

Helical nuclear spin order in a strip of stripes in the Quantum Hall regime

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.Comment: 16+ pages, 6 figures, updated reference

Low-energy properties of fractional helical Luttinger liquids

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.Comment: 9 pages, 4 figures. Final versio

Impurity Induced Quantum Phase Transitions and Magnetic Order in Conventional Superconductors: Competition between Bound and Quasiparticle states

We theoretically study bound states generated by magnetic impurities within conventional $s$-wave superconductors, both analytically and numerically. In determining the effect of the hybridization of two such bound states on the energy spectrum as a function of magnetic exchange coupling, relative angle of magnetization, and distance between impurities, we find that quantum phase transitions can be modulated by each of these parameters. Accompanying such transitions, there is a change in the preferred spin configuration of the impurities. Although the interaction between the impurity spins is overwhelmingly dominated by the quasiparticle contribution, the ground state of the system is determined by the bound state energies. Self-consistently calculating the superconducting order parameter, we find a discontinuity when the system undergoes a quantum phase transition as indicated by the bound state energies.Comment: 8 pages, 7 figure

Missing Shapiro steps and the 8π8\pi-periodic Josephson effect in interacting helical electron systems

Two-particle backscattering in time-reversal invariant interacting helical electron systems can lead to the formation of quasiparticles with charge $e/2$. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of $e/2$ charges leads to an $8 \pi$-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle backscattering to be a sub-leading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.Comment: 9 pages, 5 figures. A new submission extending and expanding our analysis in arXiv:1507.08881. (v2) References adde

Superconducting Gap Renormalization around two Magnetic Impurities: From Shiba to Andreev Bound States

We study the renormalization of the gap of an s-wave superconductor in the presence of two magnetic impurities. For weakly bound Shiba states, we analytically calculate the part of the gap renormalization that is sensitive to the relative orientation of the two impurity spins. For impurities with a strong exchange coupling to the conduction electrons, we solve the gap equation self-consistently by numerics and find that the sub-gap Shiba state turns into a supra-gap Andreev state when the local gap parameter changes sign under the impurities.Comment: 6 pages, 4 figures - final versio