Collapse of ρ xx Ringlike Structures in 2DEGs Under Tilted Magnetic Fields
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In the quantum Hall regime, the longitudinal resistivity ρ xx plotted as a density–magnetic-field (n 2D –B) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [see, e.g., Zhang et al., in Phys. Rev. Lett. 95:216801, 2005. For tilted magnetic fields, some of these ringlike structures “shrink” as the tilt angle is increased and fully collapse at θ c ≈6°. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anticrossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding n 2D –B diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as ρ xx in the n 2D –B diagram. For the ring with filling factor ν=4, we find that the anticrossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the θ=0° data, we find a collapsing angle θ c ≈3.6°. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.
KeywordsQuantum Hall ferromagnetism Magnetoresistance in 2DEGs Landau level crossings
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