The excitonic collapse of higher Landau level fractional quantum Hall effect

The scarcity of the fractional quantum Hall effect in higher Landau levels is a most intriguing fact when contrasted with its great abundance in the lowest Landau level. This paper shows that a suppression of the hard core repulsion in going from the lowest Landau level to higher Landau levels leads to a collapse of the energy of the neutral excitation, destabilizing all fractional states in the third and higher Landau levels, and almost all in the second Landau level. The remaining fractions are in agreement with those observed experimentally.Comment: 5 pages, 3 figures. To appear in Phys. Rev. B Rapid Communicatio

SO(4)SO(4) Landau Models and Matrix Geometry

We develop an in-depth analysis of the $SO(4)$ Landau models on $S^3$ in the $SU(2)$ monopole background and their associated matrix geometry. The Schwinger and Dirac gauges for the $SU(2)$ monopole are introduced to provide a concrete coordinate representation of $SO(4)$ operators and wavefunctions. The gauge fixing enables us to demonstrate algebraic relations of the operators and the $SO(4)$ covariance of the eigenfunctions. With the spin connection of $S^3$, we construct an $SO(4)$ invariant Weyl-Landau operator and analyze its eigenvalue problem with explicit form of the eigenstates. The obtained results include the known formulae of the free Weyl operator eigenstates in the free field limit. Other eigenvalue problems of variant relativistic Landau models, such as massive Dirac-Landau and supersymmetric Landau models, are investigated too. With the developed $SO(4)$ technologies, we derive the three-dimensional matrix geometry in the Landau models. By applying the level projection method to the Landau models, we identify the matrix elements of the $S^3$ coordinates as the fuzzy three-sphere. For the non-relativistic model, it is shown that the fuzzy three-sphere geometry emerges in each of the Landau levels and only in the degenerate lowest energy sub-bands. We also point out that Dirac-Landau operator accommodates two fuzzy three-spheres in each Landau level and the mass term induces interaction between them.Comment: 1+59 pages, 8 figures, 1 table, minor corrections, published versio

Skyrmion Physics Beyond the Lowest Landau Level Approximation

The effects of Landau level mixing and finite thickness of the two-dimensional electron gas on the relative stability of skyrmion and single spin-flip excitations at Landau level filling factor $\nu=1$ have been investigated. Landau level mixing is studied by fixed-phase diffusion Monte Carlo and finite thickness is included by modifying the effective Coulomb interaction. Both Landau level mixing and finite thickness lower skyrmion excitation energies and favor skyrmions with fewer spin flips. However, the two effects do not work `coherently'. When finite thickness is included the effect of Landau level mixing is strongly suppressed.Comment: 4 pages, 4 figure

The influence of magnetic steps on bulk superconductivity

We study the distribution of bulk superconductivity in presence of an applied magnetic field, supposed to be a step function, modeled by the Ginzburg-Landau theory. Our results are valid for the minimizers of the two-dimensional Ginzburg-Landau functional with a large Ginzburg-Landau parameter and with an applied magnetic field of intensity comparable with the Ginzburg-Landau parameter

Equilibrium order parameters of nematic liquid\ud crystals in the Landau-De Gennes theory

We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-De Gennes predictions match and the temperature regimes where the Landau-De Gennes predictions don’t match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-De Gennes theory since the Landau-De Gennes theory predicts large values of the equilibrium scalar order parameters - larger than unity, in the low-temperature regime. We discuss a modified Landau-De Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes

Landau-Ginzburg String Vacua

We investigate a class of (2,2) supersymmetric string vacua which may be represented as Landau--Ginzburg theories with a quasihomogeneous potential which has an isolated singularity at the origin. There are at least three thousand distinct models in this class. All vacua of this type lead to Euler numbers which lie in the range $-960 \leq \chi \leq 960$. The Euler characteristics do not pair up completely hence the space of Landau--Ginzburg ground states is not mirror symmetric even though it exhibits a high degree of symmetry. We discuss in some detail the relation between Landau--Ginzburg models and Calabi--Yau manifolds and describe a subtlety regarding Landau--Ginzburg potentials with an arbitrary number of fields. We also show that the use of topological identities makes it possible to relate Landau-Ginzburg theories to types of Calabi-Yau manifolds for which the usual Landau-Ginzburg framework does not apply.Comment: 92p