Giant Shubnikov–de Haas oscillations with V-shaped minima in a high-mobility two-dimensional electron gas: Experiment and phenomenological model

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.