arXiv subjects

Erik Koch

Publications and source records attributed to Erik Koch.

36 records · Page 2Linked to original sources

arXiv2001

Enhancing Tc in field-doped Fullerenes by applying uniaxial stress

Capitalizing on the two-dimensional nature of superconductivity in field-effect doped C60, we show that it should be possible to increase the transition temperature Tc by applying uniaxial stress perpendicular to the gate electrode. This method not only holds the promise of substantially enhancing Tc (by about 30 K per GPa), but also provides a sensitive check of the current understanding of superconductivity in the doped Fullerenes.

cond-mat.supr-con↗

arXiv2001

Static overscreening and nonlinear response in the Hubbard Model

We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down close to the Mott transition. Away from half filling RPA is much less reliable: Already for very small values of the Hubbard interaction U, the linear response becomes much more efficient than RPA, eventually leading to overscreening already beyond quite moderate values of U. To understand this behavior we give a simple argument, which implies that the response to an external perturbation at large U should actually be strongly non-linear. This prediction is confirmed by the results of exact diagonalization.

cond-mat.str-el↗

arXiv2001

Locality properties and Wannier functions for interacting systems

We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions for interacting systems. In addition we demonstrate that the characterization of metals and insulators by the decay properties of their respective density matrices does not only apply to non-interacting, but also to interacting systems. As a prototypical example of a correlated system we investigate the one-dimensional Hubbard model. We propose an expression for the density matrix of that model, and derive a relation between the decay constant of the density matrix and the gap.

cond-mat.str-el↗

arXiv1999

Metal-Insulator transitions in generalized Hubbard models

We study the Mott transition in Hubbard models with a degenerate band on different 3-dimensional lattices. While for a non-degenerate band only the half-filled system may exhibit a Mott transition, with degeneracy there can be a transition for any integer filling. We analyze the filling dependence of the Mott transition and find that $U_c$ (the Hubbard interaction $U$ at which the transition takes place) decreases away from half-filling. In addition we can change the lattice structure of the model. This allows us to study the influence of frustration on the Mott transition. We find that frustration increases $U_c$, compared to bipartite systems. The results were obtained from fixed-node diffusion Monte Carlo calculations using trial functions which allow us to systematically vary the magnetic character of the system. To gain a qualitative understanding of the results, we have developed simple hopping arguments that help to rationalize the doping dependence and the influence of frustration on the Mott transition. Choosing the model parameters to describe the doped Fullerides, we can make contact with experiment and understand why some of the Fullerides are metals, while others, which according to density functional theory should also be metallic, actually are insulators.

cond-mat.str-el↗

arXiv1999

One-electron bands, quantum Monte Carlo, and real superconductors

We use the doped Fullerenes as an example of how realistic systems can be described by simple models. Starting from the band structure we set up a tight-binding model that describes the t_{1u} conduction band. Adding correlation terms we arrive at a generalized Hubbard Hamiltonian that we treat using quantum Monte Carlo. To address the problem of superconductivity in the doped Fullerenes, we study the screening of a point charge. We find surprisingly efficient metallic screening even for strong correlations, almost up to the Mott transition, and discuss the implications on superconductivity, in particular the effect of the efficient screening on the Coulomb pseudopotential and the electron-phonon coupling.

cond-mat.supr-con↗

arXiv1999

Filling dependence of the Mott transition in the degenerate Hubbard model

Describing the doped Fullerenes using a generalized Hubbard model, we study the Mott transition for different integer fillings of the t_1u band. We use the opening of the energy-gap E_g as a criterion for the transition. E_g is calculated as a function of the on-site Coulomb interaction U using fixed-node diffusion Monte Carlo. We find that for systems with doping away from half-filling the Mott transitions occurs at smaller U than for the half-filled system. We give a simple model for the doping dependence of the Mott transition.

cond-mat.str-el↗

arXiv1999

Screening of a point charge: a fixed-node diffusion Monte Carlo study

We study the static screening in a Hubbard-like model using fixed-node diffusion Monte Carlo. We find that the random phase approximation is surprisingly accurate even for metallic systems close to the Mott transition. As a specific application we discuss the implications of the efficient screening for the superconductivity in the doped Fullerenes. In the Monte Carlo calculations we use trial functions with two Gutzwiller-type parameters. To deal with such trial functions, we introduce a method for efficiently optimizing the Gutzwiller parameters, both in variational and in fixed-node diffusion Monte Carlo.

cond-mat.str-el↗

arXiv1999

Optimization of Gutzwiller Wavefunctions in Quantum Monte Carlo

Gutzwiller functions are popular variational wavefunctions for correlated electrons in Hubbard models. Following the variational principle, we are interested in the Gutzwiller parameters that minimize e.g. the expectation value of the energy. Rewriting the expectation value as a rational function in the Gutzwiller parameters, we find a very efficient way for performing that minimization. The method can be used to optimize general Gutzwiller-type wavefunctions both, in variational and in fixed-node diffusion Monte Carlo.

cond-mat.str-el↗

arXiv1999

Screening, Coulomb pseudopotential, and superconductivity in alkali-doped Fullerenes

We study the static screening in a Hubbard-like model using quantum Monte Carlo. We find that the random phase approximation is surprisingly accurate almost up to the Mott transition. We argue that in alkali-doped Fullerenes the Coulomb pseudopotential $μ^\ast$ is not very much reduced by retardation effects. Therefore efficient screening is important in reducing $μ^{\ast}$ sufficiently to allow for an electron-phonon driven superconductivity. In this way the Fullerides differ from the conventional picture, where retardation effects play a major role in reducing the electron-electron repulsion.

cond-mat.str-el↗

arXiv1998

Fixed-node DMC for Fermions on a lattice: Application to the doped Fullerides

Fullerides are crystals made from C60 molecules. When doped with alkali metals the valence electrons of the alkali atoms are transfered to the C60 molecules. We show how to set up a model Hamiltonian to describe the correlated hopping of these electrons between C60 molecules. Then we discuss Monte Carlo methods for such lattice Hamiltonians, putting special emphasis on the optimization of Gutzwiller wavefunctions both in variational and fixed-node diffusion Monte Carlo. As application of these methods we analyze the metal-insulator transition in the integer-doped Fullerides.

cond-mat.str-el↗

arXiv1998

Dielectric screening in doped Fullerides

For conventional superconductors the electron-electron interaction is strongly reduced by retardation effects, making the formation of Cooper pairs possible. In the alkali-doped Fullerides, however, there are no strong retardation effects. But dielectric screening can reduce the electron-electron interaction sufficiently, if we assume that the random-phase approximation (RPA) is valid. It is not clear, however, if this assumption holds, since the alkali-doped Fullerides are strongly correlated systems close to a Mott transition. To test the validity of the RPA for these systems we have calculated the screening of a test charge using quantum Monte Carlo.

cond-mat.str-el↗

arXiv1998

Quantum Monte Carlo calculations for integer-doped Fullerides

The doped Fullerides can be well described by a Hubbard model, which comprises the partly filled, threefold-degenerate t_1u orbital and the on-site Coulomb interaction U. The orbital degeneracy is known to shift the critical ratio U_c/W for the Mott-Hubbard transition towards larger values. This puts the half-filled alkali-doped Fullerides A_3 C_60 on the metallic side of the transition. Prompted by the recent synthesis of isostructural families of integer-doped Fullerides with different fillings, we investigate how the orbital degeneracy affects the Mott transition at integer fillings different from 3. The calculations are done by fixed-node diffusion Monte Carlo, using a trial function, which permits us to systematically vary the magnetic character of the system.

cond-mat.str-el↗

arXiv1998

Periodic orbit theory for realistic cluster potentials: The leptodermous expansion

The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic-orbit-expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials and show that it describes the shift of the supershells as the surface of a cluster potential gets softer. As a byproduct of our work, we find that the electronic shell and supershell structure is not affected by a lattice contraction, which might be present in small clusters.

cond-mat.mes-hall↗

arXiv1997

Mott-Hubbard insulators for systems with orbital degeneracy

We study how the electron hopping reduces the Mott-Hubbard band gap in the limit of a large Coulomb interaction U and as a function of the orbital degeneracy N. The results support the conclusion that the hopping contribution grows as roughly \sqrt{N}W, where W is the one-particle band width, but in certain models a crossover to a \sim NW behavior is found for a sufficiently large N.

cond-mat.str-el↗

arXiv1996

Mott Transition in Degenerate Hubbard Models: Application to Doped Fullerenes

The Mott-Hubbard transition is studied for a Hubbard model with orbital degeneracy N, using a diffusion Monte-Carlo method. Based on general arguments, we conjecture that the Mott-Hubbard transition takes place for U/W \propto \sqrt{N}, where U is the Coulomb interaction and W is the band width. This is supported by exact diagonalization and Monte-Carlo calculations. Realistic parameters for the doped fullerenes lead to the conclusion that stoichiometric A_3 C_60 (A=K, Rb) are near the Mott-Hubbard transition, in a correlated metallic state.

cond-mat↗

arXiv1996

Density dependence of the electronic supershells in the homogeneous jellium model

We present the results of self-consistent calculations of the electronic shell and supershell structure for clusters having up to 6000 valence electrons. The ionic background is described in terms of a homogeneous jellium. The calculations were performed for a series of different electron densities, resembling Cs, Rb, K, Na, Li, Au, Cu, Tl, In, Ga, and Al, respectively. By analyzing the occupation of the energy levels at the Fermi energy as a function of cluster size, we show how the shell and supershell structure for a given density arises from the specific arrangement of energy levels. We investigate the electronic shells and supershells obtained for different electron densities. Using a scaling argument, we find a surprisingly simple dependence of the position of the supernodes on the electron density.

cond-mat↗

arXiv1996

On the 3n+l Quantum Number in the Cluster Problem

It has recently been suggested that an exactly solvable problem characterized by a new quantum number may underlie the electronic shell structure observed in the mass spectra of medium-sized sodium clusters. We investigate whether the conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l and 2n+l, which characterize the hydrogen problem and the isotropic harmonic oscillator in three dimensions.

cond-mat↗

arXiv1996

Supershells in Metal Clusters: Self-Consistent Calculations and their Semiclassical Interpretation

To understand the electronic shell- and supershell-structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals a surprisingly simple dependence of the supershells on the jellium density. It is shown how this can be understood in the framework of a periodic-orbit-expansion by analytically extending the well-known semiclassical treatment of a spherical cavity to more realistic potentials.

cond-mat↗