Anisotropy-driven topological quantum phase transition in magnetic impurities

Abstract

A few years ago, a topological quantum phase transition (TQPT) has been found in Anderson andKondo 2-channel spin-1 impurity models that include a hard-axis anisotropy term DS2 z with D > 0.The most remarkable manifestation of the TQPT is a jump in the spectral density of localizedelectrons, at the Fermi level, from very high to very low values as D is increased. If the twoconduction channels are equivalent, the transition takes place at the critical anisotropyDc ∼ 2.5 TK, where TK is the Kondo temperature for D = 0. This jump might be important todevelop a molecular transistor. The jump is due to a corresponding one in the Luttinger integral,which has a topological non-trivial value π/2 for D > Dc . Here, we review the main results for thespectral density and highlight the significance of the theory for the interpretation of measurementsconducted on magnetic atoms or molecules on metallic surfaces. In these experiments, where D isheld constant, the energy scale TK is manipulated by some parameters. The resulting variation givesrise to a differential conductance dI/dV, measured by scanning-tunneling spectroscopy, which isconsistent with a TQPT at an intermediate value of TK. For non-equivalent channels and non-zeromagnetic field, the topological phase is lost but still a peculiar behaviour in the spectral density isobtained which agrees with experimental observations. We also show that the theory can beextended to integer spin S > 1 and two-impurity systems. This is also probably true for half-integerspin and non-equivalent channels in some cases.