Transport measurements in twisted bilayer graphene: Electron-phonon coupling and Landau level crossing

We investigate electronic transport in twisted bilayer graphene (tBLG) under variable temperatures ($T$), carrier densities ($n$), and transverse magnetic fields, focusing on samples with small-twist-angles ($\theta$). These samples show prominent signatures associated with the van Hove singularities (VHSs) and superlattice-induced mini-gaps (SMGs). Temperature-dependent field effect measurement shows that the difference between temperature-dependent resistivity and residual resistivity, $\rho_{xx}(n,T) - \rho_{0}(n)$, follows $~T^\beta$ for $n$ between the main Dirac point (DP) and SMG. The evolution of the temperature exponent $\beta$ with $n$ exhibits a W-shaped dependence, with minima of $\beta$ ~0.9 near the VHSs and maxima of $\beta$ ~1.7 toward the SMGs. This W-shaped behavior can be qualitatively understood with a theoretical picture that considers both the Fermi surface smearing near the VHSs and flexural-acoustic phonon scattering. In the quantum Hall regime, we observe only Landau level crossings in the massless Dirac spectrum originating from the main DP but not in the parabolic band near the SMG. Such crossings enable the measurement of an enhanced interlayer dielectric constant, attributed to a reduced Fermi velocity. Moreover, we measure the Fermi velocity, interlayer coupling strength, VHS energy relative to the DP, and gap size of SMG, four important parameters used to describe the peculiar band structure of the small-$\theta$ tBLG.