arXiv subjects

M. Letz

Publications and source records attributed to M. Letz.

18 recordsLinked to original sources

arXiv2006

Charge centers in CaF$_2$: Ab initio calculation of elementary physical properties

Charge centers in ionic crystals provide a channel for elementary interaction between electromagnetic radiation and the lattice. We calculate the electronic ground state energies which are needed to create a charge center -- namely a $F$- and a $H$-center. In well agreement with common understanding the $F$-center results in being accompanied by a small lattice distortion whereas the $H$-center is accompanied by a very large lattice deformation. Opposite to the common understanding the additional positive charge in the charge center results rather to be localized on a F$_4^{3-}$ complex than on a F$_2^-$-complex. From the ground states of the charge centers we derive binding energies, diffusion barriers and agglomeration energies for $M$-center formation. These microscopic quantities are of fundamental interest to understand the dynamic processes which are initiated if the crystals interact with extreme intense deep ultra violet radiation. We further derive the equilibrium concentrations of charge centers in grown crystals.

cond-mat.mtrl-sci↗

arXiv2003

Spatial anisotropy of the exciton level in CaF$_2$ at 11.1 eV and its relation to the weak optical anisotropy at 157 nm

The energy level of the exciton around the $Γ$ point in CaF$_2$ at about 11.1 eV was investigated by reflection measurements on oriented surfaces using dispersed synchrotron radiation. A small but clear energy shift of the exciton resonance structure was observed which depends on the crystal orientation with respect to the incoming beam. By interpreting the results in terms of the complex dielectric function it becomes possible to determin the respective exciton levels and lifetimes. For crystal samples oriented in the (111) direction, the exciton has an excitation energy 0.02 eV above the energy of samples oriented in the (100) direction. The results obtained suggest that the exciton-energy shift is related to the spatial anisotropy recently measured in CaF$_2$ at 157 nm.

cond-mat.mtrl-sci↗

arXiv2002

Spatial dispersion in CaF$_2$ caused by the vicinity of an excitonic bound state

The microscopic mechanism beyond the optical anisotropy of an ionic crystal which occurs for short wavelengths is investigated. The electron-hole, two particle propagator and its analytical behaviour close to the band edge of the one particle continuum plays a major role for the mechanism of this optical anisotropy. Especially for an ionic crystal the two particle bound state, the exciton, is of special importance. In this way we argue that the so called ``intrinsic birefringence'' in CaF$_2$ is neither intrinsic to the material nor it is birefringence. Instead it is spatial dispersion caused by the vicinity of a dispersive optical absorption given by the excitonic bound state. We propose a model which connects the bound state dispersion with the band structure and a model potential for a screened coulomb interaction. Based on these considerations we predict a wavelength dependence of the dielectric function approaching close to the bound state level $ε\sim (λ- λ_0)^{-1}$, where $λ_0$ is the wavelength of the excitonic bound state level.

cond-mat.str-el↗

arXiv2001

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin.

cond-mat.dis-nn↗

arXiv2001

Microscopic Dynamics of Hard Ellipsoids in their Liquid and Glassy Phase

To investigate the influence of orientational degrees of freedom onto the dynamics of molecular systems in its supercooled and glassy regime we have solved numerically the mode-coupling equations for hard ellipsoids of revolution. For a wide range of volume fractions $ϕ$ and aspect ratios $x_{0}$ we find an orientational peak in the center of mass spectra $χ_{000}^{''}(q,ω)$ and $ϕ_{000}^{''} (q,ω)$ about one decade below a high frequency peak. This orientational peak is the counterpart of a peak appearing in the quadrupolar spectra $χ_{22m}^{''}(q,ω)$ and $ϕ_{22m}^{''}(q,ω)$. The latter peak is almost insensitive on $ϕ$ for $x_{0}$ close to one, i.e. for weak steric hindrance, and broadens strongly with increasing $x_{0}$. Deep in the glass we find an additional peak between the orientational and the high frequency peak. We have evidence that this intermediate peak is the result of a coupling between modes with $l=0$ and $l=2$, due to the nondiagonality of the static correlators.

cond-mat.dis-nn↗

arXiv2001

Microscopic dynamics of molecular liquids and glasses: Role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phase, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior which ranges from a simple hard sphere fluid to a long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra $ϕ_{lm}^{\prime \prime}(q,ω)$ and $χ_{lm}''(q,ω)$. In the center of mass spectra $ ϕ_{00}''(q,ω)$ and $χ_{00}''(q,ω)$ we found besides a high frequency peak at $ω_{hf}$ a peak at $ω_{op}$, about one decade below $ω_{hf}$. $ω_{op}$ has almost no $q$-dependence and exhibits an ``isotope'' effect $ω_{op}\propto I^{-1/2}$, with $I$ the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of the medium ranged orientational order. It is shown that some of these feature also exist for schematic mode coupling models.

cond-mat.dis-nn↗

arXiv2000

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities $ρ_{lm}(q)$ with $l=0$ and $l=2$. $l$, $m$ denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger \cite{schilling97} for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous {\em phenomenological} theories. We emphasize the importance of the helicity index $m$ for the microscopic theory by showing, that only the existence of $m=1$ components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived.

cond-mat.soft↗

arXiv2000

The electron gas with a strong pairing interaction: Three particle correlations and the Thouless instability

We derive simplified Faddeev type equations for the three particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean field theory these equations are partially solved numerically for the attractive Hubbard model. It is shown that the three particle T-matrix contains a term vanishing $\sim T^2$ at the Thouless (or BCS) instability where the two-particle T-matrix diverges. Based on the three particle term we further derive the low density - strong coupling extension for the two-particle vertex function. We therefore understand our equations as a step towards a systematic low density expansion from the weak coupling BCS theory towards the stronger coupling limit.

cond-mat.str-el↗

arXiv2000

Ideal glass transitions for hard ellipsoids

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X$_0$. With increasing aspect ratio we find the idealized glass transition to become primarily be driven by orientational degrees of freedom. For needle or plate like systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition lines. The first one ($ϕ_c^{(B)}$) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one ($ϕ_c^{(B')}$) which occurs for rather non-spherical particles a glass phase is formed which consists of domains. Within each domain there is a nematic order where the center of mass motion is quasi--ergodic, whereas the inter--domain orientations build an orientational glass. The third glass transition line ($ϕ_c^{(A)}$) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g. 180$^o$ flips, freeze independently from the positions.

cond-mat.soft↗

arXiv1999

Mode coupling theory for molecular liquids: What can we learn from a system of hard ellipsoids?

Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which can serve as a paradigm to understand these couplings is a system of hard ellipsoids of revolution. To test this we compare at the ideal glass transition the static molecular correlators of a linear A-B Lennard-Jones molecule obtained from a molecular dynamics simulation with a selected fluid of hard ellipsoids for which the static correlators have been obtained using Percus-Yevick theory. We also demonstrate that the critical non-ergodicity parameters obtained from molecular mode coupling theory for both systems show a remarkable similarity at the glass transition, provided the aspect ratio is chosen properly. Therefore we conclude that a system of hard ellipsoids can indeed be used to understand part of the essential behaviour of such a simple molecular system like the A-B Lennard-Jones molecules in the vicinity of the ideal glass transition.

cond-mat.soft↗

arXiv1999

Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory

An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard ellipsoids of revolution. Our results compare well with Monte Carlo Simulations and density functional theory.

cond-mat.soft↗

arXiv1999

Crossover from BCS superconductivity to BEC of pairs: The role of the lifetime of the pairs

The understanding of an electron gas with short coherence length pairs formed by an attractive interaction is believed to be one of the major keys to our theoretical knowledge of the high-T_c-superconductors. Mainly the deviations of the cuprates from usual metallic Fermi liquid behaviour already in the normal state like e.g. a linear resistivity or the observation of a pseudo gap can result from electron-electron correlations. We therefore investigate the negative U Hubbard model in two dimensions at low densities using the T-matrix approximation. In the non selfconsistent formulation of the theory the system always shows an instability towards Bose condensation of pairs into an infinite lifetime two-particle bound state. If the calculations are performed selfconsistently pair-pair scattering is included which causes the pairs to have finite lifetime. The physics of these finite lifetime pairs is discussed.

cond-mat.str-el↗

arXiv1999

Self-consistent treatment of dynamical correlation functions using a spectral representation technique

A system of equations resulting from an approximation of the equation of motion of Green functions for correlated electron systems is usually solved using Matsubara technique. In this work we propose an alternative method which works entirely along the real frequency axis. Using the example of the attractive Hubbard model studied in the T-matrix approximation both self-consistently and non-self-consistently we demonstrate how powerful such a treatment is especially when dynamic quantities are calculated.

cond-mat.str-el↗

arXiv1998

The Attractive Hubbard Model in 2D: Is it capable of describing a pseudogap and preformed pairs?

Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences seem to be related to pre-transitional features appearing at temperatures above T$_c$. The observation of a pseudogap, e.g. in ARPES experiments, is a familiar example of this physics. One potential explanation for this behaviour involves preformed pairs with finite lifetimes existing in the normal state above T$_c$. In this way two characteristic temperatures can be established. A higher one T$^*$ at which pairs begin to form and the actual T$_c$ at which a phase-coherent superconducting phase is established. In order to test these ideas we have investigated the negative U Hubbard model in two dimensions in the fully self-consistent ladder approximation at low electron densities. In the non self-consistent version of this theory the system always shows an instability towards Bose-condensation of infinite lifetime pairs. In contrast to this, pairs obtain a finite lifetime due to pair-pair interaction and the sharp two-particle bound state is strongly lifetime broadened when self-consistency is applied. A quasi-particle scattering rate which varies linearly with temperature is also found. The fully self-consistent calculation we were able to perform using a ${\bf {\vec k}}$--averaged approximation in which the self-energy loses its ${\bf {\vec k}}$-dispersion due to a ${\bf {\vec k}}$-average. This approximation is found to preserve the essential physics.

cond-mat.str-el↗

arXiv1998

Spectral Properties of the Attractive Hubbard Model

Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences are possibly related to pre-formed pairs appearing at temperatures above T_c. In order to test these ideas we have investigated the attractive Hubbard model within a self-consistent, conserving ladder approximation. In this version of the theory, no feature is present which can be related to the pseudo gap found in the high-T_c materials. Further, the interactions between two-particle bound states change the physics of the superconducting instability in a profound fashion, and lead to a completely different phenomenology that one predicts based on the non-self-consistent version of the same theory.

cond-mat.str-el↗

arXiv1998

Quasiparticle lifetime behaviour in a simplified self-consistent T-matrix treatment of the attractive Hubbard model in 2D

The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly with the inverse temperature, consistent with experiment.

cond-mat.str-el↗

arXiv1998

A self-consistent, conserving theory of the attractive Hubbard model in two dimensions

We have investigated the attractive Hubbard model in the low density limit for the 2D square lattice using the ladder approximation for the vertex function in a self-consistent, conserving formulation. In the parameter region where the on-site attraction is of the order of the bandwidth, we found no evidence of a pseudo gap. Further, we have observed that the suppression of the Fermi surface known to destroy superconductivity in one and two dimensions, when these systems are treated using a non self-consistent theory (Schmitt-Rink, et al., Phys. Rev. Lett. 63, 445 (1989)), does not occur when pair-pair interactions are included. However, we do find a quasiparticle lifetime that varies linearly with temperature, similar to many experiments. Thus, although this system has a Fermi surface, it shows non Fermi liquid type behaviour over a wide temperature range. We stress that our work uses thermal Green's functions along the real time axis, and thus allows for a more accurate determination of the dynamical properties of a model than theories that require extrapolations from the imaginary frequency axis.

cond-mat.str-el↗

arXiv1997

Level statistics and localization in a 2D quantum percolation problem

A two dimensional model for quantum percolation with variable tunneling range is studied. For this purpose the Lifshitz model is considered where the disorder enters the Hamiltonian via the nondiagonal elements. We employ a numerical method to analyze the level statistics of this model. It turns out that the level repulsion is strongest around the percolation threshold. As we go away from the maximum level repulsion a crossover from a GOE type behavior to a Poisson like distribution is indicated. The localization properties are calculated by using the sensitivity to boundary conditions and we find a strong crossover from localized to delocalized states.

cond-mat↗