Abstract:

The elegant concept of Landau levels must be abandoned, whenever a quantum well (QW) is subjected to an in-plane or tilted magnetic field, because carriers move under the competing influence of the Lorentz force and the force due to the QW confining potential. The equal-energy surfaces [1, 2] or equivalently the density of states (DOS) [3, 4] are qualitatively and quantitatively modified because the spatial and the magnetic confinement compete. In the general case, handling of such problems involves self-consistent computations [2, 4, 5] of the energy dispersion, E_i,σ(k_x), where i is the subband index, σ denotes the spin and k_x is the in-plane wave vector perpendicular to the external in-plane magnetic field (applied along y), H. The envelope functions along the "growth" z-axis depend on k_x, i.e., ψ_i,σ,k_x,k_y (r) κ ζ_i,σ,k_x (z)e^ikxxe^ikyy. The impact on the physical properties was initially realized in transport experiments [6, 7, 8, 9]. The character of plasmons in single [10] and double [11] QWs is also affected. The N-type kink was theoretically predicted [12] and recently verified in photoluminescence experiments [13]. In this chapter, employing a self-consistent envelope function approach: (a) I summarize fundamental quantum mechanical relations pertinent to QWs under in-plane magnetic field, and I stage a compact DOS formula which holds for any type of interplay between spatial and magnetic confinement [4, 5]. (b) I describe the influence of an in-plane magnetic field on fundamental thermodynamic properties of dilutemagnetic- semiconductor narrow to wide single QWs. I discuss the entropy, S, the internal energy, U, the free energy, F, and the magnetization, M. (c) I examine the spin-subband populations and the spin-polarization of dilute-magnetic-semiconductor narrow to wide single QWs [5, 14].

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