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RKKY interaction induced by two-dimensional hole gases

We analytically compute the RKKY range function as induced by two-dimensional (2D) hole gases. The bulk valence-band includes heavy-hole (HH) and light-hole (LH) states and their dynamics is described by the Luttinger Hamiltonian which we adopt as our framework. We show that even for situations where only the lowest HH-like subband is occupied the resulting form of the RKKY function can be very different as compared to the one of a 2D electron gas. The associated spin susceptibility tensor has entries along the quantum-well directions and perpendicular to it. Our formluae for the spin susceptibility tensor reveal the crucial influence of HH-LH mixing which gives rise to large anisotropies both among the in-plane components as well as among the in-plane components and the component perpendicular to the quantum-well.