Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets

Abstract

When two Landau levels are brought to a close coincidence between them and with the chemical potential in the Integer Quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb interaction among the electrons. We have found that the general pseudospin anisotropy classification scheme used in bilayers applies also to the trilayer situation, with the simple crossing corresponding to an easy-axis ferromagnetic anisotropy analogy, and the collapse case corresponding to an easy-plane ferromagnetic analogy. An isotropic case is also possible, with the levels just crossing or collapsing depending on the filling factor and the quantum numbers of the two nearby levels. While our results are valid for any integer filling factor ν (=1,2,3,...), we have analyzed in detail the crossings at ν = 3 and 4, and we have given clear predictions that will help in their experimental search. In particular, the present calculations suggest that by increasing the bias, the trilayer system at these two filling factors can be driven from an easy-plane anisotropy regime to an easy-axis regime, and then can be driven back to the easy-plane regime. This kind of reentrant behavior is an unique feature of the trilayers, compared with the bilayers. arXiv:1607.07909v1 [cond-mat.mes-hall]

Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit

“…as given elsewhere [15]. Here L m n (x) are the generalized Laguerre polynomials, and n < = min(n, m), n > = max(n, m).…”

“…The z-dependence of the EE potential can be useful for the study of coupled 2D electron gases like bilayers [24] and trilayers [13,15,25,26], in which this dependence appears as an inter-layer exchange term.…”

Exact exchange: A pathway for a density functional theory of the integer quantum Hall effect

“…Very recently, a new DFT formalism for the FQHE has been presented, based in the composite-fermion description of the FQHE [12]. Detailed Hartree-Fock calculations [13][14][15][16] have established a classification of the ferromagnetic regimes within the Integer Quantum Hall effect (IQHE). Notably, the application of DFT methods to this regime has been much less considered and limited to local density approximations [17,18], or solutions in limiting regimes [19,20].…”

“…Here (5) as given elsewhere [16]. Here L m n (x) are the generalized Laguerre polynomials, and n < = min(n, m), n > = max(n, m).…”