singleimpurity

A single impurity refers to an isolated defect or dopant introduced into an otherwise perfect crystal lattice. Its presence perturbs the local electronic potential and lattice structure, influencing the behavior of itinerant electrons in its vicinity. In modeling, the impurity is treated as a localized degree of freedom embedded in a host material, and its effects can range from simple scattering to complex many-body phenomena.

Two primary theoretical frameworks are used to study single impurities. In noninteracting models, the impurity is represented by a localized potential that scatters conduction electrons; this approach yields phase shifts, possible bound states, and Friedel oscillations in the electron density. In many-body theory, the Anderson impurity model describes a localized orbital with on-site electron-electron repulsion that hybridizes with a conduction band. At low temperatures, this can give rise to a magnetic moment and, in certain regimes, the Kondo effect, where conduction electrons screen the impurity spin. The Kondo model often serves as an effective low-energy description of a magnetic impurity.

Physical consequences of a single impurity include localized bound or resonant states, altered local density of states, and modifications to electronic transport. Magnetic impurities can produce a Kondo resonance at the Fermi level, influencing conductance, while impurities in superconductors can introduce in-gap Shiba states. In nanoscale systems, single impurities are central to studies of quantum dots and artificial atoms, where tuning parameters reveals impurity-related many-body physics.

Experimental contexts include doped semiconductors, magnetic adatoms on surfaces, and two-dimensional materials like graphene, where scanning tunneling microscopy and spectroscopy probe the properties of individual impurities. The single-impurity problem serves as a fundamental building block for understanding more complex impurity ensembles.