Absorption saturation studies of Landau levels in quasi-two-dimensional systems

We report the first far-infrared linear and non-linear (saturation) magneto absorption experiments of coupled subband-Landau level excitations in a series of modulation-doped double-coupled multiple quantum-well (MQW) structures. Non-linear spectroscopy is carried out with a free electron laser. A plot of energy versus magnetic field for 4 laser lines at low intensity and high intensity is compared with linear (Fourier transform) spectroscopy at low and high temperatures. An exact numerical solution of the Schrödinger equation for this coupled system is also obtained and compared with experiments. Results show that the feature observed at high laser intensity and high temperature is due to transitions from the 1st-excited state of the coupled system to the higher excited states. Based on this, a simple 2-level model is developed, and with a layer-by-layer analysis for MQW systems, the electron lifetime of the first-excited state is obtained.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.     

The Landau theory and the tricritical point

We show from the Landau theory of the tricritical point that the transition line has not necessarily a continuous slope and that it is possible to find behavior analogous to those of the tricritical points of first and second kind, analyzed by Reatto.     

Landau theory for helical nematic phases

We propose Landau phenomenology for the phase transition from the conventional nematic into the conical helical orientationally non-uniform structure recently identified in liquid crystals formed by “banana”-shaped molecules. The mean field predictions are mostly in agreement with experimental data. Based on the analogy with de Gennes model, we argue that fluctuations of the order parameter turn the transition to the first order phase transition rather than continuous one predicted by the mean-field theory. This conclusion is in agreement with experimental observations. We discuss the new Goldstone mode to be observed in the low-temperature phase.     

A Landau theory of the Peierls-BCS transition

We introduce a Landau type theory of the Peierls instability-superconductor transition involving two complex order parameters. Under a particular inequality condition among expansion parameters, the theory predicts that the superfluid conductivity should vary as $\text{(T?T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ above the critical region and as $\text{(T}{}^1{}_{\mathrm{<mtext>c</mtext>}}\text{?T)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ below the critical region.     

Landau theory of the isotropic-nematic critical point

Landau theory is used to analyze the effect of an applied on nematics with positive dielectric (or diamagnetic) anisotropy. Analytic results are given for the phase boundary, stability limits, and location of the critical points in the field-temperature phase diagram. For biphenyl compounds having a dielectric anisotropy ?_a≈10, it is argued that the critical point should occur at E_c≈10² kV/cm, which is experimentally accessible.     

Landau theory of crystallization and self-assembly of octagonal quasicrystals

The theory of crystallization of quasicrystal structures that does not use the concept of multidimensional crystallography for describing the quasicrystal order has been proposed. It has been shown using the structure of the MnSiAl octagonal quasicrystal as an example that the coordinates of the sites in the corresponding quasicrystal lattice can be calculated by conditional minimization of the Landau free energy. The abandonment of the unconditional minimization of the free energy has been justified by special features of the local atomic order in the considered structure. The proposed theory gives a new physical meaning to the traditional concepts of multidimensional crystallography and can also be used for explaining the formation of quasicrystal structures with other quasicrystal lattices.     

Symmetry,Landau theory and polytope models of glass

Order in supercooled liquids and metallic glasses is related to a regular icosahedral “crystal” consisting of 120 particles inscribed on the surface of a sphere in four dimensions. Hyperspherical harmonics and the discrete symmetry group of this four-dimensional platonic solid can be used to construct an order parameter for glasses in three-dimensional flat space. A uniformly frustrated Landau expansion in this order parameter suggests a ground state with a regular array of wedge disclination lines. Homotopy theory is used to classify all topologically stable defects. A generalization of Bloch's theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.     

Landau theory of the finite temperature mott transition

In the context of the dynamical mean-field theory of the Hubbard model, we identify microscopically an order parameter for the finite temperature Mott end point. We derive a Landau functional of the order parameter. We then use the order parameter theory to elucidate the singular behavior of various physical quantities which are experimentally accessible.     

Application of the Landau theory to spontaneous metamagnetism

The free energy of a two-sublattice magnet has been expanded in series of symmetry invariants. This model shows both order-disorder transitions and spontaneous metamagnetic phase changes. Conditions for all allowed transitions are given and good agreement with experimental data has been achieved.     

Landau theory of phase transitions in thick films

A simple expression is used for the free energy density with a one-component order parameter, and the boundary conditions at the surfaces of a film of thickness L are given by means of an extrapolation length δ. Exact expressions are given for the critical temperature and the order parameter profile in terms of elliptic functions, and the nature of the phase transition is discussed.     

Laser threshold and nonlinear Landau fluctuation theory of phase transitions

The threshold region for a single mode laser is treated by Landau's theory of order parameter fluctuations. Taking into account a kinetic energy in the Landau functional, approximate equations of motion for the laser field are derived which include coupling of phase and amplitude. From these it is easy to get the correlation functions and linewidths for intensity and field as well as the transient behaviour of intensity throughout the nonlinear transition region. In addition, a dynamical decoupling scheme of noise theory is applied to calculate the same quantities. Although these methods are very simple the results agree fairly well with those of the much more involved Fokker-Planck theory.     

Landau theory of charge and spin ordering in the nickelates

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 RNiO3, where R=Pr, Nd,Sm, Eu, Ho, Y, and Lu. While the Landau theory has general applicability, we show that for the most conducting materials, R=Pr, Nd, both types of order can be understood in terms of a nearly nested spin-density wave. Furthermore, we argue that in this regime, the charge ordering is reliant upon the orthorhombic symmetry of the sample, and therefore proportional to the magnitude of the orthorhombic distortion. The first order nature of the phase transitions is also explained. We briefly show by example how the theory is readily adapted to modified geometries such as nickelate films.     

Dynamical bifurcations and competing instabilities in Landau and Landau-Ginzburg theory

We discuss the case of a Landau theory for systems with competing instabilities and the behavior of its solutions at the phase transition. We show that when one takes into account the finite speed of variation of control parameters in any real experiment, the jumping effects characteristic of dynamical bifurcation theory lead to an enhancement of the critical mode; we then apply our discussion to the Landau-Ginzburg equation. We corroborate our discussion by the results of numerical simulations.