Orbital magnetism of classically chaotic quantum systems

– We employ orbital magnetic response functions as a tool to investigate fluxdependent spectral correlations of chaotic quantum dots in the ballistic regime. We compare for the first time results for the persistent current and susceptibility from a semiclassical theory (without adjustable parameters) with accurate quantum-mechanical calculations for the case of an ensemble of chaotic rings threaded by a magnetic flux. We discuss the temperature dependence and suggest this to be a natural and physically relevant parameter in order to study (experimentally) the signature of different semiclassical timescales in smoothed spectral correlation functions. Orbital magnetic properties of mesoscopic quantum systems have attracted considerable theoretical interest in the last decade; especially after experiments by Lévy et al. [1] provided evidence for the existence of a thermodynamic magnetic moment in non-superconducting rings threaded by a magnetic flux, nowadays referred to as persistent current (PC). The averaged PC of an ensemble of rings is a direct measure of the flux dependence of quantum fluctuations in the particle number. These are closely related to the two-point correlation function of the density of states. Orbital magnetic response functions thus represent prominent examples of universal (flux-dependent) spectral correlation functions probing the quantum nature of mesoscopic devices. Since the first experiments were performed using metallic rings with diffusive electron dynamics, most of the theoretical approaches have focussed on this regime [2]. Recently, measurements of the PC were achieved in rings lithographically defined on high-mobility semiconductor heterostructures [3] where impurity scattering is suppressed and the classical electron motion is ballistic. Such devices are of particular interest in the context of quantum chaos since they represent experimentally realizable systems which allow to study the interplay between the underlying classical dynamics and quantum properties as for instance persistent current [4], [5] or magnetic susceptibility [6], [7]. The dynamics of the electrons in the above-mentioned experiment on ballistic rings can be considered to be regular. A corresponding semiclassical treatment assuming integrability gives reasonable agreement with the measured PC [5]. In this letter we treat orbital magnetic