Distribution of electron density and magnetocapacitance in the regime of the fractional quantum Hall effect

Fractional Quantum Hall States in a Ge Quantum Well

Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We analyze the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long-range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarized Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.

Model for dissipative conductance in fractional quantum Hall states

We present a model of dissipative transport in the fractional quantum Hall regime. Our model takes account of tunneling through saddle points in the effective potential for excitations created by impurities. We predict the temperature range over which activated behavior is observed and explain why this range nearly always corresponds to around a factor two in temperature in both integer quantum Hall and fractional quantum Hall systems. We identify the ratio of the gap observed in the activated behavior and the temperature of the inflection point in the Arrhenius plot as an important diagnostic for determining the importance of tunneling in real samples.

Theory of interlayer tunneling in bilayer quantum Hall ferromagnets

Spielman et al. [Phys. Rev. Lett. 84, 5808 (2000] recently observed a large and sharp Josephson-like zero-bias peak in the tunnel conductance of a bilayer system in a quantum Hall ferromagnet state. We argue that disorder-induced topological defects in the pseudospin order parameter limit the peak size and destroy the predicted Josephson effect. We predict that the peak would be split and shifted by an in-plane magnetic field in a way that maps the dispersion relation of the ferromagnet's Goldstone mode. We also predict resonant structures in the dc I-V characteristic under bias by an ac electric field.