Solution of the Holstein polaron anisotropy problem

We study Holstein polarons in three-dimensional anisotropic materials. Using a variational exact diagonalization technique we provide highly accurate results for the polaron mass and polaron radius. With these data we discuss the differences between polaron formation in dimension one and three, and at small and large phonon frequency. Varying the anisotropy we demonstrate how a polaron evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby resolve the issue of polaron stability in quasi-one-dimensional substances and clarify to what extent such polarons can be described as one-dimensional objects. We finally show that even the local Holstein interaction leads to an enhancement of anisotropy in charge carrier motion.Comment: 6 pages, 7 figures; extended version accepted for publication in Phys. Rev.

A new model to describe the physics of VOPO

In the past different models for the magnetic salt vanadyl pyrophosphate (VOPO) were discussed. Neither a spin ladder nor an alternating chain are capable to describe recently measured magnetic excitations. In this paper we propose a 2D model that fits better to experimental observations.Comment: 4 pages, 6 figures include

Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass

We generalize the momentum average approximation to study the properties of single polarons in models with boson affected hopping, where the fermion-boson scattering depends explicitly on both the fermion's and the boson's momentum. As a specific example, we investigate the Edwards fermion-boson model in both one and two dimensions. In one dimension, this allows us to compare our results with exact diagonalization results, to validate the accuracy of our approximation. The generalization to two-dimensional lattices allows us to calculate the polaron's quasiparticle weight and dispersion throughout the Brillouin zone and to demonstrate the importance of Trugman loops in generating a finite effective mass even when the free fermion has an infinite mass.Comment: 15 pages, 14 figure

Luttinger liquid versus charge density wave behaviour in the one-dimensional spinless fermion Holstein model

We discuss the nature of the different ground states of the half-filled Holstein model of spinless fermions in 1D. In the metallic regime we determine the renormalised effective coupling constant and the velocity of the charge excitations by a density-matrix renormalisation group (DMRG) finite-size scaling approach. At low (high) phonon frequencies the Luttinger liquid is characterised by an attractive (repulsive) effective interaction. In the charge-density wave Peierls-distorted state the charge structure factor scales to a finite value indicating long-range order.Comment: 2 pages, 3 figures, submitted to SCES'0

Carrier-density effects in many-polaron systems

Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.Comment: 13 pages, 6 figures, accepted for publication in J. Phys.: Condens. Matter; final versio

Electron dynamics in graphene with gate-defined quantum dots

We use numerically exact Chebyshev expansion and kernel polynomial methods to study transport through circular graphene quantum dots in the framework of a tight-binding honeycomb lattice model. Our focus lies on the regime where individual modes of the electrostatically defined dot dominate the charge carrier dynamics. In particular, we discuss the scattering of an injected Dirac electron wave packet for a single quantum dot, electron confinement in the dot, the optical excitation of dot-bound modes, and the propagation of an electronic excitation along a linear array of dots.Comment: revised version, 6 pages, 7 figure