Publications - Paul Wenk

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2021

Topological transitions in two-dimensional Floquet superconductors
Paul Wenk, Milena Grifoni, John Schliemann
[arXiv]

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We demonstrate the occurrence of a topological phase transition induced by an effective magnetic field in a two-dimensional electron gas with spin-orbit coupling and in proximity to an s-wave superconductor. The effective, perpendicular magnetic field is generated by an in plane, off-resonant ac-magnetic field or by circularly polarized light. The conditions for entering the topological phase do not rely on fine parameter tuning: For fixed frequency, one requires a minimal amplitude of the effective field which can be evaluated analytically. In this phase, chiral edge states generally emerge for a system in stripe geometry unless the Rashba and Dresselhaus coupling have the same magnitude. In this special case, for magnetic field driving the edge states become Majorana flat bands, due to the presence of a chiral symmetry; the light irradiated system is a trivial superconductor.

Many-Body Localization: Transitions in Spin Models
John Schliemann, Joao Vitor I. Costa, Paul Wenk, J. Carlos Egues
Phys. Rev. B 103 174203 (2021), [arXiv]

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We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths $1/2$ and 1 are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance $(\Delta_s r)^2$ of the averaged consecutive-gap ratio $\langle r \rangle$ for different disorder realizations. For both types of systems and spin lengths we find a maximum in $\Delta_s r$ as a function of disorder strength, accompanied by an inflection point of $\langle r \rangle$, signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.

2020

Persistent spin textures and currents in wurtzite nanowire-based quantum structures
Michael Kammermeier, Adrian Seith, Paul Wenk, and John Schliemann
Phys. Rev. B 101 195418 (2020), [arXiv]

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We explore the spin and charge properties of electrons in wurtzite semiconductor nanowires where radial and axial confinement leads to tubular or ring-shaped quantum structures. Accounting for spin-orbit interaction induced by the wurtzite lattice as well as a radial potential gradient, we analytically derive the corresponding low-dimensional Hamiltonians. It is demonstrated that the resulting tubular spin-orbit Hamiltonian allows to construct spin states that are persistent in time and robust against disorder. We find that these special scenarios are characterized by distinctive features in the optical conductivity spectrum, which enable an unambiguous experimental verification. In both types of quantum structures, we discuss the dependence of the occurring persistent charge and spin currents on an axial magnetic field and Fermi energy which show clear fingerprints of the electronic subband structure. Here, the spin-preserving symmetries become manifest in the vanishing of certain spin current tensor components. Our analytic description relates the distinctive features of the optical conductivity and persistent currents to bandstructure characteristics which allows to deduce spin-orbit coefficients and other band parameters from measurements.

Floquet-Drude conductivity
Martin Wackerl, Paul Wenk, and John Schliemann
Phys. Rev. B 101 184204 (2020), [arXiv]

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A generalization of the Drude conductivity for systems which are exposed to periodic driving is presented. The probe bias is treated perturbatively by using the Kubo formula, whereas the external driving is included nonperturbatively using the Floquet theory. Using a different type of four-times Green functions disorder is approached diagrammatically, yielding a fully analytical expression for the Floquet-Drude conductivity. Furthermore, the Floquet Fermi "golden rule" is generalized to $t$-$t'$ Floquet states, connecting the Floquet-Dyson series with scattering theory for Floquet states. It is shown that a low-energy approximation like the parabolic one fails significantly to give the correct conductivity in a system under driving.

2019

In-plane magnetoelectric response in bilayer graphene
Michael Kammermeier, Paul Wenk, and Ulrich Zülicke
Phys. Rev. B 100, 075421 (2019), [arXiv],

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A graphene bilayer shows an unusual magnetoelectric response whose magnitude is controlled by the valley-isospin density, making it possible to link magnetoelectric behavior to valleytronics. Complementary to previous studies, we consider the effect of static homogeneous electric and magnetic fields that are oriented parallel to the bilayer's plane. Starting from a tight-binding description and using quasi-degenerate perturbation theory, the low-energy Hamiltonian is derived including all relevant magnetoelectric terms whose prefactors are expressed in terms of tight-binding parameters. We confirm the existence of an expected axion-type pseudoscalar term, which turns out to have the same sign and about twice the magnitude of the previously obtained out-of-plane counterpart. Additionally, small anisotropic corrections to the magnetoelectric tensor are found that are fundamentally related to the skew interlayer hopping parameter $\gamma_4$. We discuss possible ways to identify magnetoelectric effects by distinctive features in the optical conductivity.

Driven Hofstadter butterflies and related topological invariants
Martin Wackerl, Paul Wenk, and John Schliemann
Phys. Rev. B 100, 165411 (2019), [arXiv],

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The properties of the Hofstadter butterfly, a fractal, self-similar spectrum of a two-dimensional electron gas, are studied in the case where the system is additionally illuminated with monochromatic light. This is accomplished by applying Floquet theory to a tight-binding model on the honeycomb lattice subjected to a perpendicular magnetic field and either linearly or circularly polarized light. It is shown how the deformation of the fractal structure of the spectrum depends on intensity and polarization. Thereby, the topological properties of the Hofstadter butterfly in the presence of the oscillating electric field are investigated. A thorough numerical analysis of not only the Chern numbers but also the $W3$ invariants gives the appropriate insight into the topology of this driven system. This includes a comparison of a direct $W_3$ calculation to the method based on summing up Chern numbers of the truncated Floquet Hamiltonian.

Ultralong spin lifetimes in one-dimensional semiconductor nanowires
Florian Dirnberger, Michael Kammermeier, Jan König, Moritz Forsch, Paulo E. Faria Junior, Tiago Campos, Jaroslav Fabian, John Schliemann, Christian Schüller, Tobias Korn, Paul Wenk, and Dominique Bougeard
Appl. Phys. Lett. 114, 202101 (2019), [arXiv],

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We experimentally demonstrate ultralong spin lifetimes of electrons in the one-dimensional (1D) quantum limit of semiconductor nanowires. Optically probing single wires of different diameters reveals an increase in the spin relaxation time by orders of magnitude as the electrons become increasingly confined until only a single 1D subband is populated. We find the observed spin lifetimes of more than 200ns to result from the robustness of 1D electrons against major spin relaxation mechanisms, highlighting the promising potential of these wires for long-range transport of coherent spin information.

2018

Spin relaxation in wurtzite nanowires
Michael Kammermeier, Paul Wenk, Florian Dirnberger, Dominique Bougeard, and John Schliemann
Phys. Rev. B 98, 035407 (2018), [arXiv] .

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We theoretically investigate the D'yakonov-Perel' spin relaxation properties in diffusive wurtzite semiconductor nanowires and their impact on the quantum correction to the conductivity. Although the lifetime of the long-lived spin states is limited by the dominant $k$-linear spin-orbit contributions in the bulk, these terms show almost no effect in the finite-size nanowires. Here, the spin lifetime is essentially determined by the small $k$-cubic spin-orbit terms and nearly independent of the wire radius. At the same time, these states possess in general a complex helical structure in real space that is modulated by the spin precession length induced by the $k$-linear terms. For this reason, the experimentally detected spin relaxation largely depends on the ratio between the nanowire radius and the spin precession length as well as the type of measurement. In particular, it is shown that while a variation of the radius hardly affects the magnetoconductance correction, which is governed by the long-lived spin states, the change in the spin lifetime observed in optical experiments can be dramatic.

Add-on: Talk by F. Dirnberger about spin dynamics in single GaAs nanowires

2017

Magnetoconductance correction in zinc-blende semiconductor nanowires with spin-orbit coupling
Michael Kammermeier, Paul Wenk, John Schliemann, Sebastian Heedt, Thomas Gerster, and Thomas Schäpers
Phys. Rev. B 96, 235302 (2017), [arXiv]

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We study the effects of spin-orbit coupling on the magnetoconductivity in diffusive cylindrical semiconductor nanowires. Following up on our former study on tubular semiconductor nanowires, we focus in this paper on nanowire systems where no surface accumulation layer is formed but instead the electron wave function extends over the entire cross section. We take into account the Dresselhaus spin-orbit coupling resulting from a zinc-blende lattice and the Rashba spin-orbit coupling, which is controlled by a lateral gate electrode. The spin relaxation rate due to Dresselhaus spin-orbit coupling is found to depend neither on the spin density component nor on the wire growth direction and is unaffected by the radial boundary. In contrast, the Rashba spin relaxation rate is strongly reduced for a wire radius that is smaller than the spin precession length. The derived formulas are fitted to the data of magnetoconductance measurements of a heavily-doped back-gated InAs nanowire and transport parameters are extracted.

Add-on: Talk

2016

Control of spin helix symmetry in semiconductor quantum wells by crystal orientation
Michael Kammermeier, Paul Wenk, and John Schliemann
Phys. Rev. Lett. 117, 236801 (2016) (on the cover), [arXiv] , [POSTER], Media release of the University of Regensburg (in German).

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We investigate the possibility of spin-preserving symmetries due to the interplay of Rashba and Dresselhaus spin-orbit coupling in n-doped zinc-blende semiconductor quantum wells of general crystal orientation. It is shown that a conserved spin operator can be realized if and only if at least two growth-direction Miller indices agree in modulus. The according spin-orbit field has in general both in-plane and out-of-plane components and is always perpendicular to the shift vector of the corresponding persistent spin helix. We also analyze higher-order effects arising from the Dresselhaus term, and the impact of our results on weak (anti)localization corrections.

Weak (Anti-)Localization in Tubular Semiconductor Nanowires with Spin-Orbit Coupling
Michael Kammermeier, Paul Wenk, John Schliemann, Sebastian Heedt, and Thomas Schäpers
Phys. Rev. B 93, 205306 (2016) (Editor´s Suggestion), [arXiv]

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We compute analytically the weak (anti-)localization correction to the Drude conductivity for electrons in tubular semiconductor systems of zinc blende type. We include linear Rashba and Dresselhaus spin-orbit coupling (SOC) and compare wires of standard growth directions <100>, <111> and <110>. The motion on the quasi-two-dimensional surface is considered diffusive in both directions: transversal as well as along the cylinder axis. It is shown that Dresselhaus and Rashba SOC similarly affect the spin relaxation rates. For the <110> growth direction the long-lived spin states are of helical nature. We detect a crossover from weak localization to weak anti-localization depending on spin-orbit coupling strength as well as dephasing and scattering rate. The theory is fitted to experimental data of an undoped <111> InAs nanowire device which exhibits a top-gate-controlled crossover from positive to negative magnetoconductivity. Thereby, we extract transport parameters where we quantify the distinct types of SOC individually.

Add-on: Talk

Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum
Sonja Predin, Paul Wenk, and John Schliemann
Phys. Rev. B 93, 115106 (2016), [arXiv]

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We present a mainly analytical study of the entanglement spectrum of Bernal-stacked graphene bilayers in the presence of trigonal warping in the energy spectrum. Upon tracing out one layer, the entanglement spectrum shows qualitative geometric differences to the energy spectrum of a graphene monolayer. However, topological quantities such as Berry-phase-type contributions to Chern numbers agree. The latter analysis involves not only the eigenvalues of the entanglement Hamiltonian but also its eigenvectors. We also discuss the entanglement spectra resulting from tracing out other sublattices. As a technical basis of our analysis, we provide closed analytical expressions for the full eigensystem of bilayer graphene in the entire Brillouin zone with a trigonally warped spectrum.

Conserved Spin Quantity in Strained Hole Systems with Rashba and Dresselhaus Spin-Orbit Coupling
Paul Wenk, Michael Kammermeier, and John Schliemann
Phys. Rev. B 93, 115312 (2016), [arXiv] , [POSTER]

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We derive an effective Hamiltonian for a (001)-confined quasi-two-dimensional hole gas in a strained zinc-blende semiconductor heterostructure including both Rashba and Dresselhaus spin-orbit coupling. In the presence of uniaxial strain along the <110> axes, we find a conserved spin quantity in the vicinity of the Fermi contours in the lowest valence subband. In contrast to previous works, this quantity meets realistic requirements for the Luttinger parameters. For more restrictive conditions, we even find a conserved spin quantity for vanishing strain, restricted to the vicinity of the Fermi surface.

Add-on: Talk

Ballistic and spin transport in InAs nanowires
Th. Schapers, S. Heedt, A. Bringer, H. Hardtdegen, J. Schubert, D. Grutzmacher, M. Kammermeier, P. Wenk, J. Schliemann, W. Prost
IEEE Nanotechnology Materials and Devices Conference (2016)

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The transport in InAs nanowires is investigated at low temperatures. On wires with different n-type doping information on Rashba and Dresselhaus spin-orbit coupling is gained from weak antilocalization measurements. By using a short local gate quantum point contacts are formed, which show quantized conductance. From bias-depended measurements the g-factor is extracted for different subbands.

2015

Lifetimes of Magnons in Two-Dimensional Diluted Ferromagnetic Systems
Akash Chakraborty, Paul Wenk, and John Schliemann
Eur. Phys. J. B 88, 64 (2015), [arXiv]

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Spin dynamics in low dimensional magnetic systems has been of fundamental importance for a long time and has currently received an impetus owing to the emerging field of nanoelectronics. Knowledge of the spin wave lifetimes, in particular, can be favorable for future potential applications. We investigate the low-temperature spin wave excitations in two-dimensional disordered ferromagnetic systems, with a particular focus on the long wavelength magnon lifetimes. A semi-analytical Green's functions based approach is used to determine the dynamical spectral functions, for different magnetic impurity concentrations, from which the intrinsic linewidth is extracted. We obtain an unambiguous $q^4$ scaling of the magnon linewidth which is ascribed to the disorder induced damping of the spin waves, thereby settling a longstanding unresolved issue on the wave-vector dependence. Our findings are also in good agreement with previous theoretical studies on Heisenberg ferromagnets. Additionally, we demonstrate the futility of using the low moments associated with the spectral densities to evaluate the magnon dispersions and lifetimes.

2014

Signatures of spin-preserving symmetries in two-dimensional hole gases
Tobias Dollinger, Michael Kammermeier, Andreas Scholz, Paul Wenk, John Schliemann, Klaus Richter, and Roland Winkler
Phys. Rev. B 90, 115306 (2014).

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We investigate ramifications of the persistent spin helix symmetry in two-dimensional hole gases in the conductance of disordered mesoscopic systems. To this end we extend previous models by going beyond the axial approximation for III-V semiconductors. For heavy-hole subbands we identify an exact spin-preserving symmetry analogous to the electronic case by analyzing the crossover from weak antilocalization to weak localization and spin transmission as a function of extrinsic spin-orbit interaction strength.

Spin-wave excitations in presence of nanoclusters of magnetic impurities
Akash Chakraborty, Paul Wenk, Stefan Kettemann, Richard Bouzerar, Georges Bouzerar
New J. Phys. 16, 033004 (2014), [arXiv]

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Nanoscale inhomogeneities and impurity clustering are often found to drastically affect the magnetic and transport properties in disordered/diluted systems, giving rise to rich and complex phenomena. However, the physics of these systems still remains to be explored in more detail as can be seen from the scarce literature available. We present a detailed theoretical analysis of the effects of nanoscale inhomogeneities on the spin excitation spectrum in diluted magnetic systems. The calculations are performed on relatively large systems (up to $N=66^3$). It is found that even low concentrations of inhomogeneities have drastic effects on both the magnon density of states and magnon excitations. These effects become even more pronounced in the case of short-ranged magnetic interactions between the impurities. In contrast to the increase of critical temperatures $T_C$, reported in previous studies, the spin-stiffness $D$ is systematically suppressed in the presence of nanoscale inhomogeneities. Moreover D is found to strongly depend on the inhomogeneities' concentration, the cluster size, as well as the range of the magnetic interactions. The findings are discussed in the prospect of potential spintronics applications. We believe that this detailed numerical work could initiate future experimental studies to probe this rich physics with the most appropriate tool, inelastic neutron scattering.

Spin injection and spin-orbit coupling in low-dimensional semiconductor nanostructures
Sebastian Heedt, Isabel Wehrmann, Thomas Gerster, Paul Wenk, Stefan Kettemann, Kamil Sladek, Hilde Hardtdegen, Andreas Bringer, Jürgen Schubert, Natalia Demarina, Detlev Grützmacher, Thomas Schäpers
in Spintronics VII, SPIE (2014)

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Due to their strong spin-orbit coupling III-V semiconductor nanowires are excellent candidates for electrical spin manipulation. Therefore, a major goal is to tailor spin-orbit coupling in these devices. Direct electrical spin injection into quasi one-dimensional nanowires is demonstrated. Furthermore, the weak antilocalization effect was investigated in InAs nanowires. The quantum corrections to the conductivity are interpreted by developing a quasi-one-dimensional diffusive model. It turns out that by means of doping and electric gating the spin-lifetimes can be tuned significantly. By creating few-electron quantum dots inside these devices the impact of the confinement on the spin relaxation properties is investigated.

2013

Plasmons in spin-orbit coupled two-dimensional hole gas systems
Andreas Scholz, Tobias Dollinger, Paul Wenk, Klaus Richter, and John Schliemann
Phys. Rev. B 87, 085321 (2013).

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We study the dynamical dielectric function of a two-dimensional hole gas, exemplified on [001] GaAs and InAs quantum wells, within the Luttinger model extended to the two lowest subbands including bulk and structure inversion asymmetric terms. The plasmon dispersion shows a pronounced anisotropy for GaAs- and InAs-based systems. In GaAs this leads to a suppression of plasmons due to Landau damping in some orientations. Due to the large Rashba contribution in InAs, the lifetime of plasmons can be controlled by changing the electric field. This effect is potentially useful in plasmon field effect transistors as previously proposed for electron gases.

2012

Spontaneous magnetization in the presence of nanoscale inhomogeneities in diluted magnetic systems
Akash Chakraborty, Paul Wenk, Richard Bouzerar, and Georges Bouzerar
Phys. Rev. B 86, 214402 (2012), [arXiv]
Add-on: Talk by A. Chakraborty

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The presence of nanoscale inhomogeneities has been experimentally evidenced in several diluted magnetic systems, which in turn often leads to interesting physical phenomena. However, a proper theoretical understanding of the underlying physics is lacking in most of the cases. Here, we present a detailed and comprehensive theoretical study of the effects of nanoscale inhomogeneities on the temperature-dependent spontaneous magnetization in diluted magnetic systems, which is found to exhibit an unusual and unconventional behavior. The effects of impurity clustering on the magnetization response have hardly been studied until now. We show that nanosized clusters of magnetic impurities can lead to drastic effects on the magnetization compared to that of homogeneously diluted compounds. The anomalous nature of the magnetization curves strongly depends on the relative concentration of the inhomogeneities as well as the effective range of the exchange interactions. In addition, we also provide a systematic discussion of the nature of the distributions of the local magnetizations.

Spin Hall conductivity on the anisotropic triangular lattice
Paul Wenk, Stefan Kettemann, and Georges Bouzerar
Phys. Rev. B 86, 075441 (2012), [arXiv]

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We present a detailed study of the spin Hall conductivity on a ballistic two-dimensional triangular lattice in the presence of Rashba spin-orbit coupling. In particular, we focus part of our attention on the effect of the anisotropy of the nearest neighbor hopping amplitude. It is found that the presence of anisotropy has drastic effects on the spin Hall conductivity, especially in the hole doped regime where a significant increase or/and reversed sign of the spin Hall conductivity has been obtained. We also provide a systematic analysis of the numerical results in terms of Berry phases. The changes of signs observed at particular density of carriers appear to be a consequence of both Fermi surface topology and change of sign of electron velocity. In addition, in contrast to the two-dimensional square lattice, it is shown that the tight binding spin-orbit Hamiltonian should be derived carefully from the continuous model on the triangular lattice.

2011

Direction dependence of spin relaxation in confined two-dimensional systems
Paul Wenk, and Stefan Kettemann
Phys. Rev. B 83, 115301 (2011), [World Scientiffic (Open Access)] , [POSTER]

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The dependence of spin relaxation on the direction of the quantum wire under Rashba and Dresselhaus (linear and cubic) spin-orbit coupling is studied. Comprising the dimensional reduction of the wire in the diffusive regime, the lowest spin relaxation and dephasing rates for (001) and (110) systems are found. The analysis of spin relaxation reduction is then extended to nondiffusive wires where it is shown that, in contrast to the theory of dimensional crossover from weak localization to weak antilocalization in diffusive wires, the relaxation due to cubic Dresselhaus spin-orbit coupling is reduced and the linear part is shifted with the number of transverse channels.

2010

Dimensional dependence of weak localization corrections and spin relaxation in quantum wires with Rashba spin-orbit coupling
Paul Wenk, and Stefan Kettemann
Phys. Rev. B 81, 125309 (2010), [arXiv] , [POSTER]

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S. Kettemann, Phys. Rev. L 98, 176808 (2007)

Spin Relaxation in Quantum Wires
Paul Wenk, and Stefan Kettemann
In: Handbook of Nanophysics: Nanotubes and Nanowires by K. Sattler (2010), [arXiv]

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$L_\text{SO}$

Spin Polarized Transport and Spin Relaxation in Quantum Wires
Paul Wenk, Masayuki Yamamoto, Jun-ichiro Ohe, Tomi Ohtsuki, Bernhard Kramer, Stefan Kettemann
Part of the NanoScience and Technology book series (NANO) (2010), [book link]

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[1]

Thesis

Itinerant Spin Dynamics in Structures of Reduced Dimensionality
Updated version (V2, 15.02.18).

Last modified: Do 27. Mai 18:31:13 CEST 2021