Tapash Chakraborty

Properties of graphene: a theoretical perspective

The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance, the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices, such as single molecule gas sensors, ballistic transistors and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest. In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorists perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. Recent experminental observations of a metal–insulator transition in hydrogenated graphene is discussed in terms of a self-consistent theory and compared with related numerical simulations. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect and optical properties. Confinement of electrons in graphene is non-trivial due to Klein tunnelling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane–gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.

Tunable band gap and magnetic ordering by adsorption of molecules on graphene

We have studied the electronic and magnetic properties of graphene and their modification due to the adsorption of water and other gas molecules. Water and gas molecules adsorbed on nanoscale graphene were found to play the role of defects which facilitate the tunability of the bandgap and allow us to control the magnetic ordering of localized states at the edges. The adsorbed molecules push the wavefunctions corresponding to

Fractional Quantum Hall States of Dirac Electrons in Graphene

\alpha

Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

-spin (up) and

Charge Migration in DNA

\beta

Coulomb screening and collective excitations in a graphene bilayer

-spin (down) states of graphene to the opposite (zigzag) edges. This breaks the sublattice and molecular point group symmetry that results in opening of a large bandgap. The efficiency of the wavefunction displacement depends strongly on the type of molecules adsorbed

Fock-Darwin States of Dirac Electrons in Graphene-Based Artificial Atoms

We have investigated the fractional quantum Hall states of Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of electrons in graphene significantly modifies the interelectron interactions. This results in a specific dependence of the ground state energy and the energy gaps for electrons on the Landau-level index. For the valley-polarized states, i.e., at nu=1/m, m being an odd integer, the energy gaps have the largest values in the n=1 Landau level. For the valley-unpolarized states, e.g., for the 2/3 state, the energy gaps are suppressed for n=1 as compared to those at n=0. For both n=1 and n=0, the ground state of the 2/3 system is fully valley-unpolarized.

Collective excitations of Dirac electrons in a graphene layer with spin-orbit interactions

We demonstrate here that the dipole-allowed optical absorption spectrum of a parabolic quantum dot subjected to an external magnetic field reflects the interelectron interaction effects when the spin-orbit (SO) interaction is also taken into account. We have investigated the energy spectra and the dipole-allowed transition energies for up to four interacting electrons parabolically confined, and have uncovered several novel effects in those spectra that are solely due to the SO interaction.

Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

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Generation of valley polarized current in bilayer graphene

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