RESUMEN
Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.
RESUMEN
We employ the Schrödinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm-Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic inductionBc2(θ,Ï,T)at arbitrary directions and temperaturesTfor isotropics-wave and for anisotropicdx2-y2-wave superconducting order parameters. As for anisotropics-wave superconductors,Bc2is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factorα(θ,Ï). However, fordx2-y2-wave pairing and vanishing planar effective mass anisotropy,Bc2(π/2,Ï,T)exhibits a four-fold azimuthal pattern withC4symmetry the maxima of which are along the crystal axes just below the transition temperatureTc, but these maxima are rotated byπ/4about thezaxis asTis lowered to 0. However fordx2-y2-wave pairing with weak planar effective mass anisotropy,Bc2(π/2,Ï,T)exhibits a two-fold pattern withC2symmetry for allT ⩽ Tc, which also rotates byπ/4about thezaxis asTis lowered to 0. These low planar effective mass anisotropy cases provide a new method to distinguishs-wave anddx2-y2-wave pairing symmetries in clean unconventional superconductors.