Ballistic Quantum Transport: Effect of Geometrical Phases

We study the influence of nonuniform magnetic fields on the magneto conductance of mesoscopic microstructures. We show that the coupling of the electron spin to the inhomogenous field gives rise to effects of the Berry phase on ballistic quantum transport and discuss adiabaticity conditions required to observe such effects. We present numerical results for different ring geometries showing a splitting of Aharonov-Bohm conductance peaks for single rings and corresponding signatures of the geometrical phase in weak localization. The latter features can be qualitatively explained in a semiclassical approach to quantum transport.Comment: 15 pages, 6 figures. Accepted for publication in Foundations of Physic

Magnetotransport in disordered two-dimensional topological insulators: signatures of charge puddles

In this numerical study we investigate the influence and interplay of disorder, spin-orbit coupling and magnetic field on the edge-transport in HgTe/CdTe quantum wells in the framework of coherent elastic scattering. We show that the edge states remain unaffected by the combined effect of moderate disorder and a weak magnetic field at realistic spin-orbit coupling strengths. Agreement with the experimentally observed linear magnetic field dependence for the conductance of long samples is obtained when considering the existence of charge puddles.Comment: 17 pages, 6 figure

Orbital Magnetism of Graphene Nanostructures: Bulk and Confinement Effects

We consider the orbital magnetic properties of non-interacting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both, frombulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility $\chi$ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e. temperature, Landau level spacing and chemical potential. We show that for finite temperature or chemical potential, $\chi$ is not divergent although the diamagnetic contribution $\chi_{0}$ from the filled valance band exhibits the well-known $-B^{-1/2}$ dependence. We further derive oscillatory modulations of $\chi$, corresponding to de Haas-van Alphen oscillations of conventional two-dimensional electron gases. These oscillations can be large in graphene, thereby compensating the diamagnetic contribution $\chi_{0}$ and yielding a net paramagnetic susceptibility for certain energy and magnetic field regimes. Second, we predict and analyze corresponding strong, confinement-induced susceptibility oscillations in graphene-based quantum dots with amplitudes distincly exceeding the corresponding bulk susceptibility. Within a semiclassical approach we derive generic expressions for orbital magnetism of graphene quantum dots with regular classical dynamics. Graphene-specific features can be traced back to pseudospin interference along the underlying periodic orbits. We demonstrate the quality of the semiclassical approximation by comparison with quantum mechanical results for two exemplary mesoscopic systems, a graphene disk with infinite mass-type edges and a rectangular graphene structure with armchair and zigzag edges, using numerical tight-binding calculations in the latter case.Comment: 21 pages, 16 figure

Statistical description of eigenfunctions in chaotic and weakly disordered systems beyond universality

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry's Random Wave Model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wavefunction averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics

Effects of short-range interactions on transport through quantum point contacts: A numerical approach

We study electronic transport through a quantum point contact, where the interaction between the electrons is approximated by a contact potential. Our numerical approach is based on the non-equilibrium Green function technique which is evaluated at Hartree-Fock level. We show that this approach allows us to reproduce relevant features of the so-called "0.7 anomaly" observed in the conductance at low temperatures, including the characteristic features in recent shot noise measurements. This is consistent with a spin-splitting interpretation of the process, and indicates that the "0.7 anomaly" should also be observable in transport experiments with ultracold fermionic atoms.Comment: 12 pages, 10 figure

Two-dimensional topological insulator edge state backscattering by dephasing

To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow to verify this hypothesis and to extract the real dephasing time scale using our predictions. In addition, we present a new method to include the effect of dephasing in wave-packet-time-evolution algorithms.Comment: 7 pages, 5 figure

Quantum graphs whose spectra mimic the zeros of the Riemann zeta function

One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.Comment: 8 pages, 8 pdf figure

The role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.Comment: 5 page

Spin-polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena

Mesoscopic conductors are electronic systems of sizes in between nano- and micrometers, and often of reduced dimensionality. In the phase-coherent regime at low temperatures, the conductance of these devices is governed by quantum interference effects, such as the Aharonov-Bohm effect and conductance fluctuations as prominent examples. While first measurements of quantum charge transport date back to the 1980s, spin phenomena in mesoscopic transport have moved only recently into the focus of attention, as one branch of the field of spintronics. The interplay between quantum coherence with confinement-, disorder- or interaction-effects gives rise to a variety of unexpected spin phenomena in mesoscopic conductors and allows moreover to control and engineer the spin of the charge carriers: spin interference is often the basis for spin-valves, -filters, -switches or -pumps. Their underlying mechanisms may gain relevance on the way to possible future semiconductor-based spin devices. A quantitative theoretical understanding of spin-dependent mesoscopic transport calls for developing efficient and flexible numerical algorithms, including matrix-reordering techniques within Green function approaches, which we will explain, review and employ.Comment: To appear in the Encyclopedia of Complexity and System Scienc