Optical conductivity in a simple model of a pseudogap state of a two-dimensional system

Calculations of the optical conductivity are performed in a simple model of the electronic spectrum of a two-dimensional system with “hot regions” on the Fermi surface. The model leads to a strong restructuring of the spectral density (pseudogap) in these regions. It is shown that this model makes it possible to reproduce qualitatively the basic features of the optical measurements in the pseudogap state of high-temperature superconducting cuprates. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 447–452 (25 March 1999)     

ARPES spectral functions and Fermi surface for La<Subscript>1.86</Subscript>Sr<Subscript>0.14</Subscript>CuO<Subscript>4</Subscript> compared with LDA + DMFT + Σ<Subscript>k</Subscript> calculations

The slightly underdoped high-temperature system La_1.86Sr_0.14CuO₄ (LSCO) is studied by means of high-energy high-resolution angular resolved photoemission spectroscopy (ARPES) and the combined LDA + DMFT + Σ _k computational scheme. The corresponding one-band Hubbard model is solved via dynamical mean field theory (DMFT), and the model parameters needed are obtained from first principles in the local density approximation (LDA). An “external” k-dependent self-energy Σ _k describes the interaction of correlated electrons with antiferromagnetic (AFM) pseudogap fluctuations. Experimental and theoretical data clearly show a “destruction” of the LSCO Fermi surface in the vicinity of the (π, 0) point and formation of “Fermi arcs” in the nodal directions. ARPES energy distribution curves as well as momentum distribution curves demonstrate a deviation of the quasiparticle band from the Fermi level around the (π, 0) point. The same behavior of spectral functions follows from theoretical calculations suggesting the AFM origin of the pseudogap state.     

The nature of isostructural spinodal decomposition in the Al-Zn system

The electronic structure and thermodynamic properties of disordered Al-Zn alloys are investigated in the coherent potential approximation by the KKR-ASA method. Analysis of the electronic density of states and the Fermi surfaces of disordered alloys reveals the presence of eight electronic topological transitions in the concentration interval from 0 to 70 at. % Zn. It is shown that the passage of the Fermi level through two minima of the density of states, which are due to the superposition of different types of electronic topological transitions, gives rise to singularities in the concentration dependence of the second derivative of the thermodynamic potential at points corresponding to the boundaries of the region of isostructural decomposition of the high-temperature solid solution, according to the phase diagram of the Al-Zn system. Fiz. Tverd. Tela (St. Petersburg) 39, 593–596 (April 1997)     

Hopf solitons and Hopf Q-balls on S3

Field theories with a S²-valued unit vector field living on S³×ℝ space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on S³ with arbitrary values of the Hopf index. Using these results, we then find a set of hopfions with topological charge Q_H=m², m∈Z, in the integrable subsector of the pure CP¹ model. In addition, we show that the CP¹ model with a potential term provides time-dependent solitons. In the case of the so-called “new baby Skyrme” potential we find, e.g., exact stationary hopfions, i.e., topological Q-balls. Our results further enable us to construct exact static and stationary Hopf solitons in the Faddeev–Niemi model with or without the new baby Skyrme potential. Generalizations for a large class of models are also discussed.     

Renormalisation-Induced Phase Transitions for Unimodal Maps

The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential −t log | Df |. Multiple and indeed infinitely many phase transitions at positive t can occur for some quadratic maps. All unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum. The author was supported by the EU training network “Conformal Structures and Dynamics”.     

Spin gap for multichain lattice and quantum spin model linearized about Fermi points

It is shown using the exact Bethe-ansatz solution that for a multichain quantum antiferromagnetic spin S=1/2 system the excitation energy has a gap for the version of the model linearized about Fermi points and is gapless for its lattice analog. The result is generalized for multichain spin-S quantum antiferromagnet and for strongly correlated electron models with a “permutation” construction of the supersymmetric Hamiltonians. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 192–196 (10 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Mesoscopic and macroscopic dipole clusters: Structure and phase transitions

A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic” clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms of clusters is considered.     

On “Hodge” topological strings at genus zero

A “Hodge strings” construction of solutions to associativity equations based on the t-part of t−t* equations is proposed. This construction formalizes and generalizes the “integration over the position of the marked point” procedure for computation of amplitudes in topological conformal theories coupled to topological gravity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 374–379 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Two-dimensional mesoscopic dusty plasma clusters: Structure and phase transitions

A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed. Zh. éksp. Teor. Fiz. 116, 1300–1312 (October 1999)     

Hysteresis Phenomenon in Deterministic Traffic Flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic “particle-hopping” traffic flow model being a straightforward generalization to the well known Nagel–Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the “free-flowing” (or “gaseous”) phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the “jammed” (or “liquid”) phase. Between the two critical values each of these phases may take place, which can be interpreted as an “overcooled gas” phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles. This research has been partially supported by Russian Foundation for Fundamental Research and French Ministry of Education grants.     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Angular studies of the magnetoresistance in the density wave state of the quasi-two-dimensional purple bronze KMo<Subscript>6</Subscript>O<Subscript>17</Subscript>

The purple molybdenum bronze KMo₆O₁₇ is a quasi-two-dimensional compound which shows a Peierls transition towards a commensurate metallic charge density wave (CDW) state. High magnetic field measurements have revealed several transitions at low temperature and have provided an unusual phase diagram “temperature-magnetic field”. Angular studies of the interlayer magnetoresistance are now reported. The results suggest that the orbital coupling of the magnetic field to the CDW is the most likely mechanism for the field induced transitions. The angular dependence of the magnetoresistance is discussed on the basis of a warped quasi-cylindrical Fermi surface and provides information on the geometry of the Fermi surface in the low temperature density wave state.     

Effective spacetime and Hawking radiation from a moving domain wall in a thin film of 3He-A

An event horizon for “relativistic” fermionic quasiparticles can be constructed in a thin film of superfluid ³He-A. The quasiparticles see an effective “gravitational” field which is induced by a topological soliton of the order parameter. Within the soliton the “speed of light” crosses zero and changes sign. When the soliton moves, two planar event horizons (black hole and white hole) appear, with a curvature singularity between them. Aside from the singularity, the effective spacetime is incomplete at future and past boundaries, but the quasiparticles cannot escape there because the nonrelativistic corrections become important as the blueshift grows, yielding “superluminal” trajectories. The question of Hawking radiation from the moving soliton is discussed but not resolved. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 833–838 (10 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem

The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics. PACS: 03.65.Ud, 04.60.Nc     

Thermodynamics of the HMF model with a magnetic field

We study the thermodynamics of the Hamiltonian mean field (HMF) model with an external potential playing the role of a “magnetic field”. If we consider only fully stable states, the caloric curve does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the caloric curve displays a region of negative specific heat in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions similar to the “gravothermal catastrophe” and to the “isothermal collapse” of self-gravitating systems. In the present case, they correspond to the reorganization of the system from an “anti-aligned” phase (magnetization pointing in the direction opposite to the magnetic field) to an “aligned” phase (magnetization pointing in the same direction as the magnetic field). We also find that the magnetic susceptibility can be negative in the microcanonical ensemble so that the magnetization decreases as the magnetic field increases. The magnetic curves can take various shapes depending on the values of energy or temperature. We describe first order phase transitions and hysteretic cycles involving positive or negative susceptibilities. We also show that this model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking.     

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”) of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”) analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A₈₀B₂₀ , a ternary model system with components “A”, “B”, and “C” in ratios of A₈₈B₇C₅ (as in Al₈₈Y₇Fe₅ , and to atomic coordinates in a Zr₈₀Pt₂₀ system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.     

Optical vortices in the scattering field of magnetic domain holograms

Experimental investigations and theoretical-model analyses have been made of the magnetooptic diffraction of light at ferrite garnet magnetic films with a banded domain structure which includes isolated magnetic grating defects in the form of “forks” and “breaks.” An analysis of the magnetic grating structure and the light diffraction field shows that in terms of its action on laser radiation, a banded domain grating is similar to a computer-synthesized phase hologram of an isolated pure screw-wavefront dislocation. It is shown that as a result of magnetooptic diffraction at a magnetic hologram, optical vortices may be reconstructed with a helicoidal wavefront carrying the topological charge l=±1,±2. Zh. Tekh. Fiz. 68, 54–58 (December 1998)     

Phase diagram of a 2D metal system with a variable number of carriers

It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 170–175 (25 January 1997)