A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene.

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp2carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

THz photodetector using sideband-modulated transport through surface states of a 3D topological insulator.

The transport properties of the surface charge carriers of a three dimensional topological insulator under a terahertz (THz) field along with a resonant double barrier structure is theoretically analyzed within the framework of Floquet theory to explore the possibility of using such a device for photodetection purposes. We show that due to the contribution of elastic and inelastic scattering processes in the resulting transmission, side-bands are formed in the conductance spectrum. This side band formation is similar to the side-bands formation in cavity transmission spectra in an optical cavity and this information can be used to detect the frequency of unknown THz radiation. The dependence of the conductance on the bias voltage, the effect of THz radiation on resonances and the influence of zero energy points on the transmission spectrum are also discussed.

Unconventional band structure for a periodically gated surface of a three-dimensional topological insulator.

The surface states of the three-dimensional (3D) topological insulators are described by a two-dimensional (2D) massless dirac equation. A gate-voltage-induced one-dimensional potential barrier on such surfaces creates a discrete bound state in the forbidden region outside the dirac cone. Even for a single barrier it is shown that such a bound state can create an electrostatic analogue of Shubnikov de Haas oscillation which can be experimentally observed for relatively smaller size samples. However, when these surface states are exposed to a periodic arrangement of such gate-voltage-induced potential barriers, the band structure of the same was significantly modified. This is expected to significantly alter the properties of the macroscopic system. We also suggest that, within suitable limits, the system may offer ways to control electron spin electrostatically, which may be practically useful.

Scattering of massless Dirac fermions in circular p-n junctions with and without magnetic field.

In the absence of a magnetic field, a scattered wavefunction inside a circular p-n junction in graphene exhibits an interference pattern with its high intensity maximum located around the caustics. We investigate the wavefunctions in the presence of a uniform magnetic field outside the circular region to show how the loci of the high intensity region changes by forming a Landau-level structure outside the circular region and a central high intensity region inside the circular p-n junction due to the strong reflection of massless Dirac fermions by the outside magnetic field. We conclude by suggesting experimental ways to detect such changes in pattern due to the effect of the magnetic field.

Cavity optomechanics with synthetic Landau levels of ultracold fermi gas.

Ultracold fermionic atoms placed in a synthetic magnetic field arrange themselves in Landau levels. We theoretically study the optomechanical interaction between the light field and collective excitations of such fermionic atoms in synthetic magnetic field by placing them inside a Fabry-Perot cavity. We derive the effective Hamiltonian for particle hole excitations from a filled Landau level using a bosonization technique and obtain an expression for the cavity transmission spectrum. Using this we show that the cavity transmission spectrum demonstrates cold atom analog of Shubnikov-de Haas oscillation in electronic condensed matter systems. We discuss the experimental consequences for this oscillation for such a system and the related optical bistability.

Electro-optically switchable spatial-mode entangled photon pairs using a modified Mach-Zehnder interferometer.

In this Letter, we propose and analyze a switchable integrated optical waveguide device employing a modified Mach-Zehnder interferometer, capable of generating nondegenerate, maximally spatial-mode entangled photon pairs. Using an integrated electro-optic phase modulator, we show the possibility of on-demand switching of spatial-mode entangled state from a Φ+ to a Ψ+ state and vice versa. Such a versatile device with the potential of easy manipulation of the "spatial-mode" degree of freedom, should be very interesting in realizing integrated optical chips for quantum information processing.

Reversal of Klein reflection by magnetic barriers in bilayer graphene.

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schrödinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.

Electron transport and Goos-Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure.

Transport of massless Dirac fermions in graphene monolayers is analysed in the presence of a combination of singular magnetic barriers and applied electrostatic potential. Extending a recently proposed (Ghosh and Sharma 2009 J. Phys.: Condens. Matter 21 292204) analogy between the transmission of light through a medium with modulated refractive index and electron transmission in graphene through singular magnetic barriers to the present case, we find the addition of a scalar potential profoundly changes the transmission. We calculate the quantum version of the Goos-Hänchen shift that the electron wave suffers upon being totally reflected by such barriers. The combined electric and magnetic barriers substantially modify the band structure near the Dirac point. This affects transport near the Dirac point significantly and has important consequences for graphene-based electronics.

Electron optics with magnetic vector potential barriers in graphene.

An analysis of electron transport in graphene in the presence of various arrangements of delta-function like magnetic barriers is presented. The motion through one such barrier gives an unusual non-specular refraction leading to asymmetric transmission. The symmetry is restored by putting two such barriers in opposite directions side by side. Periodic arrangements of such barriers can be used as Bragg reflectors whose reflectivity has been calculated using a transfer matrix formalism. Such Bragg reflectors can be used to make resonant cavities. We also analyze the associated band structure for the case of infinite periodic structures.

Spinor dipolar bose-einstein condensates: classical spin approach.

Bose-Einstein condensates which are dominated by magnetic dipole-dipole interaction are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from the large spin limit to obtain an effective minimal Hamiltonian. This is a version extended from a nonlinear sigma model. By solving the Gross-Pitaevskii equation, we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.