arXiv subjects

K. Ziegler

Publications and source records attributed to K. Ziegler.

At least 73 records · Page 4Linked to original sources

arXiv2008

Random gap model for graphene and graphene bilayers

The effect of a randomly fluctuating gap, created by a random staggered potential, is studied in a monolayer and a bilayer of graphene. The density of states, the one-particle scattering rate and transport properties (diffusion coefficient and conductivity) are calculated at the neutrality point. All these quantities vanish at a critical value of the average staggered potential, signaling a continuous transition to an insulating behavior. The calculations are based on the self-consistent Born approximation for the one-particle scattering rate and a massless mode of the two-particle Green's function which is created by spontaneous symmetry breaking. Transport quantities are directly linked to the one-particle scattering rate. Moreover, the effect of disorder is very weak in the case of a monolayer but much stronger in bilayer graphene.

cond-mat.mes-hall↗

arXiv2008

Anderson localization in a correlated fermionic mixture

A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution for the heavy atoms and study the localization properties of the light fermions numerically by a transfer-matrix method. In a two-dimensional system one-parameter scaling of the localization length is found with a transition from delocalized states at low temperatures to localized states at high temperature. The critical exponent of the localization length is $ν\approx 0.88$.

cond-mat.dis-nn↗

arXiv2008

Long-range correlations in disordered graphene

The appearence of long-range correlations near the Dirac point of a Dirac-like spinor model with random vector potential is studied. These correlations originate from a spontaneously broken symmetry and their corresponding Goldstone modes. Using a strong-disorder expansion, correlation functions and matrix elements are analyzed and compared with results from a weak-disorder expansion. The local density of states correlation and the overlap between states above and below the Dirac point are characterized by a long-range behavior. The correlation range decreases with the distance from the Dirac point. Transport is diffusive and the diffusion coefficient is proportional to the one-particle scattering time for any strength of disorder. A consequence of the special properties of particle-hole scattering is a constant microwave conductivity for weak as well as for strong disorder, describing a deviation from conventional Drude-like transport. Some properties of the model can be linked to a kind of Kondo scale, which is generated by disorder. Finally, the properties of the wave functions at the Dirac point are characterized by their participation ratios, indicating a critical state at the Dirac point.

cond-mat.mes-hall↗

arXiv2008

Formation of vortices in a dense Bose-Einstein condensate

A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized non-linear Schrödinger equation with kinetic term for the rotating condensate. In comparison with previous calculations, based on Thomas-Fermi approximation, significant improvements are found in regions, where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.

cond-mat.other↗

arXiv2008

Light Scattering on Random Dielectric Layers

Scattering of light by a random stack of dielectric layers represents a one-dimensional scattering problem, where the scattered field is a three-dimensional vector field. We investigate the dependence of the scattering properties (band gaps and Anderson localization) on the wavelength, strength of randomness and relative angle of the incident wave. There is a characteristic angular dependence of Anderson localization for wavelengths close to the thickness of the layers. In particular, the localization length varies non-monotonously with the angle. In contrast to Anderson localization, absorptive layers do not have this characteristic angular dependence.

physics.optics↗

arXiv2008

Dimer states in atomic mixtures

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs and an exchange of fermionic spins. Low energy states of this Hamiltonian are a Néel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.

cond-mat.stat-mech↗

arXiv2008

Suppression of magnetotransport in strongly disordered graphene

A tight-binding model with randomly fluctuating atomic positions is studied to discuss the effect of strong disorder in graphene. We employ a strong-disorder expansion for the transport quantities and find a diffusive behavior, where the conductivity is decreasing with increasing disorder. Surprisingly, the magnetic field drops out of the transport quantities in leading order of this expansion. This signals a strong suppression of magnetotransport effects for sufficiently strong disorder. This result is consistent with recent experimental observations by Morozov {\it et al.}

cond-mat.mes-hall↗

arXiv2008

Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects

Graphene is a recently discovered carbon based material with unique physical properties. This is a monolayer of graphite, and the two-dimensional electrons and holes in it are described by the effective Dirac equation with a vanishing effective mass. As a consequence, electromagnetic response of graphene is predicted to be strongly non-linear. We develop a quasi-classical kinetic theory of the non-linear electromagnetic response of graphene, taking into account the self-consistent-field effects. Response of the system to both harmonic and pulse excitation is considered. The frequency multiplication effect, resulting from the non-linearity of the electromagnetic response, is studied under realistic experimental conditions. The frequency up-conversion efficiency is analysed as a function of the applied electric field and parameters of the samples. Possible applications of graphene in terahertz electronics are discussed.

cond-mat.mes-hall↗

arXiv2007

Functional-integral representation of atomic mixtures

A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body system and analyzed in terms of a mean-field approximation and Gaussian fluctuations. This provides a phase diagram with the two merging Mott insulators and an intermediate superfluid. The Gaussian fluctuations give rise to an induced repulsive dimer-dimer interaction mediated by the unpaired fermions. The effect of an unbalanced distribution of spin-up and spin-down fermions is also discussed.

cond-mat.other↗

arXiv2007

On the effect of weak disorder on the density of states in graphene

The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we conclude, that the linear density of states of pure graphene changes to a non-universal power-law, whose exponent depends on the strength of disorder like 1-4g/sqrt{3}t^2π, with g the variance of the Gaussian disorder, t the hopping integral. This can result in a significant suppression of the exponent of the density of states in the weak-disorder limit. We argue, that even a non-linear density of states can result in a conductivity being proportional to the number of charge carriers, in accordance with experimental findings.

cond-mat.mes-hall↗

arXiv2007

Interacting bosons in an optical lattice

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functional-integral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-Pitaevskii equation to the dense regime by introducing renormalized parameters in the latter.

cond-mat.other↗

arXiv2007

On the minimal conductivity of graphene

The minimal conductivity of graphene is a quantity measured in the DC limit. It is shown, using the Kubo formula, that the actual value of the minimal conductivity is sensitive to the order in which certain limits are taken. If the DC limit is taken before the integration over energies is performed, the minimal conductivity of graphene is $4/π$ (in units of $e^2/h$) and it is $π/2$ in the reverse order. The value $π$ is obtained if weak disorder is included via a small frequency-dependent selfenergy. In the high-frequency limit the minimal conductivity approaches $π/2$ and drops to zero if the frequency exceeds the cut-off energy of the particles.

cond-mat.dis-nn↗

arXiv2007

Interacting bosons in an optical lattice: Bose-Einstein condensates and Mott insulator

A dense Bose gas with hard-core interaction is considered in an optical lattice. We study the phase diagram in terms of a special mean-field theory that describes a Bose-Einstein condensate and a Mott insulator with a single particle per lattice site for zero as well as for non-zero temperatures. We calculate the densities, the excitation spectrum and the static structure factor for each of these phases.

cond-mat.stat-mech↗

arXiv2007

A new electromagnetic mode in graphene

A new, weakly damped, {\em transverse} electromagnetic mode is predicted in graphene. The mode frequency $ω$ lies in the window $1.667<\hbarω/μ<2$, where $μ$ is the chemical potential, and can be tuned from radiowaves to the infrared by changing the density of charge carriers through a gate voltage.

cond-mat.mes-hall↗

arXiv2007

A renormalized Gross-Pitaevskii Theory and vortices in a strongly interacting Bose gas

We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.

cond-mat.other↗

arXiv2006

Mixtures of fermionic atoms in an optical lattice

A mixture of light and heavy spin-polarized fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. This results in a complex interplay between light and heavy atoms caused by quantum tunneling of the light atoms. The distribution of the heavy atoms is studied. It can be described by an Ising-like distribution with a first-order transition from homogeneous to staggered order. The latter is caused by an effective nonlocal interaction due to quantum tunneling of the light atoms. A second-order transition is also possible between an ordered and a disordered phase of the heavy atoms.

cond-mat.dis-nn↗

arXiv2005

Electron-phonon interaction for adiabatic anharmonic phonons

A model with Holstein-like electron-phonon coupling is studied in the limit of adiabatic phonons. The phonon distribution is anharmonic with two degenerate maxima. This model can be related to fermions in a correlated binary alloy and describes microscopic phase separation. We discuss the weak and strong electron-phonon coupling limit and present a qualitative phase diagram. In terms of the phononic displacements it consists of a homogeneous, an alternating, and a disordered phase. There is a first order phase transition between the homogeneous and the alternating phase, and second order phase transition between the alternating and the disordered phase. The opening of a gap inside the disordered phase is treated by a dynamical mean-field theory.

cond-mat.str-el↗

arXiv2005

N-component Bose-Einstein Condensate in an Optical Lattice: Destruction of the Condensate and Quasiparticle Properties

We present a model of N-component hard-core bosons on a lattice. The limit N to infinity can be solved exactly. A saddle point approximation leads to a 1/N expansion and allows the calculation of physical quantities like the density of the condensate, the correlation between the components and the density-density correlation function and the correlation between different components. We find a superfluid phase with a tendency towards a Mott insulator at high densities and finite N.

cond-mat.other↗