Theory of Shubnikov--De Haas Oscillations Around the ν=1/2\nu=1/2 Filling Factor of the Landau Level: Effect of Gauge Field Fluctuations

We present a theory of magnetooscillations around the $\nu =1/2$ Landau level filling factor based on a model with a fluctuating Chern--Simons field. The quasiclassical treatment of the problem is appropriate and leads to an unconventional $\exp\left[-(\pi/\omega_c\tau^*_{1/2})^4\right]$ behavior of the amplitude of oscillations. This result is in good qualitative agreement with available experimental data.Comment: Revtex, 4 pages, 1 figure attached as PostScript fil

Specific heat and validity of quasiparticle approximation in the half-filled Landau level

We calculate the specific heat of composite fermion system in the half-filled Landau level. Two different methods are used to examine validity of the quasiparticle approximation when the two-body interaction is given by $V(q) = V_0 / q^{2-\eta}$ ($1 \le \eta \le 2$). The singular part of the specific heat is calculated from the free energy of the gauge field, which is compared with the specific heat calculated from the quasiparticle approximation via the singular self-energy correction due to the gauge field fluctuations. It turns out that two results are in general different and they coincide only for the case of the Coulomb interaction ($\eta = 1$). This result supports the fact that the quasiparticle approximation is valid only for the case of the Coulomb interaction. It is emphasized that this result is obtained by looking at a gauge-invariant quantity -- the specific heat.Comment: 8 pages, Revte

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Instantons and the spectral function of electrons in the half-filled Landau level

We calculate the instanton-anti-instanton action $S_{M {\bar M}} (\tau)$ in the gauge theory of the half-filled Landau level. It is found that $S_{M {\bar M}} (\tau) = (3 - \eta) \left [ \Omega_0 (\eta) \ \tau \right ]^{1 / (3 - \eta)}$ for a class of interactions $v ({\bf q}) = V_0 / q^{\eta} \ ( 0 \leq \eta < 2 )$ between electrons. This means that the instanton-anti-instanton pairs are confining so that a well defined `charged' composite fermion can exist. It is also shown that $S_{M {\bar M}} (\tau)$ can be used to calculate the spectral function of electrons from the microscopic theory within a semiclassical approximation. The resulting spectral function varies as $e^{ - \left [ \Omega_0 (\eta) / \omega \right ]^{1 / ( 2 - \eta ) } }$ at low energies.Comment: 13 pages, Plain Tex, MIT-CMT-APR-9

Composite fermions traversing a potential barrier

Using a composite fermion picture, we study the lateral transport between two two-dimensional electron gases, at filling factor 1/2, separated by a potential barrier. In the mean field approximation, composite fermions far from the barrier do not feel a magnetic field while in the barrier region the effective magnetic field is different from zero. This produces a cutoff in the conductance when represented as a function of the thickness and height of the barrier. There is a range of barrier heights for which an incompressible liquid, at $\nu =1/3$, exists in the barrier region.Comment: 3 pages, latex, 4 figures available upon request from [email protected]. To appear in Physical Review B (RC) June 15t

Weiss Oscillations in Surface Acoustic Wave Propagation

The interaction of a surface acoustic wave (SAW) with a a two-dimensional electron gas in a periodic electric potential and a classical magnetic field is considered. We calculate the attenuation of the SAW and its velocity change and show that these quantities exhibit Weiss oscillations.Comment: 4 pages REVTEX, 2 figures included as eps file

Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes

The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where n and p are integers, appear to be the only incompressible states in the thermodynamic limit, although other FQH hierarchy states occur for finite size systems. This explains the success of the composite Fermion picture.Comment: RevTeX, 10 pages, 7 EPS figures, submitted fo Phys.Rev.

Numerical Study of a Mixed Ising Ferrimagnetic System

We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbor interactions are included, our nonperturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.Comment: Figures can be obtained by request to [email protected] or [email protected]

Quantum Boltzmann equation of composite fermions interacting with a gauge field

We derive the quantum Boltzmann equation (QBE) of composite fermions at/near the $\nu = 1/2$ state using the non-equilibrium Green's function technique. The lowest order perturbative correction to the self-energy due to the strong gauge field fluctuations suggests that there is no well defined Landau-quasi-particle. Therefore, we cannot assume the existence of the Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an alternative formulation, we derive the QBE for the generalized Fermi surface displacement which corresponds to the local variation of the chemical potential in momentum space. {}From this QBE, one can understand in a unified fashion the Fermi-liquid behaviors of the density-density and the current-current correlation functions at $\nu = 1/2$ (in the long wave length and the low frequency limits) and the singular behavior of the energy gap obtained from the finite temperature activation behavior of the compressibility near $\nu = 1/2$. Implications of these results to the recent experiments are also discussed.Comment: 44 pages, Plain Tex, 5 figures (ps files) available upon reques