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Guided by experiment and band structure, we introduce and study a phenomenological Landau theory for the unusual charge and spin ordering associated with the Mott transition in the perovskite nickelates, with chemical formula RNiO$_3$,…
The electronic properties of interfaces between two different solids can differ strikingly from those of the constituent materials. For instance, metallic conductivity, and even superconductivity, have been recently discovered at interfaces…
The Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It was understood later…
We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number $n$. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific…
The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization, in two-dimensional systems of noninteracting or weakly…
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…
Metal to insulator transitions (MITs) driven by strong electronic correlations are common in condensed matter systems, and are associated with some of the most remarkable collective phenomena in solids, including superconductivity and…
A theory of critical fluctuations in extreme type-II superconductors subjected to a finite but weak external magnetic field is presented. It is shown that the standard Ginzburg-Landau representation of this problem can be recast, with help…
Materials which can undergo extremely fast displacive transformations as well as very slow diffusive transformations are studied using a Ginzburg-Landau framework to understand the physics behind microstructure formation and…
Theory of low temperature kinetic phenomena in metals without inversion center is developed. Kinetic properties of a metal without inversion center are described by four kinetic equations for the diagonal (intra-band) and the off-diagonal…
The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic…
Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they…
We have computed the effective interaction between vortices in the Ginzburg-Landau model from large-scale Monte-Carlo simulations, taking thermal fluctuations of matter fields and gauge fields fully into account close to the critical…
Magnetoelectric multiferroic materials, particularly with the perovskite structure, are receiving a lot of attention because of their inherent coupling between electrical polarization and magnetic ordering. However, very few types of direct…
We consider a model for the two-dimensional electron gas formed at the interface of oxide heterostructures, which includes a Rashba spin-orbit coupling proportional to the electric field perpendicular to the interface. Based on the standard…
Recently the memristive electrical transport properties in NbO$_2$ have attracted much attention for their promising application to the neuromorphic computation. At the center of debates is whether the metal-to-insulator transition (MIT)…
Electromechanical activity, remanent polarization states, and hysteresis loops in paraelectric TiO2 and SrTiO3 are observed. The coupling between the ionic dynamics and incipient ferroelectricity in these materials is analyzed using…
Classical Landau theory considers structural phase transitions and crystallization as a condensation of several critical density waves whose wave vectors are symmetrically equivalent. Analyzing the simplest nonequilibrium Landau potentials…
A wide range of quasi-one-dimensional materials, consisting of weakly coupled chains, undergo three-dimensional phase transitions that can be described by a complex order parameter. A Ginzburg-Landau theory is derived for such a transition.…
Supplementing the Heisenberg model with a Hubbard-commuting kinetic of electrons adds to its spectrum without interference. One consequence is the precise incorporation of canonical linear spin wave theory within the time-dependent…