We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding
calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the pi-pi* band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.
We study the bilayer quantum Hall system at total filling factor u_T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is
comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation firstly assuming that only one momentum Q0 is macroscopically occupied and later we consider the same situation for two modes pm Q0. We find strong evidences that a first-order quantum phase transition at small interlayer separation takes place from a zero-momentum condensate phase, which corresponds to Halperin 111 state, to a finite-momentum condensate of magnetic excitons.
We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the
known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-$T_c$ superconductors.
We study various properties of an ultracold two-dimensional (2D) Bose gas that are beyond a mean-field description. We first derive the effective interaction for such a system as realized in current experiments, which requires the use of an energy de
pendent $T$-matrix. Using this result, we then solve the mean-field equation of state of the modified Popov theory, and compare it with the usual Hartree-Fock theory. We show that even though the former theory does not suffer from infrared divergences in both the normal and superfluid phases, there is an unphysical density discontinuity close to the Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field description by using a renormalization group approach and show how the density discontinuity is resolved. The flow equations in two dimensions, in particular, of the symmetry-broken phase, already contain some unique features pertinent to the 2D XY model, even though vortices have not been included explicitly. We also compute various many-body correlators, and show that correlation effects beyond the Hartree-Fock theory are important already in the normal phase as criticality is approached. We finally extend our results to the inhomogeneous case of a trapped Bose gas using the local-density approximation and show that close to criticality, the renormalization group approach is required for the accurate determination of the density profile.
We extend the Blume-Emery-Griffiths (BEG) model to a two-component BEG model in order to study 2D systems with two order parameters, such as magnetic superconductors or two-component Bose-Einstein condensates. The model is investigated using Monte Ca
rlo simulations, and the temperature-concentration phase diagram is determined in the presence and absence of an external magnetic field. This model exhibits a rich phase diagram, including a second-order transition to a phase where superconductivity and magnetism coexist. Results are compared with experiments on Cerium-based heavy-fermion superconductors. To study cold atom mixtures, we also simulate the BEG and two-component BEG models with a trapping potential. In the BEG model with a trap, there is no longer a first order transition to a true phase-separated regime, but a crossover to a kind of phase-separated region. The relation with imbalanced fermi-mixtures is discussed. We present the phase diagram of the two-component BEG model with a trap, which can describe boson-boson mixtures of cold atoms. Although there are no experimental results yet for the latter, we hope that our predictions could help to stimulate future experiments in this direction.
