Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling

18 pages, 5 figures; typos corrected and Sec. IV A rewritten; published versionInternational audienceWe theoretically investigate the spectral properties and the spatial dependence of the local density of states (LDoS) in disordered two-dimensional electron gases (2DEG) in the quantum Hall regime, taking into account the combined presence of electrostatic disorder, random Rashba spin-orbit in- teraction, and finite Zeeman coupling. To this purpose, we extend a coherent-state Green's function formalism previously proposed for spinless 2DEG in the presence of smooth arbitrary disorder, that here incorporates the nontrivial coupling between the orbital and spin degrees of freedom into the electronic drift states. The formalism allows us to obtain analytical and controlled nonperturbative expressions of the energy spectrum in arbitrary locally flat disorder potentials with both random electric fields and Rashba coupling. As an illustration of this theory, we derive analytical microscopic expressions for the LDoS in different temperature regimes which can be used as a starting point to interpret scanning tunneling spectroscopy data at high magnetic fields. In this context, we study the spatial dependence and linewidth of the LDoS peaks and explain an experimentally-noticed correlation between the spatial dispersion of the spin-orbit splitting and the local extrema of the potential landscape