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We study current versus voltage ͑I-V ͒ when tunneling into the edge of the fractional quantum Hall effect over a continuum of filling factors ͑n͒ from 1͞4 to 1. Our devices manifest the power law I-V behavior previously observed by Chang et al. at discrete fillings, but now with as many as six decades in current and over the whole range of filling factor suggesting the existence of a continuum of chiral Luttinger liquids. Surprisingly the exponent behaves approximately as 1͞n and does not exhibit the strong plateau features predicted in recent theoretical works based on the intermixing of copropagating and counterpropagating multiple edge modes. [S0031-9007(97)05218-6] 0031-9007͞98͞80(5)͞1062(4)$15.00

Double quantum dots provide an ideal model system for studying interactions between localized impurity spins. We report on the transport properties of a series-coupled double quantum dot as electrons are added one by one onto the dots. When the many-body molecular states are formed, we observe a splitting of the Kondo resonance peak in the differential conductance. This splitting reflects the energy difference between the bonding and antibonding states formed by the coherent superposition of the Kondo states of each dot. The occurrence of the Kondo resonance and its magnetic field dependence agree with a simple interpretation of the spin status of a double quantum dot.

We describe the implementation of a scanning Hall probe microscope of outstanding magnetic field sensitivity (∼0.1 G) and unprecedented spatial resolution (∼0.35 μm) to detect surface magnetic fields at close proximity to a sample. Our microscope combines the advantages of a submicron Hall probe fabricated on a GaAs/Al0.3Ga0.7As heterostructure chip and the scanning tunneling microscopy technique for precise positioning. We demonstrate its usefulness by imaging individual vortices in high Tc La1.85Sr0.15CuO4 films and superconducting networks, and magnetic bubble domains.