Landau theory

About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

Abstract: The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi2O6, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P21/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P tr, thus giving Landau parameters of K 0 = 138.3(2) GPa, K′ = 7.46(5), λ V = 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) GPa.

Lattice models and Landau theory for type-II incommensurate crystals

Abstract: Ground-state properties and phonon dispersion curves of a classical linear-chain model describing a crystal with an incommensurate phase are studied. This model is the DIFFOUR (discrete frustrated ${\ensuremath{\varphi}}^{4})$ model with an extra fourth-order term added to it. The incommensurability in these models may arise if there is frustration between nearest-neighbor and next-nearest-neighbor interactions. We discuss the effect of the additional term on the phonon branches and phase diagram of the DIFFOUR model. We find some features not present in the DIFFOUR model such as the renormalization of the nearest-neighbor coupling. Furthermore, the ratio between the slopes of the soft phonon mode in the ferroelectric and paraelectric phase can take on values different from $\ensuremath{-}2.$ Temperature dependences of the parameters in the model are different above and below the paraelectric transition, in contrast with the assumptions made in Landau theory. In the continuum limit this model reduces to the Landau free-energy expansion for type-II incommensurate crystals and it can be seen as the lowest-order generalization of the simplest Lifshitz-point model. Part of the numerical calculations have been done by an adaption of the effective potential method, originally used for models with nearest-neighbor interaction, to models with also next-nearest-neighbor interactions.

Hamiltonian Theory of the Fractional Quantum Hall Effect: Effect of Landau Level Mixing

Abstract: We derive an effective Hamiltonian in the lowest Landau level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy, $\ensuremath{\kappa}{=(e}^{2}/\ensuremath{\varepsilon}l)/{\ensuremath{\omega}}_{c}.$ We then transcribe the Hamiltonian to the composite fermion basis using our Hamiltonian approach, and compute the effect of LL mixing on transport gaps.