arXiv subjects

Klaus Richter

Publications and source records attributed to Klaus Richter.

At least 55 records · Page 3Linked to original sources

arXiv2020

Gate-tunable two-dimensional superlattices in graphene

We report an efficient technique to induce gate-tunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with lattice constant $a=40$ nm well pronounced satellite Dirac points and signatures of the Hofstadter butterfly including a non-monotonic quantum Hall response are observed. Furthermore, the experimental results are accurately reproduced in transport simulations and show good agreement with features in the calculated band structure. Overall, we present a comprehensive picture of graphene-based superlattices, featuring a broad range of miniband effects, both in experiment and in theoretical modeling. The presented technique is suitable for studying more advanced geometries which are not accessible by other methods.

cond-mat.mes-hall↗

arXiv2020

2D-Dirac surface states and bulk gap probed via quantum capacitance in a 3D topological insulator

BiSbTeSe$_2$ is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low temperature surface transport in this material is heralded by Shubnikov-de Haas oscillations and the quantum Hall effect. Here, we experimentally probe and model the electronic density of states (DOS) in thin layers of BiSbTeSe$_2$ by capacitance experiments both without and in quantizing magnetic fields. By probing the lowest Landau levels, we show that a large fraction of the electrons filled via field effect into the system ends up in (localized) bulk states and appears as a background DOS. The surprisingly strong temperature dependence of such background DOS can be traced back to Coulomb interactions. Our results point at the coexistence and intimate coupling of Dirac surface states with a bulk many-body phase (a Coulomb glass) in 3D-TIs.

cond-mat.mes-hall↗

arXiv2020

Crossed Andreev reflection in topological insulator nanowire T-junctions

We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model systems of micronsize, typical of experimental setups, but computationally too heavy for 3D models.

cond-mat.mes-hall↗

arXiv2020

Universal S-matrix correlations for complex scattering of many-body wavepackets: theory, simulation and experiment

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of non-stationary many-body scattering where the incoming states are localized wavepackets. Contrary to the stationary case the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

cond-mat.stat-mech↗

arXiv2020

Theory of magnetotransport in shaped topological insulator nanowires

We show that shaped topological insulator (TI) nanowires, i.e. such that their cross-section radius varies along the wire length, can be tuned into a number of different transport regimes when immersed in a homogeneous coaxial magnetic field. This is in contrast with widely studied tubular nanowires with constant cross-section, and is due to magnetic confinement of Dirac surface carriers. In flat 2D systems such a confinement requires non-homogeneous magnetic fields, while for shaped nanowires of standard size homogeneous fields of the order of $B\sim\,1$T are sufficient. We put recent work [Kozlovsky et al., Phys. Rev. Lett. 124, 126804 (2020)] into broader context and extend it to deal with axially symmetric wire geometries with arbitrary radial profile. A dumbbell-shaped TI nanowire is used as a paradigmatic example for transport through a constriction and shown to be tunable into five different transport regimes: (i) conductance steps, (ii) resonant transmission, (iii) current suppression, (iv) Coulomb blockade, and (v) transport through a triple quantum dot. Switching between regimes is achieved by modulating the strength of a coaxial magnetic field and does not require strict axial symmetry of the wire cross-section. As such, it should be observable in TI nanowires fabricated with available experimental techniques.

cond-mat.mes-hall↗

arXiv2020

Classical, semiclassical and quantum signatures of quantum phase transitions in a (pseudo) relativistic many-body system

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

cond-mat.quant-gas↗

arXiv2020

Breakdown of the Hebel-Slichter effect in superconducting graphene due to the emergence of Yu-Shiba-Rusinov states at magnetic resonant scatterers

Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an $s$-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities---the Hebel-Slichter effect---and decreases when impurities have spin-orbit coupling. This distinct temperature~dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that the Hebel-Slichter picture breaks down at resonances. The emergence of Yu-Shiba-Rusinov bound states within the superconducting gap redistributes the spectral weight away from magnetic resonances. The result is opposite to the Hebel-Slichter expectation: the spin relaxation decreases with decreasing temperature. Our findings hold for generic $s$-wave superconductors with resonant magnetic impurities, but also, as we show, for resonant magnetic Josephson junctions.

cond-mat.mes-hall↗

arXiv2020

Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

Magnetotransport through cylindrical topological insulator (TI) nanowires is governed by the interplay between quantum confinement and geometric (Aharonov-Bohm and Berry) phases. Here, we argue that the much broader class of TI nanowires with varying radius -- for which a homogeneous coaxial magnetic field induces a varying Aharonov-Bohm flux that gives rise to a non-trivial mass-like potential along the wire -- is accessible by studying its simplest member, a TI nanocone. Such nanocones allow to observe intriguing mesoscopic transport phenomena: While the conductance in a perpendicular magnetic field is quantized due to higher-order topological hinge states, it shows resonant transmission through Dirac Landau levels in a coaxial magnetic field. Furthermore, it may act as a quantum magnetic bottle, confining surface Dirac electrons and leading to a largely interaction-dominated regime of Coulomb blockade type. We show numerically that the above-mentioned effects occur for experimentally accessible values of system size and magnetic field, suggesting that TI nanocone junctions may serve as building blocks for Dirac electron optics setups.

cond-mat.mes-hall↗

arXiv2020

Floquet oscillations in periodically driven Dirac systems

Electrons in a lattice exhibit time-periodic motion, known as Bloch oscillation, when subject to an additional static electric field. Here we show that a corresponding dynamics can occur upon replacing the spatially periodic potential by a time-periodic driving: Floquet oscillations of charge carriers in a spatially homogeneous system. The time lattice of the driving gives rise to Floquet bands that take on the role of the usual Bloch bands. For two different drivings (harmonic driving and periodic kicking through pulses) of systems with linear dispersion we demonstrate the existence of such oscillations, both by directly propagating wave packets and based on a complementary Floquet analysis. The Floquet oscillations feature richer oscillation patterns than their Bloch counterpart and enable the imaging of Floquet bands. Moreover, their period can be directly tuned through the driving frequency. Such oscillations should be experimentally observable in effective Dirac systems, such as graphene, when illuminated with circularly polarized light.

cond-mat.mes-hall↗

arXiv2020

Gate-controlled Spin Extraction from Topological Insulator Surfaces

Spin-momentum locking, a key property of the surface states of three-dimensional topological insulators (3DTIs), provides a new avenue for spintronics applications. One consequence of spin-momentum locking is the induction of surface spin accumulations due to applied electric fields. In this work, we investigate the extraction of such electrically-induced spins from their host TI material into adjoining conventional, hence topologically trivial, materials that are commonly used in electronics devices. We focus on effective Hamiltonians for bismuth-based 3DTI materials in the ${\rm Bi}_2{\rm Se}_3$ family, and numerically explore the geometries for extracting current-induced spins from a TI surface. In particular, we consider a device geometry in which a side pocket is attached to various faces of a 3DTI quantum wire and show that it is possible to create current-induced spin accumulations in these topologically trivial side pockets. We further study how such spin extraction depends on geometry and material parameters, and find that electron-hole degrees of freedom can be utilized to control the polarization of the extracted spins by an applied gate voltage.

cond-mat.mes-hall↗

arXiv2019

Steering Zitterbewegung in driven Dirac systems -- from persistent modes to echoes

Although zitterbewegung -- the jittery motion of relativistic particles -- is known since 1930 and was predicted in solid state systems long ago, it has been directly measured so far only in so-called quantum simulators, i.e. quantum systems under strong control such as trapped ions and Bose-Einstein condensates. A reason for the lack of further experimental evidence is the transient nature of wave packet zitterbewegung. Here we study how the jittery motion can be manipulated in Dirac systems via time-dependent potentials, with the goal of slowing down/preventing its decay, or of generating its revival. For the harmonic driving of a mass term, we find persistent zitterbewegung modes in pristine, i.e. scattering free, systems. Furthermore, an effective time-reversal protocol -- the "Dirac quantum time mirror" -- is shown to retrieve zitterbewegung through echoes.

cond-mat.mes-hall↗

arXiv2019

Enhancement of many-body quantum interference in chaotic bosonic systems

Although highly successful, the truncated Wigner approximation (TWA) leaves out many-body quantum interference between mean-field Gross-Pitaevskii solutions as well as other quantum effects, and is therefore essentially classical. Turned around, this implies that if a system's quantum properties deviate from TWA, they must be exhibiting some quantum phenomenon, such as localization, diffraction, or tunneling. Here, we consider in detail a particular interference effect arising from discrete symmetries, which can lead to a significant enhancement of quantum observables with respect to the TWA prediction, and derive an augmented version of the TWA in order to incorporate them. Using the Bose-Hubbard model for illustration, we further show strong evidence for the presence of dynamical localization due to remaining differences between the TWA predictions and quantum results.

cond-mat.quant-gas↗

arXiv2019

Reversible quantum information spreading in many-body systems near criticality

Quantum chaotic interacting $N$-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales $\sim\!\log N$. Here we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-$N$ limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing $\hbar/τ$, again given by $τ\! \sim\! \log N$. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasi-periodic recurrences indicating reversibility.

quant-ph↗

arXiv2019

Electrostatic Superlattices on Scaled Graphene Lattices

A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moiré patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moiré superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple model Hamiltonian that does not comprise higher-order terms of effective vector potential and Dirac mass terms. In the case of gate-controllable superlattices, no higher-order terms are involved, and the simulations are expected to be numerically exact. Revisiting a recent experiment on graphene subject to a gated square superlattice with periodicity of 35 nm, our simulations show excellent agreement, revealing the emergence of multiple extra Dirac cones at stronger superlattice modulation.

cond-mat.mes-hall↗

arXiv2019

The Electronic Thickness of Graphene

The van-der-Waals stacking technique enables the fabrication of heterostructures, where two conducting layers are atomically close. In this case, the finite layer thickness matters for the interlayer electrostatic coupling. Here we investigate the electrostatic coupling of two graphene layers, twisted by 22 degrees such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance C and is therefore suited to extract C. We explain the large observed value of C by considering the finite dielectric thickness d of each graphene layer and determine d=2.6 Angstrom. In a second experiment we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi-wavelength in each layer, showing that the layers are decoupled. We find that the Fermi wavelength exceeds 600nm at the lowest densities and can differ by an order of magnitude between the upper and lower layer. These findings are reproduced using tight-binding calculations.

cond-mat.mes-hall↗

arXiv2019

Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales

Despite considerable progress during the last decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg time $T_H$) is still missing. This challenge, corresponding to resolving spectral structures on energy scales below the mean level spacing, is intimately related to the quest for semiclassically restoring quantum unitarity, which is reflected in real-valued spectral determinants. Guided through insights for quantum graphs we devise a periodic-orbit resummation procedure for quantum chaotic systems invoking periodic-orbit self encounters as the structuring element of a hierarchical phase space dynamics. We propose a way to purely semiclassically construct real spectral determinants based on two major underlying mechanisms: (i) Complementary contributions to the spectral determinant from regrouped pseudo orbits of duration $T < T_H$ and $T_H-T$ are complex conjugate to each other. (ii) Contributions from long periodic orbits involving multiple traversals along shorter orbits cancel out. We furthermore discuss implications for interacting $N$-particle quantum systems with a chaotic classical large-$N$ limit that have recently attracted interest in the context of many-body quantum chaos.

nlin.CD↗

arXiv2019

Partial Fermionization---Spectral Universality in 1D Repulsive Bose Gases

Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few up to many particles share the same underlying spectral features. In our derivation we supplement quantum cluster expansions with short-time dynamical information. Our nonperturbative analytical results are in excellent agreement with numerics for systems of experimental relevance in cold atom physics, such as interacting bosons on a ring (Lieb-Liniger model) or subject to harmonic confinement. Our method provides predictions for excitation spectra that enable access to finite-temperature thermodynamics in large parameter ranges.

cond-mat.quant-gas↗

arXiv2018

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators

Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems. They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time $τ_{\rm E}$ in the quantum correlated regime. Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic $N$-particle systems. We first show how the growth of OTOCs up to $τ_{\rm E} = (1/λ) \log N$ is related to the Lyapunov exponent $λ$ of the corresponding chaotic mean-field dynamics in the semiclassical large-$N$ limit. Beyond $τ_{\rm E}$, where simple mean-field approaches break down, we identify the underlying quantum mechanism responsible for the saturation. To this end we express OTOCs by coherent sums over contributions from different mean-field solutions and compute the dominant many-body interference term amongst them. Our method further applies to the complementary semiclassical limit $\hbar \rightarrow 0$ for fixed $N$, including quantum-chaotic single- and few-particle systems.

cond-mat.stat-mech↗