We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T -matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.

We study the collective states formed by two-dimensional electrons in Landau levels of index n > or = near half filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes q(3/2) like as in an ordinary Wigner crystal, and not like q(5/2) as was found in previous studies where the energy of shear deformations was neglected.

We study the cohesive energy and elastic properties as well as normal modes of the Wigner and bubble crystals of the two-dimensional electron system (2DES) in higher Landau levels. Using a simple Hartree-Fock approach, we show that the shear moduli (c66's) of these electronic crystals show a non-monotonic behavior as a function of the partial filling factor ν * at any given Landau level, with c66 increasing for small values of ν * , before reaching a maximum at some intermediate filling factor ν * m , and monotonically decreasing for ν * > ν * m . We also go beyond previous treatments, and study how the phase diagram and elastic properties of electron solids are changed by the effects of screening by electrons in lower Landau levels, and by a finite thickness of the experimental sample. The implications of these results on microwave resonance experiments are briefly discussed.

We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two hyperfine (isospin) states and the bosons have Bose-Einstein condensed (BEC). The coupling between the fermionic atoms and the bosonic fluctuations of the BEC has similarities with the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site (half-filling). We find that tuning of the lattice parameters and interaction strengths (for fermion-fermion, fermion-boson and boson-boson interactions) drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity or a charge density wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account by keeping the frequency dependence of the interaction vertices and self-energies. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem. , just to name a few indicative ones. The experimental control over a wide range of parameters associated with these type of systems renders them a favorite physics playground both for experimentalists and theorists alike. In particular, a boson-fermion mixture (BFM) system can provide a fascinating testing ground for a large section of theoretical physics[5] furthering our understanding of condensed matter phenomena.Previous work has explored part of the vast and rich phase space associated with this two-species system by employing mean-field or variational type of approaches and allowing for fluctuating occupation numbers for both fermions and bosons [6,7,8,9,10]. As expected, these approaches provide a good general picture of the rich phasespace but are unable to capture the delicate interplay and competition of correlation effects in a quantitative manner which can be a useful reference for experimentalists. A more recent work, based on our methodology of analysis [11], was the first approach to study this type of system beyond mean-field limitations but (as in all previous studies) was applied only for the regime v F ≪ v s , where retardation effects between the fermionic dynamics dictated by the Fermi velocity v F and the bosonic dynamics dictated by the sound velocity v s are not important. It is very important to investigate the physics beyond this regime since v F ≥ v s is experimentally accessible and in fact, retardation can play a crucial role in the interplay of orders. The above considerations have prompted us to focus our attention on this type of system and complement on the physical understanding of it by applying our theoretical apparatus originally developed for the electron-phonon type of system [12].The framework under which we work is based on functional renormalization group (fRG) analysis for twodimensional fermions [13] in the presence of phonons when full retardation is taken into consideration [14]. This approach has the ...

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d x 2 −y 2-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electronphonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half filling the Fermi surface is nested, a spin-density wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method ͓Tsai et al., Phys. Rev. B 72, 054531 ͑2005͔͒ that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.