Effect of Holstein phonons on the optical conductivity of gapped graphene

We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion of the renormalized Fermi energy and the band gap effects are indeed crucial to get reasonable feature for the optical conductivity.Comment: 12 pages, 4 figures. To appear in Eur. Phys. J.

Analytical study of non-linear transport across a semiconductor-metal junction

In this paper we study analytically a one-dimensional model for a semiconductor-metal junction. We study the formation of Tamm states and how they evolve when the semi-infinite semiconductor and metal are coupled together. The non-linear current, as a function of the bias voltage, is studied using the non-equilibrium Green's function method and the density matrix of the interface is given. The electronic occupation of the sites defining the interface has strong non-linearities as function of the bias voltage due to strong resonances present in the Green's functions of the junction sites. The surface Green's function is computed analytically by solving a quadratic matrix equation, which does not require adding a small imaginary constant to the energy. The wave function for the surface states is given

Electronic Properties of Two-Dimensional Carbon

We present a theoretical description of the electronic properties of graphene in the presence of disorder, electron-electron interactions, and particle-hole symmetry breaking. We show that while particle-hole asymmetry, long-range Coulomb interactions, and extended defects lead to the phenomenon of self-doping, local defects determine the transport and spectroscopic properties. Our results explain recent experiments in graphitic devices and predict new electronic behavior.Comment: 4 pages, 5 figures. The paper was originally submitted on May, 12th, 200

Adatoms in Graphene

We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility.Comment: For the Proceedings of the "Graphene Week 2008" at the ICTP in Trieste, Italy. 8 pages, 8 figure

Transport Properties through Double Barrier Structure in Graphene

The mode-dependent transmission of relativistic ballistic massless Dirac fermion through a graphene based double barrier structure is being investigated for various barrier parameters. We compare our results with already published work and point out the relevance of these findings to a systematic study of the transport properties in double barrier structures. An interesting situation arises when we set the potential in the leads to zero, then our 2D problem reduces effectively to a 1D massive Dirac equation with an effective mass proportional to the quantized wave number along the transverse direction. Furthermore we have shown that the minimal conductivity and maximal Fano factor remain insensitive to the ratio between the two potentials V_2/V_1=\alpha.Comment: 18 pages, 12 figures, clarifications and reference added, misprints corrected. Version to appear in JLT

Spin-wave spectrum in La2CuO4 -- double occupancy and competing interaction effects

The recently observed spin-wave energy dispersion along the AF zone boundary in La2CuO4 is discussed in terms of double occupancy and competing interaction effects in the $t-t'$ Hubbard model on a square lattice.Comment: 4 pages, 2 figure

Finite-Temperature Transport in Finite-Size Hubbard Rings in the Strong-Coupling Limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.Comment: 15 pages and 6 figures; accepted for PR

Thermodynamic properties of the periodic Anderson model:X-boson treatment

We study the specific dependence of the periodic Anderson Model (PAM) in the limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic regime (HF-LMM). We obtain a multiple peak structure for the specific heat in agreement with experimental results as well as the increase of the electronic effective mass at low temperatures associated with the HF-K regime. The entropy per site at low T tends to zero in the HF-K regime, corresponding to a singlet ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a doublet ground state at each site. The linear coefficient $\gamma(T)=C_{v}/T$ of the specific heat qualitatively agrees with the experimental results obtained for differents materials in the two regimes considered here.Comment: 9 pages, 14 figure

Continuous-distribution puddle model for conduction in trilayer graphene

An insulator-to-metal transition is observed in trilayer graphene based on the temperature dependence of the resistance under different applied gate voltages. At small gate voltages the resistance decreases with increasing temperature due to the increase in carrier concentration resulting from thermal excitation of electron-hole pairs. At large gate voltages excitation of electron-hole pairs is suppressed, and the resistance increases with increasing temperature because of the enhanced electron-phonon scattering. We find that the simple model with overlapping conduction and valence bands, each with quadratic dispersion relations, is unsatisfactory. Instead, we conclude that impurities in the substrate that create local puddles of higher electron or hole densities are responsible for the residual conductivity at low temperatures. The best fit is obtained using a continuous distribution of puddles. From the fit the average of the electron and hole effective masses can be determined.Comment: 18 pages, 5 figure

Graphene based superconducting quantum point contacts

We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$ is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.Comment: 8 pages, 5 figure