arXiv subjects

Stefan Ludwig

Publications and source records attributed to Stefan Ludwig.

12 recordsLinked to original sources

arXiv2026

Current density distribution for the quantum Hall effect

Our microscopic understanding of the integer quantum Hall effect is still incomplete. For decades, there has been a controversial discussion about "where the current flows" if the Hall resistance is quantized. Here, we qualitatively analyze the current density distribution in a Hall bar based on the screening properties of a two-dimensional electron system in the quantum Hall regime. Beyond previous publications, we include a closed loop persistent current that exists inside a Hall bar if the Hall resistance is quantized. We find, that the persistent current density decreases with increasing Hall voltage. Accounting for this dependence, we find, that the current flows in the opposite directions along opposite edges of the Hall bar, while the imposed current flows unidirectionally and only on the side of the Hall bar connected with its higher electrical potential edge.

cond-mat.mes-hall↗

arXiv2025

Nature of current flow in the regime of the quantum Hall effect

The integer quantum Hall effect (QHE) belongs to the most fundamental phenomena of solid state physics and has an important application as resistance standard. It serves as a basis to understand the fractional, anomalous or spin QHEs, candidates for applications in quantum technology due to their topological properties. For optimizing all these applications it is essential to understand where the current flows inside the Hall bar, a question disputed for decades. We perform multiterminal current measurements on a Hall bar and compare the results with limiting models. We confirm, based on these experiments, that the current flow is chiral for the plateaus of quantized Hall resistance. Everywhere else, including the ranges between plateaus, our results comply with the Drude model, which predicts homogeneous current flow across a homogeneous Hall-bar.

cond-mat.mes-hall↗

arXiv2025

Transition from edge- to bulk-currents in the quantum Hall regime

The integer quantum Hall effect can be observed in a two-dimensional conductor penetrated by a perpendicular magnetic field and with edges connecting the current carrying contacts. Its signature is a state of quantized Hall and simultaneously vanishing longitudinal resistances. A widely accepted model is the Landauer-Büttiker picture, which assumes an incompressible, i.e., electrically insulating bulk state surrounded by current carrying one-dimensional edge channels. This single-particle model is challenged by the screening theory. It derives, that electron-electron interaction leads to a fragmentation of the Hall bar into compressible and incompressible strips, where the current flows inside the incompressible strips. Because the latter gradually shift from the sample edges into the bulk as the magnetic field is increased, it suggests a transition from edge- to bulk-current. We present a direct experimental proof of this transition. Our results support the screening theory.

cond-mat.mes-hall↗

arXiv2023

Visualized Wave Mechanics by Coupled Macroscopic Pendula: Classical Analogue to Driven Quantum Bits

Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle, classical mechanics is often seen as a theory for large systems where quantum coherence is completely averaged out. Surprisingly, it is still possible to reconstruct the coherent dynamics of a quantum bit (qubit) by using a classical model system. This classical-to-quantum analogue is based on wave mechanics, which applies to both, the classical and the quantum world. In this spirit we investigate the dynamics of macroscopic physical pendula with a modulated coupling. As a proof of principle, we demonstrate full control of our one-to-one analogue to a qubit by realizing Rabi oscillations, Landau-Zener transitions and Landau-Zener-Stückelberg-Majorana interferometry. Our classical qubit demonstrator can help comprehending and developing useful quantum technologies.

quant-ph↗

arXiv2021

Atomic force microscopy calibration of standing surface acoustic wave amplitudes

Atomic force microscopy is an important tool for characterizing surface acoustic waves, in particular for high frequencies, where the wavelength is too short to be resolved by laser interferometry. A caveat is, that the cantilever deflection is not equal to the amplitude of the surface acoustic wave. We show, that the energy transfer from the moving surface to the cantilever instead leads to a deflection exceeding the surface modulation. We present a method for an accurate calibration of surface acoustic wave amplitudes based on comparing force-curve measurements with the equation of motion of a driven cantilever. We demonstrate our method for a standing surface acoustic wave on a GaAs crystal confined in a focusing cavity with a resonance frequency near 3 GHz.

cond-mat.mes-hall↗

arXiv2020

Electrostatic potential shape of gate defined quantum point contacts

Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but the precise potential shapes are usually unknown. Here, we measure the one-dimensional subband spacings of various QPCs as a function of their conductance and compare our findings with models of lateral parabolic versus hard wall confinement. We find that a gate-defined QPC near pinch-off is compatible with the parabolic saddle point scenario. However, as the number of populated subbands is increased Coulomb screening flattens the potential bottom and a description in terms of a finite hard wall potential becomes more realistic.

cond-mat.mes-hall↗

arXiv2020

Coherent Electron Optics with Ballistically Coupled Quantum Point Contacts

The realization of integrated quantum circuits requires precise on-chip control of charge carriers. Aiming at the coherent coupling of distant nanostructures at zero magnetic field, here we study the ballistic electron transport through two quantum point contacts (QPCs) in series in a three terminal configuration. We enhance the coupling between the QPCs by electrostatic focusing using a field effect lens. To study the emission and collection properties of QPCs in detail we combine the electrostatic focusing with magnetic deflection. Comparing our measurements with quantum mechanical and classical calculations we demonstrate how the coherent and ballistic dynamics depend on the details of the QPC confinement potentials.

cond-mat.mes-hall↗

arXiv2018

Optimization of ohmic contacts to n-type GaAs nanowires

III-V nanowires are comprehensively studied because of their suitability for optoelectronic quantum technology applications. However, their small dimensions and the spatial separation of carriers from the wire surface render electrical contacting difficult. Systematically studying ohmic contact formation by diffusion to $n$-doped GaAs nanowires, we provide a set of optimal annealing parameters for Pd/Ge/Au ohmic contacts. We reproducibly achieve low specific contact resistances of $\sim2\times10^{-7}\,Ω\text{cm}^2$ at room temperature becoming an order of magnitude higher at $T\simeq4.2\,$K. We provide a phenomenological model to describe contact resistances as a function of diffusion parameters. Implementing a transfer-matrix method, we numerically study the influence of the Schottky barrier on the contact resistance. Our results indicate that contact resistances can be predicted using various barrier shapes but further insights into structural properties would require a full microscopic understanding of the complex diffusion processes.

cond-mat.mes-hall↗

arXiv2015

Multistability and spin diffusion enhanced lifetimes in dynamic nuclear polarization in a double quantum dot

The control of nuclear spins in quantum dots is essential to explore their many-body dynamics and exploit their prospects for quantum information processing. We present a unique combination of dynamic nuclear spin polarization and electric-dipole-induced spin resonance in an electrostatically defined double quantum dot (DQD) exposed to the strongly inhomogeneous field of two on-chip nanomagnets. Our experiments provide direct and unrivaled access to the nuclear spin polarization distribution and allow us to establish and characterize multiple fixed points. Further, we demonstrate polarization of the DQD environment by nuclear spin diffusion which significantly stabilizes the nuclear spins inside the DQD.

cond-mat.mes-hall↗

arXiv2014

On the relation between the 0.7-anomaly and the Kondo effect: Geometric Crossover between a Quantum Point Contact and a Kondo Quantum Dot

Quantum point contacts (QPCs) and quantum dots (QDs), two elementary building blocks of semiconducting nanodevices, both exhibit famously anomalous conductance features: the 0.7-anomaly in the former case, the Kondo effect in the latter. For both the 0.7-anomaly and the Kondo effect, the conductance shows a remarkably similar low-energy dependence on temperature $T$, source-drain voltage $V_{\rm sd}$ and magnetic field $B$. In a recent publication [F. Bauer et al., Nature, 501, 73 (2013)], we argued that the reason for these similarities is that both a QPC and a KQD feature spin fluctuations that are induced by the sample geometry, confined in a small spatial regime, and enhanced by interactions. Here we further explore this notion experimentally and theoretically by studying the geometric crossover between a QD and a QPC, focussing on the $B$-field dependence of the conductance. We introduce a one-dimensional model that reproduces the essential features of the experiments, including a smooth transition between a Kondo QD and a QPC with 0.7-anomaly. We find that in both cases the anomalously strong negative magnetoconductance goes hand in hand with strongly enhanced local spin fluctuations. Our experimental observations include, in addition to the Kondo effect in a QD and the 0.7-anomaly in a QPC, Fano interference effects in a regime of coexistence between QD and QPC physics, and Fabry-Perot-type resonances on the conductance plateaus of a clean QPC. We argue that Fabry-Perot-type resonances occur generically if the electrostatic potential of the QPC generates a flatter-than-parabolic barrier top.

cond-mat.str-el↗

arXiv2012

Large nuclear spin polarization in gate-defined quantum dots using a single-domain nanomagnet

The electron-nuclei (hyperfine) interaction is central to spin qubits in solid state systems. It can be a severe decoherence source but also allows dynamic access to the nuclear spin states. We study a double quantum dot exposed to an on-chip single-domain nanomagnet and show that its inhomogeneous magnetic field crucially modifies the complex nuclear spin dynamics such that the Overhauser field tends to compensate external magnetic fields. This turns out to be beneficial for polarizing the nuclear spin ensemble. We reach a nuclear spin polarization of ~50%, unrivaled in lateral dots, and explain our manipulation technique using a comprehensive rate equation model.

cond-mat.mes-hall↗

arXiv2012

Few electron double quantum dot in an isotopically purified $^{28}$Si quantum well

We present a few electron double quantum dot (QD) device defined in an isotopically purified $^{28}$Si quantum well (QW). An electron mobility of $5.5 \cdot 10^4 cm^2(Vs)^{-1}$ is observed in the QW which is the highest mobility ever reported for a 2D electron system in $^{28}$Si. The residual concentration of $^{29}$Si nuclei in the $^{28}$Si QW is lower than $10^{3} ppm$, at the verge where the hyperfine interaction is theoretically no longer expected to dominantly limit the $T_{2}$ spin dephasing time. We also demonstrate a complete suppression of hysteretic gate behavior and charge noise using a negatively biased global top gate.

cond-mat.mes-hall↗