Visualizing Critical Correlations Near the Metal-Insulator Transition in Ga _{1- x} Mn _x As

Abstract

Electronic states in disordered conductors on the verge of localization are predicted to exhibit critical spatial characteristics indicative of the proximity to a metal-insulator phase transition. We have used scanning tunneling microscopy to visualize electronic states in Ga 1-x Mn x As samples close to this transition. Our measurements show that doping-induced disorder produces strong spatial variations in the local tunneling conductance across a wide range of energies. Near the Fermi energy, where spectroscopic signatures of electron-electron interaction are the most prominent, the electronic states exhibit a diverging spatial correlation length. Power-law decay of the spatial correlations is accompanied by log-normal distributions of the local density of states and multifractal spatial characteristics. Our method can be used to explore critical correlations in other materials close to a quantum critical point.Since Anderson first proposed that disorder could localize electrons in solids fifty years ago (1), studies of the transition between extended and localized quantum states have been at the forefront of physics (2). Realizations of Anderson localization occur in a wide range of physical systems from seismic waves to ultracold atomic gases, in

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“…Our study also allows us to address another interesting question that has thus far been ignored in Ga 1−x Mn x As: what (if any) are the quantum corrections to the anomalous Hall conductivity? This question is particularly germane within the context of Ga 1−x Mn x As where the confluence of ferromagnetism, disorder and interactions invariably occurs in close vicinity of the metal-insulator transition (MIT) [17]. Earlier studies [6,18] on metallic ferromagnets in the weak disorder limit (k F l e ≫ 1, where k F and l e are the Fermi wave vector and the elastic mean free path, respectively) show that the quantum correction to the anomalous Hall conductivity is distinctly different for the skew scattering and side jump mechanisms, thus providing an alternative route to test the origin of the AHE.…”

Quasiparticle Scattering off Defects and Possible Bound States in Charge-Ordered YBa2Cu3OyZhou1, Hirata2, Wu3 et al. 2017Phys. Rev. Lett.111331View full textAdd to dashboardCite

“…4. We are not aware of any other physical phenomenon giving rise to a similar distribution of N (E F ), except for Anderson localization [41,42] that should be irrelevant here. We therefore conclude that the asymmetric broadening must be related to quasiparticle bound states around defects in the high-field CDW state.…”

More than just room temperature

“…Electronic states generated by hole doping in (Ga,Mn)As show the spatial structure anticipated for electrons near the metal-insulator transition 10 .…”