arXiv subjects
Publications and source records attributed to A. J. Millis.
Theoretical and computational results are presented clarifying the role of long-ranged strain interactions in determining the charge and orbital ordering in colossal magnetoresistance manganites. The strain energy contribution is found to be of order 20-30 meV/Mn and in particular stabilizes the anomalous 'zig-zag chain' order observed in many half-doped manganites.
We report the characterization of the crystal structure, low-temperature charge and orbital ordering, transport, and magnetization of Pr_{0.6}Ca_{0.4}MnO_{3} films grown on LaAlO_{3}, NdGaO_{3}, and SrTiO_{3} substrates, which provide compressive (LaAlO_{3}) and tensile (NdGaO_{3} and SrTiO_{3}) strain. The films are observed to exhibit different crystallographic symmetries than the bulk material, and the low-temperature ordering is found to be more robust under compressive-- as opposed to tensile-- strain. In fact, bulk-like charge and orbital ordering is not observed in the film grown on NdGaO_{3}, which is the substrate that provides the least amount of nominal and measured, but tensile, strain. This result suggests the importance of the role played by the Mn--O--Mn bond angles in the formation of charge and orbital ordering at low temperatures. Finally, in the film grown on LaAlO_{3}, a connection between the lattice distortion associated with orbital ordering and the onset of antiferromagnetism is reported.
The consistency of angle-resolved photoemission and optical conductivity experiments on high temperature superconductors is examined. In the limit (apparently consistent with angle-resolved photoemission data) of an electron self energy with a weak momentum dependence and a strong frequency dependence formulae are derived which directly related quantities measured in the two experiments. Application of the formuale to optimally and overdoped $Bi_{2}Ca_{2}SrCu_{2}O_{8+δ}$ shows that the total self energy inferred from photoemission measurements cannot be interpreted as a transport scattering rate (in agreement with work of Varma and Abrahams), but that the inelastic part may be so interpreted, if Landau parameter effects are non-negligible.
A rate equation formalism is used to determine the effect of electron-phonon coupling on the conductance of a molecule. Interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented.
Many 'interesting; correlated electron materials exhibit an unusual sensitivity of measured properties to external perturbations, and in particular to imperfections in the sample being measured. It is argued that in addition to its inconvenience, this sensitivity may indicated potentially useful properties. A partial classification of causes of such sensitivity is given.
The dynamical mean field method is used to analyze the magnetic transition temperature and optical conductivity of a model for the ferrimagnetic double perovskites such as $Sr_2FeMoO_6$. The calculated transition temperatures and optical conductivities are found to depend sensitively on the band structure. For parameters consistent with local spin density approximation band calculations, the computed transition temperatures are lower than observed, and in particular decrease dramatically as band filling is increased, in contradiction to experiment. Band parameters which would increase the transition temperature are identified.
The behavior of the residual (impurity-dominated) resistivity is computed for a material near a two dimensional quantum critical point characterized by a divergent $q=0$ susceptibility. A singular renormalization of the amplitude for back-scattering of an electron off of a single impurity is found. When the correlation length of the quantum critical point exceeds the mean free path, the singular renormalization is found to convert the familiar `Altshuler-Aronov' logarithmic correction to the conductivity into a squared-logarithmic form. Impurities can induce unconventional Friedel oscillations, which may be observable in scanning tunnelling microscope experiments. Possible connections to the metamagnetic quantum critical end point recently proposed for the material $Sr_{3}Ru_{2}O_{7}$ are discussed.
A realistic theory of the quantum paraelectric - ferroelectric transition is presented, involving parameters determined from band calculations and a renormalization group treatment of critical fluctuations. The effects of reduced dimensionality and deviations from cubic symmetry are determined. Expressions for the pressure dependence of the critical temperature, as well as pressure and temperature dependence of the specific heat are derived, and evaluated for realistic materials parameters for the systems BaTiO3 and PbTiO3. In these materials the ferroelectric soft mode dispersion apparently exhibits a very strong cubic anisotropy, which affects results in an important, albeit quantitative, manner. A change in order parameter orientation from (100) to (111) is predicted as quantum criticality is approached.
Elementary analytical extremal statistics arguments are used to analyse the possibility of quantum Griffiths effects in nearly critical systems with overdamped dynamics, such as arise in conventional theories of metallic quantum criticality. The overdamping is found to strongly suppress quantum tunnelling of rare regions, leading to superparamagnetic rather than quantum griffiths behavior. Implications for theories of non-fermi-liquid behavior in heavy fermion materials are discussed.
We propose a new semiclassical approach based on the dynamical mean field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical (static) phonon modes are treated exactly whereas the quantum (dynamical) modes are expanded to second order and give rise to an effective semiclassical potential. We determine the limits of validity of the approximation, and demonstrate its usefulness by calculating the temperature dependent resistivity in the Fermi liquid to polaron crossover regime (leading to `saturation behavior') and also isotope effects on electronic properties including the spectral function, resistivity, and optical conductivity, problems beyond the scope of conventional diagrammatic perturbation theories.
We show that claims, presented in Phys. Rev. B {\bf 65}, 125109 (2002) concerning the threshold behavior of dynamical correlations of a Coulomb Luttinger liquid, are based on an inconsistent mathematical analysis. Physical arguments are also presented, indicating that the claimed behavior is unlikely to be correct.
The dynamical mean-field method is used to formulate a computationally tractable theory of electron-phonon interactions in systems with arbitrary local electron-electron interactions in the physically relevant adiabatic limit of phonon frequency small compared to electron bandwidth or interaction scale. As applications, the phonon contribution to the effective mass of a carrier in a lightly doped Mott insulator is determined and the phase separation boundary is discussed.
We study a mechanism for superconductivity in quasi-one-dimensional materials with Ising anisotropy. In an isolated chain Ising anisotropy opens a spin gap; if inter-chain coupling is sufficiently weak, single particle hopping is suppressed and the physics of coupled chains is controlled by a competition between pair hopping and exchange interaction. Spin density wave and triplet superconductivity phases are found separated by a first order phase transition. For particular parameter values a second order transition described by SO(4) symmetry is found.
The effect of proximity to a Mott insulating phase on the superflow properties of a d-wave superconductor is studied using the slave boson-U(1) gauge theory model. The model has two limits corresponding to superconductivity emerging either out of a 'renormalized fermi liquid' or out of a non-fermi-liquid regime. Three crucial physical parameters are identified: the size of the vortex \textit{as determined from the supercurrent it induces;} the coupling of the superflow to the quasiparticles and the 'nondissipative time derivative' term. As the Mott phase is approached, the core size as defined from the supercurrent diverges, the coupling between superflow and quasiparticles vanishes, and the magnitude of the nondissipative time derivative dramatically increases. The dissipation due to a moving vortex is found to vary as the third power of the doping. The upper critical field and the size of the critical regime in which paraconductivity may be observed are estimated, and found to be controlled by the supercurrent length scale.
We use a recently developed formalism (combining an adiabatic expansion and dynamical mean-field theory) to obtain expressions for isotope effects on electronic properties in correlated systems. As an example we calculate the isotope effect on electron effective mass for the Holstein model as a function of electron-phonon interaction strength and doping. Our systematic expansion generates diagrams neglected in previous studies, which turn out to give the dominant contributions. The isotope effect is small unless the system is near a lattice instability. We compare this to experiment.
The dynamical mean field method is used to calculate the frequency and temperature dependent conductivity of dilute magnetic semiconductors. Characteristic qualitative features are found distinguishing weak, intermediate, and strong carrier-spin coupling and allowing quantitative determination of important parameters defining the underlying ferromagnetic mechanism.
We use the dynamical mean field theory to develop a systematic and computationally tractable method for studying electron-phonon interactions in systems with arbitrary electronic correlations. The method is formulated as an adiabatic expansion around the limit of static phonons. No specific electronic groundstate is assumed. We derive an effective low-frequency phonon action whose coefficients are static local correlation functions of the underlying electron system. We identify the correct expansion parameters. At a critical electron-phonon interaction strength the system undergoes a transition to a polaronic state. We determine the location of this polaronic instability in the presence of electron-electron interactions, doping, and quantum lattice fluctuations and present the formalism needed for study of the electron self-energy and effective mass.
The effect of proximity to a Mott insulating phase on the charge transport properties of a superconductor is determined. An action describing the low energy physics is formulated and different scenarios for the approach to the Mott phase are distinguished by different variation with doping of the parameters in the action. A crucial issue is found to be the doping dependence of the quasiparticle charge which is defined here and which controls the temperature and field dependence of the electromagnetic response functions. Presently available data on high-T$_{c}$ superconductors are analysed. The data, while neither complete nor entirely consistent, suggest that neither the quasiparticle velocity nor the quasiparticle charge vanish as the Mott phase is approached, in contradiction to the predictions of several widely studied theories of lightly doped Mott insulators. Implications of the results for the structure of vortices in high-T$_{c}$ superconductors are determined. The numerical coefficients in the field-dependent specific heat are given for square and triangular vortex lattices.