Exact wave functions for an electron on a graphene triangular quantum dot

We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the eigenenergies are determined analytically. As an application, we calculate the corrections to the quantum dot's energy levels due to distortions of the carbon-carbon bonds at the edges of the quantum dot.Comment: 14 pages, 11 eps figure

Terahertz Transverse-Electric- and Transverse-Magnetic-polarized waves localized on graphene in photonic crystals

We predict the coexistence of both TE- and TM-polarized localized electromagnetic waves that can propagate \emph{in the same frequency range} along a graphene layer inserted in a photonic crystal. In addition, we studied the excitation of these modes by an external wave and have shown that the resonance peaks of the sample transmissivity should be observed due to the excitation of the localized waves, independently of the polarization of the exciting wave. The simplicity of the derived dispersion relations for the localized modes and the possibility to excite waves of both polarizations provide a method for measuring graphene conductivity.Comment: This manuscript was extended to 7 pages and 8 figures and published in PR

Phase separation of hydrogen atoms adsorbed on graphene and the smoothness of the graphene-graphane interface

The electronic properties of a graphene sheet with attached hydrogen atoms is studied using a modified Falicov-Kimball model on the honeycomb lattice. It is shown that in the ground state this system separates into two phases: fully hydrogenated graphene (graphane) and hydrogen-free graphene. The graphene-graphane boundary acquires a positive interface tension. Therefore, the graphene-graphane interface becomes a straight line, slightly rippled by thermal fluctuations. A smooth interface may be useful for the fabrication of mesoscopic graphene-based devices.Comment: 7 pages, 4 eps figures, submitted to Phys. Rev.

Terahertz transition radiation of bulk and surface electromagnetic waves by an electron entering a layered superconductor

We theoretically study the transition radiation of bulk and surface electromagnetic waves by an electron crossing an interface between a layered superconductor and an isotropic dielectric. We assume that the direction of the electron motion and the orientation of the superconducting layers are perpendicular to the interface. We derive the analytical expressions for the strongly anisotropic radiation fields and for the time-integrated energy fluxes of bulk and oblique surface electromagnetic waves (OSWs). We show that the OSWs with frequencies close to the Josephson plasma frequency $\omega_J$ provide the main contribution to the OSWs energy flux. Moreover, for frequencies close to the Josephson plasma frequency, the spectral density of the OSWs radiation diverges at some critical value of the azimuth angle $\varphi$. At the angles $\varphi=0$ and $\varphi=90^o$, the radiation field has a transverse magnetic polarization. We have also studied the Cherenkov radiation by the electron escaping from the layered superconductor and show that this radiation is almost monochromatic. A remarkable feature of the Cherenkov radiation in a layered superconductor is that, contrary to the isotropic case, the Cherenkov radiation distinctly manifests itself in the angular dependence of the radiation energy flux.Comment: 9 pages, 7 figures, Published in PRB, Vol. 89, No. 9, 094506(9) (2014

Electronic spectrum of twisted bilayer graphene

We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range $1^{\circ}\lesssim\theta\lesssim30^{\circ}$. We show that at certain angles $\theta$ greater than $\theta_{c}\approx1.89^{\circ}$ the electronic spectrum acquires a finite gap, whose value could be as large as $80$ meV. However, in an infinitely large and perfectly clean sample the gap as a function of $\theta$ behaves non-monotonously, demonstrating exponentially-large jumps for very small variations of $\theta$. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment $\theta$ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite size $\tilde L$ the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role as $\tilde L$. In the regime of small angles $\theta<\theta_c$, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of $\theta$. The density of states in the metallic phase varies smoothly with $\theta$.Comment: 14 pages, 9 figures; the paper's title is changed, the paper itself is significantly expanded, some incorrect conclusions from the previous version are amende

Phase separation of antiferromagnetic ground states in systems with imperfect nesting

We analyze the phase diagram for a system of weakly-coupled electrons having an electron- and a hole-band with imperfect nesting. Namely, both bands have spherical Fermi surfaces, but their radii are slightly different, with a mismatch proportional to the doping. Such a model is used to describe: the antiferromagnetism of chromium and its alloys, pnictides, AA-stacked graphene bilayers, as well as other systems. Here we show that the uniform ground state of this model is unstable with respect to electronic phase separation in a wide range of model parameters. Physically, this instability occurs due to the competition between commensurate and incommensurate antiferromagnetic states and could be of importance for other models with imperfect nesting.Comment: 7 pages, 4 eps figures, in this version minor misprints are corrected, new references are adde

Many-body effects in twisted bilayer graphene at low twist angles

We study the zero-temperature many-body properties of twisted bilayer graphene with a twist angle equal to the so-called `first magic angle'. The system low-energy single-electron spectrum consists of four (eight, if spin label is accounted) weakly-dispersing partially degenerate bands, each band accommodating one electron per Moir{\'{e}} cell per spin projection. This weak dispersion makes electrons particularly susceptible to the effects of interactions. Introducing several excitonic order parameters with spin-density-wave-like structure, we demonstrate that (i)~the band degeneracy is partially lifted by the interaction, and (ii)~the details of the low-energy spectrum becomes doping-dependent. For example, at or near the undoped state, interactions separate the eight bands into two quartets (one quartet is almost filled, the other is almost empty), while for two electrons per Moir\'{e} cell, the quartets are pulled apart, and doublets emerge. When the doping is equal to one or three electrons per cell, the doublets split into singlets. Hole doping produces similar effects. As a result, electronic properties (e.g., the density of states at the Fermi energy) demonstrate oscillating dependence on the doping concentration. This allows us to reproduce qualitatively the behavior of the conductance observed recently in experiments [Cao et al., Nature {\bf 556}, 80 (2018)]. Near half-filling, the electronic spectrum loses hexagonal symmetry indicating the appearance of a many-body nematic state.Comment: 10 pages, 3 figures. Published versio

Externally controlled band gap in twisted bilayer graphene

We theoretically study the effects of electron-electron interaction in twisted bilayer graphene in applied transverse dc electric field. When the twist angle is not very small, the electronic spectrum of the bilayer consists of four Dirac cones inherited from each graphene layer. Applied bias voltage leads to the appearance of two hole-like and two electron-like Fermi surface sheets with perfect nesting among electron and hole components. Such a band structure is unstable with respect to exciton band gap opening due to the screened Coulomb interaction. The exciton order parameter is accompanied by the spin-density-wave order. The value of the gap depends on the twist angle. More importantly, it can be controlled by applied bias voltage which opens new directions in manufacturing of different nanoscale devices.Comment: 8 pages, 2 figure

Metal-insulator transition and phase separation in doped AA-stacked graphene bilayers

We investigate the doping of AA-stacked graphene bilayers. Applying a mean field theory at zero temperature we find that, at half-filling, the bilayer is an antiferromagnetic insulator. Upon doping, the homogeneous phase becomes unstable with respect to phase separation. The separated phases are an undoped antiferromagnetic insulator and a metal with a non-zero concentration of charge carriers. At sufficiently high doping, the insulating areas shrink and disappear, and the system becomes a homogeneous metal. The conductivity changes drastically upon doping, so the bilayer may be used as a switch in electronic devices. The effects of finite temperature are also discussed.Comment: 5 pages, 3 eps figures, in this version minor misprints are corrected, new references are adde

Majorana fermion from Landau quantization in 2D topological superconductors

We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a two-dimensional p-wave superconductor are discussed. It is demonstrated that in these systems a single vortex creates two Majorana fermions, one hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle of radius $r^* \propto B^{-1}$ centered at the vortex core. In the case of many vortices, the sensitivity of $r^*$ to the magnetic field B may be used to control the coupling between the Majorana fermions. The latter property could be an asset for quantum computations.Comment: 5 pages, 1 figure, several typos are corrected, possible braiding protocol is discussed, publication information is adde