ν=1/2fractional quantum Hall effect in tilted magnetic fields

Abstract

Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor ν = 1/2 as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong ν = 1/2 fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like. The evolution is qualitatively similar to the one seen, in the absence of parallel field, as a function of increasing the electron density in the quantum well, but there are some notable differences.

Unusual Landau level pinning and correlatedν=1quantum Hall effect in hole systems confined to wide GaAs quantum wells

“…The transition from 1C to 2C as a function of increasing B || has been reported previously for electrons confined to wide GaAs QWs 15,26 . In such systems, the coupling of B || to the orbital (out-of-plane) motion of electrons renders the system progressively more bilayer-like at higher B || and quenches the energy separation between the N = 0 LLs of the symmetric and antisymmetric subbands, making them essentially degenerate 15,26 . Further increasing B || does not lift this degeneracy and the system remains 2C at the highest B || .…”

Collective excitations of quantum Hall states under tilted magnetic field

“…There is already evidence for such a state in higher LLs [1,3,47] under an in-plane magnetic field. In the LLL, previous experiments [37,39,40,48,49] focus on how the spin-gap is influenced by the tilt. It would be interesting to study the transition inside spin-polarized states under a large Zeeman energy via measurements of directiondependent transport properties.…”

“…So to leading order of perturbation expansion, we need to keep A (0) , A (1) , B (0) , C (1) , and D (0) , where A (0) , B (0) , and D (0) are computed from V 0 and A (1) and C (1) are the leading order perturbation induced by V n =0 . Equation (49) does not take the form of an eigenvalue equation. But to compute the leading order perturbation, we can simply replace ω in (ω − D) −1 by ω (0) , the eigenvalue of the isotropic A (0) such that the equation again takes an eigenvalue form, which we denote as (ω − H)a =Ĩ, where…”

Anisotropic composite fermions and fractional quantum Hall effect

“…(ii) Single-layer to bilayer transition --Such a B || -induced transition in the charge distribution, as observed in 2DESs confined to very wide QWs 37,41,42 , can also reduce ∆. As discussed earlier, in a quasi-2D carrier system, B || couples to the out-of-plane motion of the carriers.…”