Influence of interlayer tunneling on the quantized Hall phases in intentionally disordered multilayer structures

Stability of the quantized Hall phases is studied in weakly coupled multilayers as a function of the interlayer correlations controlled by the interlayer tunneling and by the random variation of the well thicknesses. A strong enough interlayer disorder destroys the symmetry responsible for the quantization of the Hall conductivity, resulting in the breakdown of the quantum Hall effect. A clear difference between the dimensionalities of the metallic and insulating quantum Hall phases is demonstrated. The sharpness of the quantized Hall steps obtained in the coupled multilayers with different degrees of randomization was found consistent with the calculated interlayer tunneling energies. The observed width of the transition between the quantized Hall states in random multilayers is explained in terms of the local fluctuations of the electron density.

Influence of super-ohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.