D. Z. Liu

Universal scaling of strong-field localization in an integer quantum Hall liquid.

We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as randomly distributed scattering centers with parametrized potentials. Using a transfer matrix for a finite-width-strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure \ensuremath{\delta}-function disorder in the absence of any Landau level coupling gives rise to nonuniversal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.

Electron localization in a two-dimensional system with random magnetic flux.

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy

Scaling behavior of the activated conductivity in a quantum Hall liquid.

E_c

LOCALIZATION IN SEMICONDUCTOR QUANTUM-WIRE NANOSTRUCTURES

all states are localized and the localization length

Theory of photoluminescence from a magnetic-field-induced two-dimensional quantum Wigner crystal

\xi

Photoluminescence and the Wigner crystal : can you see it ?

diverges when the Fermi energy approaches the critical energy, {\it i.e.}

Theory of phonon shakeup effects on photoluminescence from the Wigner crystal in a strong magnetic field.

\xi(E)\propto |E-E_c|^{-\nu}

Shakeup effects on photoluminescence from the Wigner crystal

. We find that

UNIVERSALITY IN TWO–DIMENSIONAL LANDAU LEVEL LOCALIZATION

E_c

OBSERVATION OF BELOW-GAP PLASMON EXCITATIONS IN SUPERCONDUCTING YBA2CU3O7 FILMS

shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent (