Abstract: Themean-field Hubbard model is used to investigate the formation of the antiferromagnetic phase in hexagonal graphene rings with inner zigzag edges. The outer edge of the ring was taken to be either zigzag or armchair, and we found that both types of structures can have a larger antiferromagnetic interaction as compared with hexagonal dots. This difference could be partially ascribed to the larger number of zigzag edges per unit area in rings than in dots. Furthermore, edge states localized on the inner ring edge are found to hybridize differently than the edge states of dots, which results in important differences in the magnetism of graphene rings and dots. The largest staggered magnetization is found when the outer edge has a zigzag shape. However, narrow rings with armchair outer edge are found to have larger staggered magnetization than zigzag hexagons. The edge defects are shown to have the least effect on magnetization when the outer ring edge is armchair shaped. DOI: 10.1103/PhysRevB.87.085434

Abstract: The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.

Abstract: Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow variations in the single-particle density of states driven by the size quantization. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size coherent effects, overlooked previously. The many-body physics is revealed here in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. The single-particle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasi-free dispersion. This results in the formation of a series of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEC-like components.

Abstract: The energy spectrum and density of states of graphene bilayer superlattices (SLs) are evaluated. We take into account doping and/or gating of the layers as well as tunnel coupling between them. In addition, we evaluate the transmission through such SLs and through single or double barriers. The transmission exhibits a strong dependence on the direction of the incident wave vector.

Abstract: We study the structure and phonon spectrum of a two-dimensional bilayer system of classical charged dipoles oriented perpendicular to the plane of the layers for equal density in each layer. This system can be tuned through six different crystalline phases by changing the interlayer separation or the charge and/or dipole moment of the particle. The presence of the charge on the dipole particles is responsible for the nucleation of five staggered phases and a disordered phase which are not found in the magnetic dipole bilayer system. These extra phases are a consequence of the competition between the repulsive Coulomb and the attractive dipole interlayer interaction. We present the phase diagram and determine the order of the phase transitions. The phonon spectrum of the system was calculated within the harmonic approximation, and a nonmonotonic behavior of the phonon spectrum is found as a function of the effective strength of the interparticle interaction. The stability of the different phases is determined.

Abstract: We evaluate the electronic transmission and conductance in bilayer graphene through a finite number of potential barriers. Further, we evaluate the dispersion relation in a bilayer graphene superlattice with a periodic potential applied to both layers. As a model we use the tight-binding Hamiltonian in the continuum approximation. For zero bias the dispersion relation shows a finite gap for carriers with zero momentum in the direction parallel to the barriers. This is in contrast to single-layer graphene where no such gap was found. A gap also appears for a finite bias. Numerical results for the energy spectrum, conductance, and the density of states are presented and contrasted with those pertaining to single-layer graphene.

Abstract: The influence of triaxial in-plane strain on the electronic properties of a hexagonal boron-nitride sheet is investigated using density functional theory. Different from graphene, the triaxial strain localizes the molecular orbitals of the boron-nitride flake in its center depending on the direction of the applied strain. The proposed technique for localizing the molecular orbitals that are close to the Fermi level in the center of boron nitride flakes can be used to actualize engineered nanosensors, for instance, to selectively detect gas molecules. We show that the central part of the strained flake adsorbs polar molecules more strongly as compared with an unstrained sheet.

Abstract: We theoretically demonstrate that the transport inefficiency recently found experimentally for branched-out mesoscopic networks can also be observed in a quantum ring of finite width with an attached central horizontal branch. This is done by investigating the time evolution of an electron wave packet in such a system. Our numerical results show that the conductivity of the ring does not necessary improve if one adds an extra channel. This ensures that there exists a quantum analog of the Braess paradox, originating from quantum scattering and interference.

Abstract: The energy dispersion of an exciton in a coupled quantum well is modified by an external in-plane magnetic field. We find that the in-plane magnetic field can shift the ground state of the magnetoexciton from a zero in-plane center-of-mass (CM) momentum to a finite CM momentum, and render the ground state of the magnetoexciton stable against radiative recombination due to momentum conservation. At the same time, a spatial separation of the electron and hole is realized. Thus an in-plane magnetic field can be used to tailor the radiative properties of excitons in coupled quantum wells.