Small to large polaron transition in a strongly correlated system

Massimo Capone, M. Grilli, W. Stephan

I. A. Makarov, Sergei G. Ovchinnikov

In this work we investigate doping and temperature dependences of electronic structure of system with strong electronic correlations and strong electron-phonon interaction modeling cuprates in the frameworks of the three-band p-d-Holstein model by a polaronic version of the generalized tight binding (GTB) method. Within this approach the electronic structure is formed by polaronic quasiparticles constructed as excitations between initial and final polaronic multielectron states. Doping and temperature effects are taken into account by occupation numbers of local excited polaronic states and variations in the magnitude of spin-spin correlation functions. Both effects are manifested in the reconstruction of band structure, Fermi contours, density of states and redistribution of the spectral weight over the Hubbard polaron subbands. Doping leads to transformation of Fermi contour from small hole pockets around k=(pi/2,pi/2) with inhomogeneous spectral weight distribution at small hole concentration to large contour around k=(pi,pi) in the overdoped compound as a result of two quantum phase transitions. In the system with phonon subsystem and EPI doping results in the top of the valence band splitting off and new polaron subbands appearance. Temperature increasing in the system with doped holes and moderate EPI leads to formation of the flatband around k=(pi,pi) and transfer of the spectral weight to the splitted off top of the valence band.

Gerhard Wellein, Heinrich Röder, Holger Fehske

The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.

Frédéric Chevy

Yves Lépine, Y. Frongillo

An upper bound to the ground-state energy of a tight-binding polaron (a polaron in a narrow band material) in a polar crystal is obtained, in the nonadiabatic limit, from a Hamiltonian that includes two contributions to the electron–phonon coupling: a short-range deformation potential interaction and a long-range dipolar interaction. A Debye cutoff on the phonon wave vectors is also assumed. A variational ground-state energy is deduced, using a modification of a tight-binding type Ansatz used in small-polaron theory, in the nonadiabatic limit. In the weak-coupling limit the ground state corresponds to that of a large polaron, while the strong-coupling limit gives a small-polaron state. The bandwidth greatly influences the state of the system and phase diagrams are presented that show the regions where the small and the large polarons are energetically favored. We find, in this variational context, that for a narrow band, the transition between the self-trapped state and the band state is continuous and that an intermediate-polaron state is involved. For a larger but moderate bandwidth, the system is found to switch abruptly from one state to the other, with a coexistence of both states around the transition region. Each of the two types of coupling is found to have an equivalent role in increasing the trapping energy of the electron and in reducing the bandwidth exponentially. Furthermore, their effect is cumulative.

Anonymous