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Thomas Bauer

Publications and source records attributed to Thomas Bauer.

At least 55 records · Page 3Linked to original sources
arXiv2010

Weyl and Zariski chambers on K3 surfaces

The big cone of every K3 surface admits two natural chamber decompositions: the decomposition into Zariski chambers, and the decomposition into simple Weyl chambers. In the present paper we compare these two decompositions and we study their mutual relationship: First, we give a numerical criterion for the two decompositions to coincide. Secondly, we study the mutual inclusions of Zariski and simple Weyl chambers. Finally, we establish the fact that -- even though the decompositions themselves may differ -- the number of Zariski chambers always equals the number of simple Weyl chambers.

math.AG↗
arXiv2010

Dynamic charge inhomogenity in cuprate superconductors

The inelastic x-ray scattering spectrum for phonons of $Δ_{1}$-symmetry including the CuO bond-stretching phonon dispersion is analyzed by a Lorentz fit in HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$, respectively, using recently calculated phonon frequencies as input parameters. The resulting mode frequencies of the fit are almost all in good agreement with the calculated data. An exception is the second highest $Δ_{1}$-branch compromising the bond-stretching modes which disagrees in both compounds with the calculations. This branch unlike the calculations shows an anomalous softening with a minimum around the wavevector $\vc{q}=\frac{2π}{a}(0.25, 0, 0)$. Such a disparity with the calculated results, that are based on the assumption of an undisturbed translation- and point group invariant electronic structure of the CuO plane, indicates some {\it static} charge inhomogenities in the measured probes. Most likely these will be charge stripes along the CuO bonds which have the strongest coupling to certain longitudinal bond-stretching modes that in turn selfconsistently induce corresponding {\it dynamic} charge inhomogenities. The symmetry breaking by the mix of dynamic and static charge inhomogenities can lead to a reconstruction of the Fermi surface into small pockets.

cond-mat.supr-con↗
arXiv2010

Phonon dispersion and anomalies in one-layer high-temperature superconductors

Phonon dynamics, charge response and the phonon density of states are calculated for the high-temperature superconductors HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$ within a microscopic model for the electronic density response. The results are compared with previous calculations for La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$. Our main focus is on the phononanomalies which are connected with the high-frequency oxygen bond-stretching modes (OBSM) found before in our calculations for $p$-doped La$_{2}$CuO$_{4}$ and $n$-doped Nd$_{2}$CuO$_{4}$. We investigate the question if the characteristic softening of the OBSM and the related strong coupling to the electrons is also present in HgBa$_{2}$CuO$_{4}$ and Bi$_{2}$Sr$_{2}$CuO$_{6}$. In particular the importance of the contribution of the more delocalized Cu$4s$ state besides the localized Cu3d state on the softening is investigated and the different anticrossing behaviour due to the presence of several phonon modes with the same symmetry as the OBSM is studied making the identification of the anomalies quite complicate. Furthermore, the influence of electronic polarization processes at ions out of the CuO plane in the ionic layers on the phonon dynamics is calculated. In this context the qualitative type of charge response, i.e. the presence or not of possible metallic charge fluctuations at the Hg or Bi ion, respectively, linked via the apex oxygen to the CuO plane, proves to be very sensitive for certain phonon modes. All the calculations are compared to the experimental results available so far. The latter, however, are rather incomplete for the Hg and the Bi compound.

cond-mat.supr-con↗
arXiv2009

Counting Zariski chambers on Del Pezzo surfaces

Zariski chambers provide a natural decomposition of the big cone of an algebraic surface into rational locally polyhedral subcones that are interesting from the point of view of linear series. In the present paper we present an algorithm that allows to effectively determine Zariski chambers when the negative curves on the surface are known. We show how the algorithm can be used to compute the number of chambers on Del Pezzo surfaces.

math.AG↗
arXiv2009

Microscopic calculation of the phonon dynamics of Sr$_{2}$RuO$_{4}$ compared with La$_{2}$CuO$_{4}$

The phonon dynamics of the low-temperature superconductor Sr$_{2}$RuO$_{4}$ is calculated quantitatively in linear response theory and compared with the structurally isomorphic high-temperature superconductor La$_{2}$CuO$_{4}$. Our calculation corrects for a typical deficit of LDA-based calculations which always predict a too large electronic $k_{z}$-dispersion insufficient to describe the c-axis response in the real materials. With a more realistic computation of the electronic band structure the frequency and wavevector dependent irreducible polarization part of the density response function is determined and used for adiabatic and nonadiabatic phonon calculations. Our analysis for Sr$_{2}$RuO$_{4}$ reveals important differences from the lattice dynamics of $p$- and $n$-doped cuprates. Consistent with experimental evidence from inelastic neutron scattering the anomalous doping related softening of the strongly coupling high-frequency oxygen bond-stretching modes (OBSM) which is generic for the cuprate superconductors is largely suppressed or completely absent, respectively, depending on the actual value of the on-site Coulomb repulsion of the Ru4d orbitals. Also the presence of a characteristic $Λ_{1}$-mode with a very steep dispersion coupling strongly with the electrons is missing in Sr$_{2}$RuO$_{4}$. Moreover, we evaluate the possibility of a phonon-plasmon scenario for Sr$_{2}$RuO$_{4}$ which has been shown recently to be realistic for La$_{2}$CuO$_{4}$. In contrast to La$_{2}$CuO$_{4}$ in Sr$_{2}$RuO$_{4}$ the very low lying plasmons are overdamped along the c-axis.

cond-mat.supr-con↗
arXiv2009

Seshadri constants and the generation of jets

In this paper we explore the connection between Seshadri constants and the generation of jets. It is well-known that one way to view Seshadri constants is to consider them as measuring the rate of growth of the number of jets that multiples of a line bundle generate. Here we ask, conversely, what we can say about the number of jets once the Seshadri constant is known. As an application of our results, we prove a characterization of projective space among all Fano varieties in terms of Seshadri constants.

math.AG↗
arXiv2008

The impact of dynamical screening on the phonon dynamics of LaCuO

It is shown that dynamical screening of the Coulomb interaction in LaCuO leads to low-energy electronic collective excitations in a small region around the c-axis, strongly mixing with interlayer phonons. The manifestation of such a phonon-plasmon scenario based on a nonadiabatic charge response is quantitatively supported by a realistic calculation of the frequency and wavevector dependent irreducible polarization part of the density response function. The latter is used within linear response theory to calculate the coupled mode dispersion in the main symmetry directions of the Brillouin zone and the charge density redistributions excited by certain strongly coupling phonon-like and plasmon-like modes. Moreover, the corresponding mode induced orbital averaged changes of the selfconsistent potential felt by the electrons are assessed. Our analysis should be representative for the optimally to overdoped state of the cuprates where experimental evidence of a coherent three-dimensional Fermi surface and a coherent c-axis charge transport is given. It is demonstrated that modes from the outside of a small region around the c-axis can reliably be calculated within the adiabatic limit. Only a minor nonadiabatic correction is found for these modes in form of stiffening of the high-frequency oxygen-bond-stretching mode at the X-point which is attributed to dynamical reduced nesting. On the other hand, modes inside the nonadiabatic sector of the BZ have to be determined nonadiabatically owing to the poor dynamical screening of the long-ranged Coulomb interaction around the c-axis by the slow charge dynamics. In particular, the relevance of the strongly coupling phonon-like apex oxygen $Z$-point breathing mode at about 40 meV is emphasized whose mode energy decreases with less doping.

cond-mat.supr-con↗
arXiv2008

Seshadri constants on the self-product of an elliptic curve

The purpose of this paper is to study Seshadri constants on the self-product $E\times E$ of an elliptic curve $E$. We provide explicit formulas for computing the Seshadri constants of all ample line bundles on the surfaces considered. As an application, we obtain a good picture of the behaviour of the Seshadri function on the nef cone.

math.AG↗
arXiv2008

A microscopic modeling of phonon dynamics and charge response in NdCuO

A description of phonon dynamics and charge response of the $n$-doped high-temperature superconductor (HTSC) NdCuO is presented based upon a microscopic modeling of the electronic density response. This is accomplished starting from the insulating state via the underdoped strange metallic to the more conventional metallic state by consecutive orbital selective incompressibility-compressibility transitions in terms of strict sum rules for the charge response. The approach proposed in this work for the $n$-doped HTSC's modifies the modeling recently applied to the $p$-doped compounds and expresses an electron-hole asymmetry introduced by doping. A qualitative physical picture consistent with our modeling of the electronic state in the cuprates is given in which a sufficiently broad set of orbital degrees of freedom, i.e. Cu3d/$4s$ and O$2p$ is essential. Within the framework of linear response theory we calculate full phonon dispersion curves in the different phases. In particular, the strongly doping dependent anomalous high-frequency oxygen bond-stretching modes (OBSM) found experimentally in the $p$-doped HTSC's and also recently for $n$-doped Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$ are investigated and compared with experimental results from inelastic neutron scattering and inelastic x-ray scattering, respectively. We calculate an anticrossing scenario for the OBSM in $n$-doped NdCuO which is absent in the case of $p$-doped LaCuO and relate it to the different crystal structure. Phonon-induced electronic charge redistributions of the anomalous OBSM due to nonlocal electron-phonon interaction effects of charge-fluctuation type giving reason to dynamic stripes are also studied.

cond-mat.supr-con↗
arXiv2008

Seshadri constants on surfaces of general type

We study Seshadri constants of the canonical bundle on minimal surfaces of general type. First, we prove that if the Seshadri constant $\eps(K_X,x)$ is between 0 and 1, then it is of the form $(m-1)/m$ for some integer $m\ge 2$. Secondly, we study values of $\eps(K_X,x)$ for a very general point $x$ and show that small values of the Seshadri constant are accounted for by the geometry of $X$.

math.AG↗
arXiv2007

A simple proof for the existence of Zariski decompositions on surfaces

In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the decomposition, the present approach is based on the idea that the positive part can be constructed from a maximality condition. It may also be useful that this approach yields a practical algorithm for the computation of the positive part.

math.AG↗
arXiv2007

A criterion for an abelian variety to be simple

In this note we give a numerical criterion that expresses the condition that an abelian variety be simple in terms of an invariant that is closely related to the s-invariant of Ein-Cutkosky-Lazarsfeld. The criterion yields new examples where s-invariants are irrational. It may also be viewed as a statement about the geometry of the ample cone.

math.AG↗
arXiv2007

A microscopic modeling of phonon dynamics and charge response in metallic BaBiO$_3$

We use our recently proposed microscopic modeling in the framework of linear response theory to investigate the complete phonon dispersion, the phonon density of states, certain phonon-induced electronic charge distributions and charge fluctuations (CF's) for anomalous soft modes of metallic BaBiO$_{3}$ in its simple cubic phase where superconductivity with $T_{c}$ up to 32 K appears. The theoretical approach already has been applied successfully to the cuprate high-temperature superconductors (HTSC's), simple ionic crystals (NaCl, MgO) and perovskite oxides (SrTiO$_{3}$, BaTiO$_{3}$). It is well suited for materials with a strong component of ionic binding and especially for "ionic" metals. In particular, the giant phonon anomalies related to the breathing vibration of the oxygen as found experimentally in superconducting doped Ba$_{0.6}$K$_{0.4}$BiO$_{3}$, resembling those observed in the high $T_{c}$ cuprates, are investigated. The origin of these anomalies is explored and attributed to a strong nonlocal coupling of the displaced oxygen ions to CF's of ionic type, essentially of the Bi6s- and Bi6p orbital. This points to the importance of both of these states at the Fermi energy. Starting from an ab-initio rigid ion model (RIM) we calculate the effect on the lattice dynamics and charge response of the most important electronic polarization processes in the material, i.e. CF's and dipole fluctuations (DF's). Taking into account these electronic degrees of freedom in linear response theory, we obtain a good agreement with the measured phonon dispersion and in particular with the strong phonon anomalies.

cond-mat.supr-con↗
arXiv2006

Modeling of the electronic state of the High-Temperature Superconductor LaCuO: Phonon dynamics and charge response

A modeling of the normal state of the p-doped high-temperature superconductors (HTSC's) is presented. This is achieved starting from a more conventional metallic phase for optimal- and overdoping and passing via the underdoped to the insulating state by consecutive orbital selective compressibility-incompressibility transitions in terms of sum rules for the charge response. The modeling is substantiated by corresponding phonon calculations. Extending investigations of the full dispersion and in particular of the strongly doping dependent anomalous phonon modes in LaCuO, which so far underpin our treatment of the density response of the electrons in the p-doped HTSC's, gives additional support for the modeling of the electronic state, compares well with recent experimental data and predicts the dispersion for the overdoped regime. Moreover, phonon densities of states have been calculated and compared for the insulating, underdoped, optimally doped and overdoped state of LaCuO. From our modeling of the normal state a consistent picture of the superconducting phase also can be extracted qualitatively pointing in the underdoped regime to a phase ordering transition. On the other hand, the modeling of the optimal and overdoped state is consistent with a quasi-particle picture with a well defined Fermi surface. Thus, in the latter case a Fermi surface instability with an evolution of pairs of well defined quasiparticles is possible and can lead to a BCS-type ordering. So, it is tempting to speculate that optimal $T_C$ in the HTSC's marks a crossover region between these two forms of ordering.

cond-mat.supr-con↗
arXiv2003

Zariski chambers, volumes, and stable base loci

The purpose of this paper is to investigate the behaviour of certain asymptotic invariants of line bundles on projective surfaces. In particular, we describe the volume of line bundles and their destabilizing numbers.

math.AG↗
arXiv2001

A reduction map for nef line bundles

In a recent preprint, H. Tsuji gave a number of interesting assertions on the structure of pseudo-effective line bundles on projective manifolds. In particular, he postulated the existence of an almost-holomorphic "reduction map", whose fibers are maximal subvarieties on which the line bundle is numerically trivial. The purpose of this note is to give a simple, algebraic proof of the existence of a reduction map in the case where the line bundle is nef.

math.AG↗
arXiv1999

Seshadri constants on algebraic surfaces

Seshadri constants are local invariants, introduced by Demailly, which measure the local positivity of ample line bundles. Recent interest in Seshadri constants stems on the one hand from the fact that bounds on Seshadri constants yield, via vanishing theorems, bounds on the number of points and jets that adjoint linear series separate. On the other hand it has become increasingly clear by now that Seshadri constants are highly interesting invariants quite in their own right. Except in the simplest cases, however, they are already in the case of surfaces very hard to control or to compute explicitly---hardly any explicit values of Seshadri constants are known so far. The purpose of the present paper is to study these invariants on algebraic surfaces. On the one hand, we prove a number of explicit bounds for Seshadri constants and Seshadri submaximal curves, and on the other hand, we give complete results for abelian surfaces of Picard number one. A nice feature of this result is that it allows to explicitly compute the Seshadri constants---as well as the unique irreducible curve that accounts for it---for a whole class of surfaces. It also shows that Seshadri constants have an intriguing number-theoretic flavor in this case.

math.AG↗