arXiv subjects

Klaus Richter

Publications and source records attributed to Klaus Richter.

At least 127 records · Page 7Linked to original sources

arXiv2012

Spin transmission control in helical magnetic fields

We calculate spin transport in two-dimensional waveguides in the presence of spatially modulated Zeeman-split energy bands. We show that in a regime where the spin evolution is predominantly adiabatic the spin backscattering rate can be tuned via diabatic Landau-Zener transitions between the spin-split bands [C. Betthausen et. al., Science 337, 324 (2012)]. This mechanism is tolerant against spin-independent scattering processes. Completely spin-polarized systems show full spin backscattering, and thus current switching. In partially spin-polarized systems a spatial sequence of Landau-Zener transition points enhances the resistance modulation via reoccupation of backscattered spin-polarized transport modes. We discuss a possible application as a spin transistor.

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arXiv2012

Intensity distribution of non-linear scattering states

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they arise in the context of the transport of Bose-Einstein condensates. We specifically show that, extending standard methods for non-interacting systems, the body of the statistical distribution of intensities for scattering states solving the Gross-Pitaevskii equation is very well described by a local Gaussian ansatz with a position-dependent variance. We propose a semiclassical approach based on interfering classical paths to fix the single parameter describing the universal deviations from a global Gaussian distribution. Being tail effects, rare events like rogue waves characteristic of non-linear field equations do not affect our results.

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arXiv2012

Bloch-Zener Oscillations in Graphene and Topological Insulators

We show that superlattices based on zero-gap semiconductors such as graphene and mercury telluride exhibit characteristic Bloch--Zener oscillations that emerge from the coherent superposition of Bloch oscillations and multiple Zener tunneling between the electron and hole branch. We demonstrate this mechanism by means of wave packet dynamics in various spatially periodically modulated nanoribbons subject to an external bias field. The associated Bloch frequencies exhibit a peculiar periodic bias dependence which we explain within a two-band model. Supported by extensive numerical transport calculations, we show that this effect gives rise to distinct current oscillations observable in the I-V characteristics of graphene and mercury telluride superlattices.

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arXiv2012

Spin-dependent Klein tunneling in graphene: Role of Rashba spin-orbit coupling

Within an effective Dirac theory the low-energy dispersions of monolayer graphene in the presence of Rashba spin-orbit coupling and spin-degenerate bilayer graphene are described by formally identical expressions. We explore implications of this correspondence for transport by choosing chiral tunneling through pn and pnp junctions as a concrete example. A real-space Green's function formalism based on a tight-binding model is adopted to perform the ballistic transport calculations, which cover and confirm previous theoretical results based on the Dirac theory. Chiral tunneling in monolayer graphene in the presence of Rashba coupling is shown to indeed behave like in bilayer graphene. Combined effects of a forbidden normal transmission and spin separation are observed within the single-band n to p transmission regime. The former comes from real-spin conservation, in analogy with pseudospin conservation in bilayer graphene, while the latter arises from the intrinsic spin-Hall mechanism of the Rashba coupling.

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arXiv2011

Conductance fluctuations in chaotic systems with tunnel barriers

Quantum effects are expected to disappear in the short-wavelength, semiclassical limit. As a matter of fact, recent investigations of transport through quantum chaotic systems have demonstrated the exponential suppression of the weak localization corrections to the conductance and of the Fano factor for shot-noise when the Ehrenfest time exceeds the electronic dwell time. On the other hand, conductance fluctuations, an effect of quantum coherence, retain their universal value in the limit of the ratio of Ehrenfest time over dwell time to infinity, when the system is ideally coupled to external leads. Motivated by this intriguing result we investigate conductance fluctuations through quantum chaotic cavities coupled to external leads via (tunnel) barriers of arbitrary transparency. Using the trajectory-based semiclassical theory of transport, we find a linear Ehrenfest time-dependence of the conductance variance showing a nonmonotonous, sinusoidal behavior as a function of the transperancy. Most notably, we find an increase of the conductance fluctuations with the Ehrenfest time, above their universal value, for the transparency less than 0.5. These results, confirmed by numerical simulations, show that, contrarily to the common wisdom, effects of quantum coherence may increase in the semiclassical limit, under special circumstances.

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arXiv2011

Universal spatial correlations in random spinor fields

We identify universal spatial fluctuations in systems with non trivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations and spin currents both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction and a single magnetic impurity. We support or claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.

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arXiv2011

Ehrenfest-time dependence of counting statistics for chaotic ballistic systems

Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of arbitrarily many pairs of scattering matrices at different energies on the Ehrenfest time using trajectory based semiclassical methods. This enables us to verify the prediction from effective random matrix theory that one part of the correlation function obtains an exponential damping depending on the Ehrenfest time, while also allowing us to obtain the additional contribution which arises from bands of always correlated trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for secondary gaps in the density of states of Andreev billiards, can also be seen to have strong effects on other transport quantities like the distribution of delay times.

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arXiv2011

The density of states of chaotic Andreev billiards

Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, are ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase shifted superconductors. Therefore we are able to see how these effects can remold and eventually suppress the gap. Furthermore the semiclassical framework is able to cover the effect of a finite Ehrenfest time which also causes the gap to shrink. However for intermediate values this leads to the appearance of a second hard gap - a clear signature of the Ehrenfest time.

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arXiv2011

Switching spin and charge between edge states in topological insulator constrictions

Since the prediction of a new topological state of matter in graphene, materials acting as topological insulators have attracted wide attention. Shortly after the theoretical proposal for a mercury telluride (HgTe)-based two-dimensional topological insulator, the observation of the quantum spin Hall effect and non-local edge transport brought compelling experimental evidence for quantized conductance due to edges states. The spin orientation and propagation direction of such helical edge states are inherently connected, providing protection against backscattering. However, these features conversely render controlled spin operations such as spin switching difficult. Here we therefore propose constrictions as connectors between opposite edge (and spin) states in HgTe. We demonstrate how the coupling between edge states, which overlap in the constriction, can be employed both for steering the charge flow into different edge modes and for controlled spin switching. This gives rise to a three-state charge and spin transistor function. Unlike in a conventional spin transistor, the switching does not rely on a tunable Rashba spin-orbit interaction, but on the energy dependence of the edge state wavefunctions. Based on this mechanism, and supported by numerical transport calculations, we present two different ways to control spin- and charge-currents depending on the gating of the constriction.

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arXiv2011

Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents

We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations.

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arXiv2011

BCS superconductivity in metallic nanograins: Finite-size corrections, low energy excitations, and robustness of shell effects

We combine the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements to describe analytically how the superconducting gap depends on the size and shape of a 2d and 3d superconducting grain. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we find shell effects i. e. for certain values of the electron number $N$ a small change in N leads to large changes in the energy gap. With regard to possible experimental tests we provide a detailed analysis of the dependence of the gap on the coherence length and the robustness of shell effects under small geometrical deformations.

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arXiv2011

Conductance and Thermopower of Ballistic Andreev Cavities

When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting and normal conducting leads. In the case of two superconductors with the same chemical potential we will also see how the conductance and the sign of quantum corrections are affected by their phase difference. As far as random matrix theory results exist these are reproduced by our calculations. Furthermore in the case that the chemical potential of the superconductors is the same as that of one of the two normal leads the conductance shows, under certain conditions, similar effects as a normal metal-superconductor junction. The semiclassical framework is also able to treat the thermopower of chaotic Andreev billiards consisting of one chaotic dot, two normal leads and two superconducting islands and shows it to be antisymmetric in the phase difference of the superconductors.

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arXiv2010

Weak localization in mesoscopic hole transport: Berry phases and classical correlations

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magneto-conductance profile distinctly different from electron transport. Non-universal classical correlations determine the strength of these Berry phase effects and the effective symmetry class, leading even to antilocalization-type features for circular quantum dots and Aharonov-Bohm rings in the absence of additional spin-orbit interaction. Our semiclassical predictions are quantitatively confirmed by numerical transport calculations.

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arXiv2010

Spin-Orbit Based Coherent Spin Ratchets

The concept of ratchets, driven asymmetric periodic structures giving rise to directed particle flow, has recently been generalized to a quantum ratchet mechanism for spin currents mediated through spin-orbit interaction. Here we consider such systems in the coherent mesoscopic regime and generalize the proposal of a minimal spin ratchet model based on a non-interacting clean quantum wire with two transverse channels by including disorder and by self-consistently treating the charge redistribution in the nonlinear (adiabatic) ac-driving regime. Our Keldysh-Green function based quantum transport simulations show that the spin ratchet mechanism is robust and prevails for disordered, though non-diffusive, mesoscopic structures. Extending the two-channel to the multi-channel case does not increase the net ratchet spin current efficiency but, remarkably, yields a dc spin transmission increasing linearly with channel number.

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arXiv2010

Semiclassical gaps in the density of states of chaotic Andreev billiards

The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an Andreev billiard semiclassically where the density of states is expressed in terms of the classical trajectories of electrons (and holes) that leave and return to the superconductor. We show how classical orbit correlations lead to the formation of the hard gap, as predicted by random matrix theory in the limit of negligible Ehrenfest time $\tE$, and how the influence of a finite $\tE$ causes the gap to shrink. Furthermore, for intermediate $\tE$ we predict a second gap below $E=π\hbar /2\tE$ which would presumably be the clearest signature yet of $\tE$-effects.

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arXiv2009

Charge ratchet from spin flip: space-time symmetry paradox

Traditionally the charge ratchet effect is considered as a consequence of either the spatial symmetry breaking engineered by asymmetric periodic potentials, or time asymmetry of the driving fields. Here we demonstrate that electrically and magnetically driven quantum dissipative systems with spin-orbit interactions represent an exception from this standard idea. In contrast to the so far well established belief, a charge ratchet effect appears when both the periodic potential and driving are symmetric. We show that the source of this paradoxical charge ratchet mechanism is the coexistence of quantum dissipation with the spin flip processes induced by spin-orbit interactions.

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arXiv2009

Quantum Corrections to Fidelity Decay in Chaotic Systems

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.

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arXiv2009

Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength $α)$ and Dresselhaus (with strength $β)$ spin-orbit interaction. Using a diffusion equation approach we find that magnetoelectric effects disappear and that there is thus no spin accumulation when both interactions have the same strength, $α=\pm β$. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin and Magarill, [Physica E {\bf 13}, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B {\bf 75}, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point $α=\pm β$. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finite-sized systems of size $L$, (ii) in the presence of a cubic Dresselhaus interaction of strength $γ$, or (iii) for finite frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) $|α|-|β| \lesssim 1/mL$, (ii)$|α|-|β| \lesssim γp_{\rm F}^2$, and (iii) $|α|-|β| \lesssiM \sqrt{ω/m p_{\rm F}\ell}$ with $\ell$ the elastic mean free path and $p_{\rm F}$ the Fermi momentum. We attribute the absence of spin accumulation close to $α=\pm β$ to the underlying U (1) symmetry. We illustrate and confirm our predictions numerically.

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