Ulrich Eckern

Persistent Currents of Single Mesoscopic Rings

We study the stochastic fluctuations (from sample to sample) in the persistent current I() of mesoscopic rings threaded by a flux . We find that it is necessary to include the Coulomb interaction between the electrons. Then we obtain I21/2 ~ (L/l)I ~ evF/L; and h/e for the dominant period in . This agrees well with a recent experiment on single gold rings. Furthermore, we predict that the persistent currents have a Gaussian probability distribution, since the total electron number of a typical ring is still very large.

Relaxation Processes in a Condensed Bose Gas

We develop, on the basis of the self-consistent mean-field approximation, the kinetic theory for a dilute Bose gas below the Bose-Einstein transition temperature. The collision operator in the Boltzmann equation is calculated by golden rule arguments, and the momentum and temperature dependences of the scattering rates are determined. As an application, we consider the relaxation of a nonequilibrium distribution of the quasiparticles. We discuss the relevance of our calculation for the (hypothetical) condensed state of spinpolarized hydrogen.

Stability of superconducting states out of thermal equilibrium

Quasiparticles of superconductors can be manipulated either by irradiation or tunnel injection such that substantial changes of the gap (order parameter) occur which are most pronounced close to the transition temperature. These phenomena are investigated by a theory which is based on the combined system of the Boltzmann equation and the BCS gap equation. Several stationary, spatially homogeneous states are found in some range of temperatures. A linear stability analysis reveals two types of behavior, depending, essentially, on whether quasiparticle diffusion increases or decreases the stability. In a representative situation of the first type, two states turn out to be locally stable. An investigation of a nonlinear equation of motion for the order parameter leads to the conclusion that a first-order phase transition between these two states occurs at a given temperature. In a situation of the second type, one finds that fluctuations of a definite wave vector destroy the spatially homogeneous state and lead to a stable state of layered structure.

Anderson Localization versus Delocalization of Interacting Fermions in One Dimension

Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is determined with high accuracy for systems up to a size of 60 lattice constants. This quantity is found to be log-normally distributed. The fluctuations grow algebraically with system size with a universal exponent of ~2/3 in the localized region of the phase diagram. Surprizingly, we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.

Covalent bonding and hybridization effects in the corundum-type transition-metal oxides V2O3 and Ti2O3

The electronic structure of the corundum-type transition-metal oxides V2O3 and Ti2O3 is studied by means of the augmented spherical wave method, based on density-functional theory and the local density approximation. Comparing the results for the vanadate and the titanate allows us to understand the peculiar shape of the metal 3d a1g density of states, which is present in both compounds. The a1g states are subject to pronounced bonding-antibonding splitting due to metal-metal overlap along the c-axis of the corundum structure. However, the corresponding partial density of states is strongly asymmetric with considerably more weight on the high-energy branch. We argue that this asymmetry is due to an unexpected broadening of the bonding a1g states, which is caused by hybridization with the egπ bands. In contrast, the antibonding a1g states display no such hybridization and form a sharp peak. Our results shed new light on the role of the a1g orbitals for the metal-insulator transitions of V2O3. In particular, due to a1g-egπ hybridization, an interpretation in terms of molecular orbital singlet states on the metal-metal pairs along the c-axis is not an adequate description.

Exact results of the ground state and excitation properties of a two-component interacting Bose system

We study a one-dimensional Bose system with repulsive δ-function interaction in the presence of an SU(2) intrinsic degree of freedom on the basis of the coordinate Bethe ansatz. The ground state and the low-lying excitations are determined by both numerical and analytical methods. It is shown that the ground state is an isospin-ferromagnetic state, and the excitations are composed of three elementary particles: holons, antiholons, and isospinons. The isospinon is a triplet coupled to the ferromagnetic background anti-parallelly.

From VO2 to V2O3: The metal-insulator transition of the Magnéli phase V6O11

The metal-insulator transition (MIT) of V6O11 is studied by means of electronic structure calculations using the augmented spherical wave method. The calculations are based on density functional theory and the local density approximation. Changes of the electronic structure at the MIT are discussed in relation to the structural transformations occurring simultaneously. The analysis is based on a unified point of view of the crystal structures of V6O11, VO2, and V2O3. This allows to group the electronic bands into states behaving similarly to the dioxide or the sesquioxide. While the sesquioxide-like V 3dyz states show rather weak changes on entering the low-temperature structure, some of the dioxide-like V 3dx2 − y2 states display splittings and shifts similar to those known from VO2. The MIT of V6O11 arises as a combination of changes appearing in both of these compounds. Our results shed new light onto the role of particular electronic states for the MIT of V2O3.

Persistent Currents Versus Phase Breaking in Mesoscopic Metallic Samples

Persistent currents in mesoscopic normal metal rings represent, even a decade after their first experimental observation, a challenge to both, theorists and experimentalists. After giving a brief review of the existing - experimental and theoretical - results, we concentrate on the (propsed) relationship of the size of the persistent current to the phase breaking rate. In particular, we consider effects induced by noise, scattering at two-level systems, and magnetic impurities.

Magnetic, electronic, and vibrational properties of metal and fluorinated metal phthalocyanines

The magnetic and electronic properties of metal phthalocyanines (MPc) and uorinated metal phthalocyanines (F16MPc) are studied by means of spin density functional theory (SDFT). Several metals (M) such as Ca, all rst d-row transition metals and Ag are investigated. By considering dierent open shell transition metals it is possible to tune the electronic properties of MPc, in particular the electronic molecular gap and total magnetic moment. Besides assigning the structural and electronic properties of MPc and F16MPc, the vibrational modes analysis of the ScPc{ZnPc series have been studied and correlated to experimental measurements when available.

The metal-insulator transition of the Magnéli phase V4O7: Implications for V2O3

The metal-insulator transition (MIT) of the Magneli phase V4O7 is studied by means of electronic-structure calculations using the augmented spherical wave method. The calculations are based on the density-functional theory and the local density approximation. Changes of the electronic structure at the MIT are discussed in relation to the structural transformations occurring simultaneously. The analysis is based on a unified point of view of the crystal structures of all Magneli phase compounds VnO2n − 1 (3 ≤ n ≤ 9) as well as of VO2 and V2O3. This allows to group the electronic bands into states behaving similarly to the dioxide or the sesquioxide. In addition, the relationship between the structural and electronic properties near the MIT of these oxides can be studied on an equal footing. For V4O7, a strong influence of metal-metal bonding across octahedral faces is found for states both parallel and perpendicular to the hexagonal chex-axis of V2O3. Furthermore, the structural changes at the MIT cause localization of those states, which mediate in-plane metal-metal bonding via octahedral edges. This band narrowing opens the way to an increased influence of electronic correlations, which are regarded as playing a key role for the MIT of V2O3.