Stability of correlated electronic systems under the influence of the electron-phonon interaction

We have used an exact diagonalization technique to study the stability of the $t-J$-Holstein and Hubbard-Holstein models under the influence of the electron-phonon interaction. Previous results have been obtained using frozen-phonon technique or introducing only a few dynamical phonon modes due to the large Hilbert space. To check these results we have done exact diagonalization in a small cluster (four sites) including all the phonon modes allowed by symmetry. We compare our results with those obtained by using the adiabatic approximation.Comment: 10 pages, 2 Postscript figure

Tuning the polarized quantum phonon transmission in graphene nanoribbons

We propose systems that allow a tuning of the phonon transmission function T($\omega$) in graphene nanoribbons by using C$^{13}$ isotope barriers, antidot structures, and distinct boundary conditions. Phonon modes are obtained by an interatomic fifth-nearest neighbor force-constant model (5NNFCM) and T($\omega$) is calculated using the non-equilibrium Green's function formalism. We show that by imposing partial fixed boundary conditions it is possible to restrict contributions of the in-plane phonon modes to T($\omega$) at low energy. On the contrary, the transmission functions of out-of-plane phonon modes can be diminished by proper antidot or isotope arrangements. In particular, we show that a periodic array of them leads to sharp dips in the transmission function at certain frequencies $\omega_{\nu}$ which can be pre-defined as desired by controlling their relative distance and size. With this, we demonstrated that by adequate engineering it is possible to govern the magnitude of the ballistic transmission functions T$(\omega)$ in graphene nanoribbons. We discuss the implications of these results in the design of controlled thermal transport at the nanoscale as well as in the enhancement of thermo-electric features of graphene-based materials

Spectral gap induced by structural corrugation in armchair graphene nanoribbons

We study the effects of the structural corrugation or rippling on the electronic properties of undoped armchair graphene nanoribbons (AGNR). First, reanalyzing the single corrugated graphene layer we find that the two inequivalent Dirac points (DP), move away one from the other. Otherwise, the Fermi velocity decrease by increasing rippling. Regarding the AGNRs, whose metallic behavior depends on their width, we analyze in particular the case of the zero gap band-structure AGNRs. By solving the Dirac equation with the adequate boundary condition we show that due to the shifting of the DP a gap opens in the spectra. This gap scale with the square of the rate between the high and the wavelength of the deformation. We confirm this prediction by exact numerical solution of the finite width rippled AGNR. Moreover, we find that the quantum conductance, calculated by the non equilibrium Green's function technique vanish when the gap open. The main conclusion of our results is that a conductance gap should appear for all undoped corrugated AGNR independent of their width.Comment: 7 pages, 5 figure

The role of atomic vacancies and boundary conditions on ballistic thermal transport in graphene nanoribbons

Quantum thermal transport in armchair and zig-zag graphene nanoribbons are investigated in the presence of single atomic vacancies and subject to different boundary conditions. We start with a full comparison of the phonon polarizations and energy dispersions as given by a fifth-nearest-neighbor force-constant model (5NNFCM) and by elasticity theory of continuum membranes (ETCM). For free-edges ribbons we discuss the behavior of an additional acoustic edge-localized flexural mode, known as fourth acoustic branch (4ZA), which has a small gap when it is obtained by the 5NNFCM. Then, we show that ribbons with supported-edges have a sample-size dependent energy gap in the phonon spectrum which is particularly large for in-plane modes. Irrespective to the calculation method and the boundary condition, the dependence of the energy gap for the low-energy optical phonon modes against the ribbon width W is found to be proportional to 1/W for in-plane, and 1/W$^2$ for out-of-plane phonon modes. Using the 5NNFCM, the ballistic thermal conductance and its contributions from every single phonon mode are then obtained by the non equilibrium Green's function technique. We found that, while edge and central localized single atomic vacancies do not affect the low-energy transmission function of in-plane phonon modes, they reduce considerably the contributions of the flexural modes. On the other hand, in-plane modes contributions are strongly dependent on the boundary conditions and at low temperatures can be highly reduced in supported-edges samples. These findings could open a route to engineer graphene based devices where it is possible to discriminate the relative contribution of polarized phonons and to tune the thermal transport on the nanoscale