K. A. Müller

Bio: K. A. Müller is an academic researcher from IBM. The author has contributed to research in topics: Type (model theory) & Order (ring theory). The author has an hindex of 13, co-authored 17 publications receiving 2098 citations. Previous affiliations of K. A. Müller include Sapienza University of Rome.

Sr 1 − x Ca x Ti O 3 : An XY Quantum Ferroelectric with Transition to Randomness

Abstract: A series of twenty homogeneous ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}\mathrm{Ti}{\mathrm{O}}_{3}$ mixed crystals has been measured dielectrically between 4.2 and 300 K. In the tetragonal phase, the dielectric constant perpendicular to the $c$ axis becomes peaked above ${x}_{c}=0.0018$, the quantum mechanical onset for displacive ferroelectricity. The polarization $\ensuremath{\perp}c$ can be switched between the two equivalent $a$ axes, i.e., the system is an $\mathrm{XY}$, $n=2$, quantum ferroelectric. Above ${x}_{r}=0.016\ifmmode\pm\else\textpm\fi{}0.002$, the $\ensuremath{\epsilon}(T)$ peaks round in a distinct manner which we attribute to the onset of a random-field-induced domain state.

Origin of superconductive glassy state and extrinsic critical currents in high-Tc oxides.

Abstract: The short coherence length of high-${\mathrm{T}}_{\mathrm{c}}$ oxides is shown to induce considerable weakening of the pair potential at surfaces and interfaces. It is argued that this effect is responsible for the existence of internal Josephson junctions at twin boundaries, which are at the origin of the superconductive glassy state, as well as for gapless tunneling characteristics.

Characteristic Structural Phase Transition in Perovskite-Type Compounds

Abstract: The tetragonal rotation of Ti${\mathrm{O}}_{6}$ octahedra in SrTi${\mathrm{O}}_{3}$ and the trigonal rotation of Al${\mathrm{O}}_{6}$ octahedra in LaAl${\mathrm{O}}_{3}$ were measured by paramagnetic resonance below their respective phase transitions. The normalized rotation angles $\ensuremath{\alpha}$ vary quantitatively in the same way as a function of reduced temperature. Thus $\ensuremath{\alpha}$ is the order parameter in such transitions, which are characteristic for perovskite compounds.

Static Critical Exponents at Structural Phase Transitions

Abstract: The temperature dependence of the rotational displacement parameters below the second-order phase transitions in SrTi${\mathrm{O}}_{3}$ and LaAl${\mathrm{O}}_{3}$ at ${T}_{a}=105.5 \mathrm{and} 797$\ifmmode^\circ\else\textdegree\fi{}K is described by an exponent $\ensuremath{\beta}=0.33\ifmmode\pm\else\textpm\fi{}0.02$ down to $t=\frac{T}{{T}_{a}}=0.95$. For smaller $t$'s there occurs a change to Landau behavior approximately followed between $t=0.9 \mathrm{and} 0.7$. The observation of static critical exponents near displacive phase transitions confirms now the notion of universality in this field.

Structural Phase Transitions in Perovskite-Type Crystals

Abstract: We introduce a simple model Hamiltonian for the study of phase transitions in perovskite compounds $\mathrm{AB}{\mathrm{O}}_{3}$ involving rotations of $B{\mathrm{O}}_{6}$ octahedra. Depending on the relative magnitude of the anharmonic coefficients, we find a transition to the tetragonal or to the trigonal phase. We obtain the temperature dependence of the rotation angle below the transition temperature ${T}_{a}$, and of the soft-mode frequencies associated with the transition both above and below ${T}_{a}$. The coupling to an elastic deformation field is briefly discussed.

Possible high Tc superconductivity in the Ba-La-Cu-O system

Abstract: Metallic, oxygen-deficient compounds in the Ba−La−Cu−O system, with the composition BaxLa5−xCu5O5(3−y) have been prepared in polycrystalline form. Samples withx=1 and 0.75,y>0, annealed below 900°C under reducing conditions, consist of three phases, one of them a perovskite-like mixed-valent copper compound. Upon cooling, the samples show a linear decrease in resistivity, then an approximately logarithmic increase, interpreted as a beginning of localization. Finally an abrupt decrease by up to three orders of magnitude occurs, reminiscent of the onset of percolative superconductivity. The highest onset temperature is observed in the 30 K range. It is markedly reduced by high current densities. Thus, it results partially from the percolative nature, bute possibly also from 2D superconducting fluctuations of double perovskite layers of one of the phases present.

Theory of Dynamic Critical Phenomena

Abstract: An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Angle-resolved photoemission studies of the cuprate superconductors

Abstract: The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

Maximally-localized Wannier Functions: Theory and Applications

Abstract: The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Room-temperature ferroelectricity in strained SrTiO3.

Abstract: Systems with a ferroelectric to paraelectric transition in the vicinity of room temperature are useful for devices. Adjusting the ferroelectric transition temperature (T(c)) is traditionally accomplished by chemical substitution-as in Ba(x)Sr(1-x)TiO(3), the material widely investigated for microwave devices in which the dielectric constant (epsilon(r)) at GHz frequencies is tuned by applying a quasi-static electric field. Heterogeneity associated with chemical substitution in such films, however, can broaden this phase transition by hundreds of degrees, which is detrimental to tunability and microwave device performance. An alternative way to adjust T(c) in ferroelectric films is strain. Here we show that epitaxial strain from a newly developed substrate can be harnessed to increase T(c) by hundreds of degrees and produce room-temperature ferroelectricity in strontium titanate, a material that is not normally ferroelectric at any temperature. This strain-induced enhancement in T(c) is the largest ever reported. Spatially resolved images of the local polarization state reveal a uniformity that far exceeds films tailored by chemical substitution. The high epsilon(r) at room temperature in these films (nearly 7,000 at 10 GHz) and its sharp dependence on electric field are promising for device applications.