Effect of disorder on the electronic properties of graphene: a theoretical approach

In order to manipulate the properties of graphene, its very important to understand the electronic structure in presence of disorder. We investigate, within a tight-binding description, the effects of disorder in the on-site (diagonal disorder) term in the Hamiltonian as well as in the hopping integral (off-diagonal disorder) on the electronic dispersion and density of states by augmented space recursion method. Extrinsic off-diagonal disorder is shown to have dramatic effects on the two-dimensional Dirac-cone, including asymmetries in the band structures as well as the presence of discontinuous bands in certain limits. Disorder-induced broadening, related to the scattering length (or life-time) of electrons, is modified significantly with the increasing strength of disorder. We propose that our theory is suitable to study the effects of disorder in other 2D materials, e.g., a boron nitride monolayer.Comment: 11 pages, 8 figure

Lattice thermal conductivity of disordered binary alloys : a formulation

We present here a formulation for the calculation of the configuration averaged lattice thermal conductivity in random alloys. Our formulation is based on the augmented-space theorem, introduced by one of us, combined with a generalized diagrammatic technique. The diagrammatic approach simplifies the problem of including effects of disorder corrections to a great extent. The approach allows us to obtain an expression for the effective heat current in case of disordered alloys, which in turn is used in a Kubo-Greenwood type formula for the thermal conductivity. We show that disorder scattering renormalizes the phonon propagators as well as the heat currents. The corrections to the current terms have been shown to be related to the self-energy of the propagators. We also study the effect of vertex corrections in a simplified ladder diagram approximation. A mode dependent diffusivity $D_{\gamma}$ and then a total thermal diffusivity averaged over different modes are defined. Schemes for implementing the said formalism are discussed. A few initial numerical results on the frequency and temperature dependence of lattice thermal conductivity are presented for NiPd alloy and are also compared with experiment. We also display numerical results on the frequency dependence of thermal diffusivity averaged over modes.Comment: 16 pages, 17 figure

Optical properties of random alloys : Application to Cu_{50}Au_{50} and Ni_{50}Pt_{50}

In an earlier paper [K. K. Saha and A. Mookerjee, Phys. Rev. B 70 (2004) (in press) or, cond-mat/0403456] we had presented a formulation for the calculation of the configuration-averaged optical conductivity in random alloys. Our formulation is based on the augmented-space theorem introduced by one of us [A. Mookerjee, J. Phys. C: Solid State Phys. 6, 1340 (1973)]. In this communication we shall combine our formulation with the tight-binding linear muffin-tin orbitals (TB-LMTO) technique to study the optical conductivities of two alloys Cu_{50}Au_{50} and Ni_{50}Pt_{50}.Comment: 5 pages, 7 figure

H\"older equicontinuity of the integrated density of states at weak disorder

H\"older continuity, $|N_\lambda(E)-N_\lambda(E')|\le C |E-E'|^\alpha$, with a constant $C$ independent of the disorder strength $\lambda$ is proved for the integrated density of states $N_\lambda(E)$ associated to a discrete random operator $H = H_o + \lambda V$ consisting of a translation invariant hopping matrix $H_o$ and i.i.d. single site potentials $V$ with an absolutely continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4 combine

Augmented space recursion for partially disordered systems

Off-stoichiometric alloys exhibit partial disorder, in the sense that only some of the sublattices of the stoichiometric ordered alloy become disordered. This paper puts forward a generalization of the augmented space recursion (ASR) (introduced earlier by one of us (Mookerjee et al 1997(*))) for systems with many atoms per unit cell. In order to justify the convergence properties of ASR we have studied the convergence of various moments of local density of states and other physical quantities like Fermi energy and band energy. We have also looked at the convergence of the magnetic moment of Ni, which is very sensitive to numerical approximations towards the k-space value 0.6 $\mu_{B}$ with the number of recursion steps prior to termination.Comment: Latex 2e, 21 Pages, 13 Figures, iopb style file attache

Inelastic neutron scattering in random binary alloys : an augmented space approach

Combining the augmented space representation for phonons with a generalized version of Yonezawa-Matsubara diagrammatic technique, we have set up a formalism to seperate the coherent and incoherent part of the total intensity of thermal neutron scattering from disordered alloys. This is done exacly without taking any recourse to mean-field like approximation (as done previously). The formalism includes disorder in masses, force constants and scattering lengths. Implementation of the formalism to realistic situations is performed by an augmented space Block recursion which calculates entire Green matrix and self energy matrix which in turn is needed to evaluate the coherent and incoherent intensities. we apply the formalism to NiPd and NiPt alloys. Numerical results on coherent and incoherent scattering cross sections are presented along the highest symmetry directions. Finally the incoherent intensities are compared with the CPA and also with experiments.Comment: 18 pages, 13 figure

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation

We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary alloys.We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to $Ni_{55}Pd_{45}$, Ni_{88}Cr_12} and $Ni_{50}Pt_{50}$ alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure