Collapse of $ρ_{xx}$ ringlike structures in 2DEGs under tilted magnetic fields

Gerson J. Ferreira; J. Carlos Egues

doi:10.1007/s10948-009-0548-8

paper

Collapse of $ρ_{xx}$ ringlike structures in 2DEGs under tilted magnetic fields

arXiv:1003.1761 · doi:10.1007/s10948-009-0548-8

Abstract

In the quantum Hall regime, the longitudinal resistivity $ρ_{xx}$ plotted as a density--magnetic-field ( $n_{2 D} - B$ ) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [e.g., Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801 (2005)]. For tilted magnetic fields, some of these ringlike structures "shrink" as the tilt angle is increased and fully collapse at $θ_{c} \approx 6^{\circ}$ . 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 anti-crossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding $n_{2 D} - B$ 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 $n_{2 D} - B$ diagram. For the ring with filling factor $ν = 4$ , we find that the anti-crossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the $θ = 0^{\circ}$ data, we find a collapsing angle $θ_{c} \approx 3. 6^{\circ}$ . Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.

3 pages, 2 figures; Proceedings of the PASPS V Conference Held in August 2008 in Foz do Iguaçu, Brazil

Collapse of ρxx​ ringlike structures in 2DEGs under tilted magnetic fields

Abstract

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Collapse of $ρ_{xx}$ ringlike structures in 2DEGs under tilted magnetic fields