Spin susceptibility in interacting two-dimensional semiconductors and bilayer systems at first order: Kohn anomalies and spin density wave ordering

This work is an analytic theoretical study of a two-dimensional (2D) semiconductor with a Fermi surface that is split by the Zeeman coupling of electron spins to an external magnetic field in the presence of electron-electron interactions. We calculate the spin susceptibility for long-range and finite-range interactions diagrammatically, and we find a resonant peak structure at the Kohn anomaly already in first-order perturbation theory. In contrast to the density-density correlator that is suppressed due to the large electrostatic energy required to stabilize charge density order, the spin susceptibility does not suffer from electrostatic screening effects, thus favoring spin density wave order in 2D semiconductors. Our results impose significant consequences for determining magnetic phases in 2D semiconductors. For example, a strongly enhanced Kohn anomaly may result in helical ordering of magnetic impurities due to the Ruderman-Kittel-Kasuya-Yosida interaction. Furthermore, the spin degree of freedom can equally represent a layer pseudospin in the case of bilayer materials. In this case, the external "magnetic field"is a combination of layer bias and interlayer hopping. The sharp peak of the 2D static spin susceptibility may then be responsible for dipole-density-wave order in bilayer materials at large enough electron-phonon coupling.