Flatbands with extremely narrow bandwidths on the order of a few mili-electron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flatbands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of two in the same parameter space of twist angle θ and interlayer coupling ω, making it in principle simpler to tailor narrow bandwidth flatbands. Application of vertical pressure can enhance the first magic angle in minimal models at θ ∼ 1.05 • to larger values of up to θ ∼ 1.5 • when P ∼ 2.5 GPa, where θ ∝ ω/υF . Narrow bandwidths are expected in bi-bilayers for a continuous range of small twist angles, i.e. without magic angles, when intrinsic bilayer gaps open by electric fields, or due to remote hopping terms. We find that moderate vertical electric fields can contribute in lifting the degeneracy of the low energy flatbands by enhancing the primary gap near the Dirac point and the secondary gap with the higher energy bands. Distinct valley Chern bands are expected near 0 • or 180 • alignments.

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron–electron and electron–phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron–phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

A single molecular transistor is considered in the presence of electron-electron interaction, electron-phonon interaction, an external magnetic field and dissipation. The quantum transport properties of the system are investigated using the Anderson-Holstein Hamiltonian together with the Caldeira-Leggett model that takes care of the damping effect. The phonons are first removed from the theory by averaging the Hamiltonian with respect to a coherent phonon state and the resultant electronic Hamiltonian is finally solved with the help of the Green function technique due to Keldysh. The spectral function, spin-polarized current densities, differential conductance and spin polarization current are determined.

We consider a single molecular transistor in which a quantum dot with local electron–electron and electron–phonon interactions is coupled to two metallic leads, one of which acts like a source and the other like a drain. The system is modeled by the Anderson-Holstein (AH) model. The quantum dot is mounted on a substrate that acts as a heat bath. Its phonons interact with the quantum dot phonons by the Caldeira–Leggett interaction giving rise to dissipation in the dynamics of the quantum dot system. A simple canonical transformation exactly treats the interaction of the quantum dot phonons with the substrate phonons. The electron–phonon interaction of the quantum dot is eliminated by the celebrated Lang-Firsov transformation. The time-dependent current is finally calculated by the Keldysh Green function technique with various types of bias. The transient-time phase diagram is analysed as a function of the system parameters to explore regions that can be used for fast switching in devices like nanomolecular switches.

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron-electron and electron-phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron-phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.