Twisted trilayer graphene is a particularly promising moir\'e superlattice system, due to its tunability, strong superconductivity, and complex electronic symmetry breaking. Motivated by these properties, we study lattice relaxation the long-wavelength phonon modes of this system. We show that mirror-symmetric hosts, aside from conventional acoustic modes, two classes shear which are even odd u...

We investigate the proximity spin-orbit and exchange couplings in ABA ABC trilayer graphene encapsulated within monolayers of semiconducting transition-metal dichalcogenides ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$. Employing first-principles calculations we obtain electronic structures multilayer stacks extract relevant proximity-induced orbital spin interaction parameters by fitting low...

A wave-packet time evolution method, based on the split-operator technique, is developed to investigate scattering of quasiparticles at a normal-superconductor interface arbitrary profile and shape. As practical application, we consider system where low-energy electrons can be described as Dirac particles, which case for most two-dimensional materials, such graphene transition-metal dichalcogen...

Not only the apparent atomic arrangement but the charge distribution also defines the crystalline symmetry that dictates the electronic and vibrational structures. In this work, we report reversible and direction-controlled chemical doping that modifies the inversion symmetry of AB-bilayer and ABC-trilayer graphene. For the "top-down" and "bottom-up" hole injection into graphene sheets, we empl...

A ferromagnet–normal-metal–ferromagnet trilayer does not conserve spin current and as a result, the conduction electrons can create a torque on the magnetic moments. When the trilayer is connected to a superconducting electrode, the spin torque created by a current flowing perpendicularly to the trilayer can drive the system to a configuration where the two magnetic moments are perpendicular to...

We theoretically study optical Hall conductivities for ABA and ABC trilayer graphenes. In ABA-stacked trilayer, the resonance spectrum is shown to be a superposition of effective monolayer and bilayer contributions with band gaps, while ABC trilayer exhibits a distinct spectrum peculiar to the cubic-dispersed bands with a strong trigonal warping, where we found the signals associated with low-e...