DOI: 10.5281/zenodo.15006050
title: Hall field induced resistance oscillations by designed random obstacle arrays

description: The data supporting the results of our article “Hall field induced resistance oscillations by designed random obstacle arrays” (Bartels et al., Phys. Rev. B 111, 165301) are freely available here. All data provided here are the measured raw data. This means that they have not been symmetrized/antisymmetrized, smoothed or background subtracted. All data were generated by applying an ac current with a frequency of 17.8 Hz and an amplitude of 500 nA. The longitudinal voltage drop (Vxx) and the Hall voltage (Vxy) were measured, as well as the phases via lock-in amplifiers (model SR830DSP from Stanford Research Instruments). Phase xx (phase xy) refers to the measured phase to the associated voltage Vxx (Vxy). For the sake of simplicity, the samples are labeld n0 to n4. n0 denotes our pristine 2DEG. n1-n4 denote the 4 investigated Lorentz arrays with increasing scattering density. 




File name
Figure
Description


n0_Bsweep_no_DC.csv
Fig. 1
$r_{xx}(B)$ - Determination of $\tau_q$ from SdH oscillations and $\tau_D$


n1_Bsweep_no_DC.csv
Fig. 1
$r_{xx}(B)$ - Determination of $\tau_q$ from SdH oscillations and $\tau_D$


n2_Bsweep_no_DC.csv
Fig. 1
$r_{xx}(B)$ - Determination of $\tau_q$ from SdH oscillations and $\tau_D$


n3_Bsweep_no_DC.csv
Fig. 1
$r_{xx}(B)$ - Determination of $\tau_q$ from SdH oscillations and $\tau_D$


n4_Bsweep_no_DC.csv
Fig. 1
$r_{xx}(B)$ - Determination of $\tau_q$ from SdH oscillations and $\tau_D$


n0_Isweep.csv
Fig. 2-4a/ SI Fig. 3-4
$r_{xx}(I_{DC})$ for the pristine 2DEG


n1_Isweep.csv
Fig. 2-4a/ SI Fig. 3-4
$r_{xx}(I_{DC})$ for $n^\star = 0.0098$ 


n2_Isweep.csv
Fig. 2-4a/ SI Fig. 3-4
$r_{xx}(I_{DC})$ for $n^\star = 0.0196$


n3_Isweep.csv
Fig. 2-4a/ SI Fig. 3-4
$r_{xx}(I_{DC})$ for $n^\star = 0.0393$


n4_Isweep.csv
Fig. 2-4a / SI Fig. 3-4
$r_{xx}(I_{DC})$ for $n^\star = 0.0785$


n0_Bsweep_with_dc_currents
Fig 4b / SI Fig. 2
$r_{xx}(B)$ for $n^\star = 0$ and four different DC currents


Hallvoltage_measurements.csv
SI Fig.1
$r_{xy}(B)$ - Determination of $n_e$ from Hall slope




 
description: Hall field induced resistance oscillations (HIROs) are studied in two-dimensional electron gases with resistivities dominated by scattering at identical but randomly distributed circular obstacles with hard walls. For sufficiently high number densities, these obstacles dominate the HIROs, even though they remain sparse in comparison to the intrinsic scatterers. With increasing obstacle density, we observe a monotonous increase of the HIRO period up to a factor of two. The results are interpreted in terms of a substantial localization of the Hall field around the designed obstacles, providing an alternative explanation for the HIRO scaling factor $\gamma$ in pristine two-dimensional electron gases in terms of spatially varying Hall fields.
description: All measurements are performed in the mixing chamber of a $^3$He/$^4$He dilution refrigerator with a base temperature of $8\,\mathrm{mK}$. The electron temperature is estimated to $\approx 80\,\mathrm{mK}$. To obtain the magnetoresistivity at quasi-equilibrium, an ac current with an amplitude of $500\,\mathrm{nA}$ and a frequency of $17.8\,\mathrm{Hz}$ was applied, and the voltage drop in longitudinal and transverse directions are measured via voltage probes connected to lock-in amplifiers (model SR 830 DSP from Stanford Research Instruments). The distance between the measurement contacts in both longitudinal as well as transverse direction equals $100\,\mathrm{\mu m}$. Magnetic fields $B$ oriented perpendicularly to the 2DEG can be applied via a tunable superconducting solenoid. HIRO are observed in the differential longitudinal resistivity $r_{xx}$ as a function of $B$ or of the dccurrent $I_{\mathrm{dc}}$, given by $r_{xx}(I_{dc}, B)\equiv V_{xx,ac}(I_{\mathrm{dc}}, B)/I_{\mathrm{ac}}$. The ac current is superimposed to $I_{\mathrm{dc}}$ generated by a Yokogawa GS200 current source, and the corresponding acvoltage $V_{xx,ac}$ is detected as a function of $B$ up to $300\,\mathrm{mT}$ or of $I_{\mathrm{dc}}$, varied between $0$ and $130\,\mathrm{\mu A}$.