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The electronic properties of bilayer graphene strongly depend on relative orientation of the two atomic lattices. Whereas Bernal-stacked graphene is most commonly studied, a rotational mismatch between layers opens up a whole new field of…
A review work is done for electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid…
Twisted bilayer graphene (TBG) exhibits a wide range of intriguing physical properties, such as superconductivity, ferromagnetism, and superlubricity. Depending on the twist angle, periodic moir\'e superlattices form in twisted bilayer…
Trilayer graphene {(TLG)} consists of three layers of graphene arranged in a particular stacking order. In the case of ABC-ABA-ABC stacking, the layers are arranged in an A-B-C sequence, followed by an A-B-A sequence, and again an A-B-C…
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB…
In this thesis we will focus on a particular variant of few-layer graphene -- ABA-stacked trilayer graphene. Bernal (ABA) stacked trilayer graphene (TLG) is a multiband system consisting of a pair of Dirac-like massless linear bands and a…
Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer…
Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we…
We study the Landau quantization of the electronic spectrum for graphene bilayers that are rotationally faulted to produce periodic superlattices. Commensurate twisted bilayers exist in two families distinguished by their sublattice…
We present an analytical model to study the electronic properties, including full band structure, low energy dispersions around the Dirac point and density of states of the ABC-stacking $N$-layer graphene (ABCNLG). An ABCNLG can be…
We report on magneto-transport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the twelve-fold degeneracy…
We report on the transport properties of ABC and ABA stacked trilayer graphene using dual, locally gated field effect devices. The high efficiency and large breakdown voltage of the HfO2 top and bottom gates enables independent tuning of…
Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density…
Starting with twisted bilayer graphene, graphene-based moir\'e materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene…
Stacking geometry in multilayer graphene (MLG) provides an interesting degree of freedom to engineer its electronic structure near the Fermi level, wherein the linear bands in single layer graphene could retain or evolve into parabolic or…
A generalized tight-binding model, which is based on the subenvelope functions of the different sublattices, is developed to explore the novel magnetic quantization in monolayer gray tin. The effects due to the $sp^{3}$ bonding, the…
Two-dimensional systems with flat bands support correlated phases such as superconductivity and charge fractionalization. While twisted moire systems like twisted bilayer graphene have revealed such states, they remain complex to control.…
Using a Green's function approach, we study phonon-mediated superconducting pairing symmetries that may arise in bilayer graphene where the monolayers are displaced in-plane with respect to each other. We consider a generic coupling…
The Landau level spectra and the quantum Hall effect of ABA-stacked multilayer graphenes are studied in the effective mass approximation. The low-energy effective mass Hamiltonian may be partially diagonalized into an approximate…
The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square…