Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well. PACS numbers: 73.43.-f, 02.30.Jr.     

Hall effect plateaus and giant Shubnikov-de Haas oscillations in (BiSb)Telayered single crystals near the quantum limit

On bulk layered single crystals (Bi_0.25Sb_0.75)₂Te₃ with a hole concentration cm^-3 and a mobility cm²/Vs magnetoresistance and Hall effect investigations were performed in the temperature range T = 1.4 K ... 20 K in magnetic fields up to 18 T. For the magnetic field perpendicular to the layered structure giant Shubnikov-de Haas oscillations are measured; the positions of the maxima are triplets in the reciprocally scaled magnetic field. From the damping of the amplitudes with increasing temperature the cyclotron mass m _c = 0.12m ₀ is evaluated. Correlated with the SdH oscillations doublets of Hall effect plateaus (or kinks in low fields) are found. The weak well known Shubnikov-de Haas oscillations from the generally accepted multivallied highest valence band can be detected as a modulation on the giant oscillation. The high anisotropy of the SdH oscillations and their triplet structure in connection with the layered crystal structure lead us to suggest that the effects are caused by hole carrier pairing (mediated by the bipolaron mechanism) in quasi 2D sheets parallel to the crystal layer stacks. The measured Hall plateau resistances coincide with the quantum Hall effect values considering the number of layer stacks and the valley degeneracy of the 3D hole carrier reservoir. The ratio of spin splitting to Landau (cyclotron) splitting is observed to be . Received: 12 September 1997 / Revised: 8 January 1998 / Accepted: 22 January 1998