Density functional study of collective electron localization: detection by persistentcurrent

Abstract

We apply the optimized effective potential (OEP) implementation of density functionaltheory (DFT) to the model system of interacting spinless electrons on a quantum ring.The ring encircles a magnetic flux that induces a persistent current. In a perfectrotationally invariant system the current does not depend on the electron–electroninteraction (the latter is characterized by a standard dimensionless parameterrS) and hence is not sensitive to the microscopic structure of the electron correlated state.This changes, however, if a symmetry-breaking external potential is introduced or, in arealistic system, due to the crystal lattice potential (Hamer et al 1987 J. Phys. A: Math.Gen. 20 5677–93). In our model, we calculate the persistent current as a function ofrS in thepresence of a weak Gaussian-shaped ‘impurity’ potential. We find that while below a threshold valuerS<rSc≈2.05 the current isindependent of rS, itdecays exponentially for rS>rSc. This signals the formation of an electron Wigner crystal pinnedby the impurity potential. The electron density, homogeneous belowrSc, indeed shows a periodic modulation atrS>rSc. The modulationamplitude follows a (rS−rSc)1/2 behaviour which is characteristic for a second-order phase transition, as expected in themean-field-type DFT-OEP approach. Our calculation shows that the macroscopic current,which is a quantity directly accessible in DFT, can serve as an indicator of the formation ofa correlated electron state.