Dynamics and disorder at the Kosterlitz-Thouless transition

This thesis describes theoretical investigations into the dynamics of superfluid films and the effects of disorder on the roughening transition of crystal surfaces. The dynamic theory of superfluid helium films, due to Ambegaokar et al., is refined to improve the precision of the predictions made. A detailed comparison is made between the predictions of the modified theory and the results from experiments on helium films and on superconducting systems. It is found that, despite the modifications in the theory, agreement with experiments on helium films remains only qualitative. Consideration is then given to the effects on the roughening transition of disorder arising from screw dislocations. A crystal surface which is threaded by screw dislocation pairs may be in one of three different states depending on the temperature of the system and the way in which screw pairs are distributed. At high temperatures the interface is rough: it is not pinned to the lattice. At low temperatures the state of the interface depends on how the screw dislocations are distributed: when distributed as closely spaced pairs they lead to a faceted state with a single ground state energy; when distributed randomly they lead to a state of the interface which, though pinned to the underlying crystal lattice, has a degenerate ground state. It is then shown that the dynamic sine-Gordon formulation of the roughening transition can be used, via a Hubbard-Stratonovich transformation, to model the dynamic behaviour of superfluid systems. This method provides a re-normalization group framework within which the a.c. linear response can be studied. The ways in which the approach could be extended to study the effects of disorder and atomic layering are also discussed

A Study of Magnetism and Possible Mixed-State Superconductivity in Phosphorus-Doped Graphene

Evidence of superconducting vortices, and consequently mixed-state superconductivity, has been observed in phosphorus-doped graphene at temperatures as high as 260 K. The evidence includes transport measurements in the form of resistance versus temperature curves, and magnetic measurements in the form of susceptibility and magnetic Nernst effect measurements. The drops in resistance, periodic steps in resistance, the appearance of Nernst peaks and hysteresis all point to phosphorus-doped graphene having a broad resistive region due to flux flow as well as a Berezinskii-Kosterlitz-Thouless (BKT) transition at lower temperatures. The observation of irreversible behavior in phosphorus-doped graphene under the influence of a thermal gradient and an orthogonal applied magnetic field is a direct sign of mixed-state superconductivity, as it demonstrates the presence of vortices. The observations are based on cyclic Nernst measurements that show clear hysteresis that diminishes as the sample is warmed to temperatures higher than 200 K; voltage steps and anomalous structures related to field screening are observed at temperatures below 70 K; and finally, smaller Nernst peaks are seen at temperatures near 230 K pointing to vortex stacks having a high depinning and thermal energies

Study of Charge Carrier Transport in Graphene and Graphite as Two Dimensional and Quasi-Two Dimensional Materials and Their Interfaces

Evidence of superconductivity in phosphorous-doped graphite and graphene has been observed at temperatures in the vicinity of 260 K. This evidence includes transport current, magnetic susceptibility, Hall and Nernst measurements. All of these measurements indicate a transition of a type II superconductor without a phase of type I until below the limits of the measurement capabilities. Vortex states are inferred from periodically repeated steps in the R vs. T characteristics of Highly Oriented Pyrolytic Graphite and exfoliated doped multilayer graphene. The presence of vortices has been confirmed with thermal gradient driven Nernst measurements. Magnetic susceptibility measurements have shown results qualitatively similar to those expected (and experimentally observed by others) for ultra-thin films (thickness \u3c\u3c the London penetration depth). The magnetic susceptibility is negative for field-cooled and zero-field-cooled measurements. The susceptibility for field-cooled and zero-field-cooled measurements begin to diverge at approximately 260 K. Hall effect measurements show a sign reversal in the Hall voltage as the temperature is reduced from 300 K to 78 K. The Nernst effect confirms a Berezinskii-Kosterlitz-Thouless (BKT) vortex transition at T~ 40 K and several pinned vortices’ melting temperatures which correlate with the resistive measurements. Finally, in completeness, we have observed a charge BKT transition at T~ 4 K in both susceptibility and resistive measurements, and a vortex BKT transition in both the resistive, Nernst, and susceptibility measurements at T~ 40 K

Non-thermal fixed points and superfluid turbulence in ultracold quantum gases

In this thesis the non-equilibrium dynamics of ultracold quantum gases is studied numerically and analytically in one, two, and three spatial dimensions. We focus on the regime of large occupation numbers, where the system can be described by an ensemble of non-linear waves. A goal of this work is to investigate the existence of non-thermal fixed points in the dynamics of ultracold Bose gases. It is shown that a two- or three-dimensional Bose gas features a non-thermal fixed point which is characterised by a dilute random distribution of vortices or vortex lines. This state is accompanied by particle and energy fluxes and decays via the formation of vortex-antivortex correlations. By making use of superfluid turbulence methods, we give a detailed analysis of the underlying vortex dynamics. Furthermore, we focus on the relevance of the non-thermal fixed point for the dynamics of phase ordering kinetics and Bose-Einstein condensation. Then, we explore the possibility of a non-thermal fixed point in a one-dimensional ultracold Bose gas as well as a two-component Bose gas in two dimensions. Finally, we discuss the realisation of a non-thermal fixed point in a relativistic scalar field theory as well as for the case of a two-component Bose gas in two dimensions. After a brief discussion of experimental prospects, we summarise our results and close with an outlook

The Flux-Line Lattice in Superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do not exist as postscript file

Characterization of topological phases in models of interacting fermions

The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions. In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z_N charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z_N symmetry, we find a non-Abelian group structure under the addition of phases. In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i)~the Hall conductivity, (ii)~the spectral flow and level counting in the ES, (iii)~the topological entanglement entropy, and (iv)~the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order. In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI) induced by next-nearest neighbor interactions has been predicted by mean field theory. However, various subsequent studies challenged this picture and it was still unclear whether the CI would survive quantum fluctuations. We therefore map out the phase diagram of the model as a function of the interactions on an infinite cylinder with DMRG and find evidence for the absence of the CI phase. However, we report the detection of two novel charge-ordered phases and corroborate the existence of the remaining phases that had been predicted in mean field theory. Furthermore, we characterize the transitions between the various phases by studying the behavior of correlation length and entanglement entropy at the phase boundaries. Finally, we develop an improvement to the DMRG algorithm for fermionic lattice models on cylinders. By using a real space representation in the direction along the cylinder and a real space representation in the perpendicular direction, we are able to use the momentum around the cylinder as conserved quantity to reduce computational costs. We benchmark the method by studying the interacting Hofstadter model and report a considerable speedup in computation time and a severely reduced memory usage

Interacting fermions in external fields, at finite temperature and non-zero density

In this thesis we investigate a certain class of low-dimensional fermionic quantum field theories with four-Fermi interactions. Such theories are commonly used as effective low-energy models for quantum chromodynamics, the theory of strong interactions, and have applications in the realm of condensed-matter physics as well. For our purposes, their most important properties are the notion of chiral symmetry as well as its spontaneous breakdown, which is why a major part of this thesis is devoted to their study. On the one hand, we investigate a certain two-dimensional four-Fermi theory, the so-called chiral Gross-Neveu model, which has a continuous chiral symmetry group. We study the possibility of the model at finite temperature and density to exhibit inhomogeneous regions, where the order parameter for chiral symmetry breaking shows oscillatory behavior with the spatial coordinate. We find that remnant inhomogeneous structures can indeed be found even beyond the mean-field limit, albeit likely only on short scales. On the other hand, we consider a related theory with a discrete chiral group, referred to as the Gross-Neveu model, in three space-time dimensions. There, we shall be concerned with the influence of an external magnetic field on chiral symmetry and its spontaneous breaking. While mean-field approaches predict a rich phase structure for non-zero magnetic field and chemical potential, our simulations suggest that this is not the case in the full quantum theory. For all parameter values within the region of spontaneously broken chiral symmetry, we find the magnetic field to enhance the symmetry breaking even further, a phenomenon referred to as magnetic catalysis. In fact, a major goal of this thesis is to contrast the findings of our lattice simulations with existing mean-field results in order to understand to which extent the latter are capable of representing the full theory