Giant Shubnikov-de Haas Oscillations with V-Shaped Minima in a High-Mobility Two-Dimensional Electron Gas: Experiment and Phenomenological Model

TL;DR

This work addresses the challenge of describing giant Shubnikov–de Haas oscillations with V-shaped minima in a high-mobility 2DEG, where conventional theories fail to capture the full magnetoresistance behavior. It introduces a phenomenological model based on Gaussian Landau-level broadening, a DOS that scales with the field via $\tau_B(E)=\tau_{\text{tr}}\frac{\nu_0}{\nu(B,E)}$, and magnetic-field–driven oscillations of the Fermi level at fixed density, enabling direct calculation of $R(B)$ across wide $B$ and $T$ ranges. The model accurately reproduces both the oscillatory features and the smooth positive background, yielding robust extraction of $\tau_q$ and $\tau_{\text{tr}}$ (with $\tau_q$ temperature-independent and $\tau_{\text{tr}}$ decreasing with temperature due to acoustic phonons). It is validated on microscopic Hall bars and macroscopic samples, providing a practical tool for 2DEG spectroscopy in micro/nano structures with weak disorder and highlighting the role of $E_F(B)$ oscillations in shaping SdHO. Overall, the approach offers a unified framework to analyze magnetotransport in high-mobility 2DEGs and to quantify scattering mechanisms beyond conventional regimes.

Abstract

Giant Shubnikov-de Haas oscillations (SdHO) with V-shaped minima are experimentally studied in a high-mobility two-dimensional electron gas based on GaAs/AlGaAs heterostructures. A phenomenological model with two parameters (transport momentum relaxation time $τ_{\text{tr}}$ and quantum scattering time $τ_q$) is developed, accurately describing experimentally measured magnetoresistance over an unexpectedly wide range of magnetic fields (up to 3.5 T) and temperatures (from 2 K to 15 K). The model combines: (i) a quasiclassical density of states with a magnetic-field-dependent Gaussian broadening of Landau levels, (ii) a momentum relaxation time scaling with the density of states, and (iii) oscillations of the Fermi level at a fixed electron density. This model reproduces V-shaped oscillation minima with zero-resistance points, a smooth background of positive magnetoresistance, and enables the extraction of $τ_q$ and $τ_{\text{tr}}$ even in microstructures where ballistic and viscous effects dominate at low fields. As expected, the temperature dependence reveals that $τ_{\text{tr}}$ scales inversely with temperature due to acoustic phonon scattering, while $τ_q$ remains temperature-independent.

Figures (5)

• Figure 1: Experimental (a) and calculated (b) longitudinal magnetoresistance $R(B)$ at temperatures from 2 K to 15 K. Inset: Optical micrograph of the sample.
• Figure 2: Theoretical magnetoresistance $R(B)$ at 2K without (dashed red) and with (solid black) $E_F$ oscillations. Inset: $E_F(B)$ oscillations at 2K, 8K, and 15K.
• Figure 3: (a) Experimental and theoretical magnetoresistance $R(B)$ at 2K with upper/lower envelopes. Inset: High-field region showing deviation between the experiment and the theory due to spin splitting. (b) Color map of relative deviation of the envelope difference $\Theta$ versus filling factor $\gamma$ and temperature $T$.
• Figure 4: Dingle plot: Experimental (black solid) and theoretical Dingle factors versus $1/B$ for Gaussian (red solid), Lorentzian (blue fine dashed), and the modified SCBA Vavilov2004 (green dash-dotted) broadening models. Thick dashed line: First harmonic approximation. All data is shown for $T=$ 4 K.
• Figure 5: Magnetoresistance $R(B)$ for a macroscopic Hall bar ($15\times10$ µm) at 4K. Black solid: experiment. Red solid: full model. Dashed blue: nonoscillating background from Eq. \ref{['eq:nonosc']}, accounting for thermal suppression of SdHO.