Kondo

The Kondo effect is a many-body phenomenon in condensed matter physics that occurs when a localized magnetic impurity resides in a metal and interacts with conduction electrons. This interaction leads to anomalous scattering and a characteristic resistivity behavior, including a minimum in resistivity at low temperatures and a resistivity upturn as temperature decreases further, reflecting the increasing importance of spin-flip scattering.

The effect was explained by Jun Kondo in 1964, who showed that spin-flip scattering of conduction electrons by the impurity produces a logarithmic contribution to electrical resistivity. As temperature is lowered below a characteristic scale called the Kondo temperature, TK, perturbation theory becomes invalid and a many-body singlet forms between the impurity spin and the surrounding conduction electrons, effectively screening the impurity.

Theoretical descriptions of the Kondo effect rely on models such as the Kondo model (the s-d exchange model) and the Anderson impurity model. Renormalization-group analyses reveal that the exchange coupling grows at low energies, steering the system toward a strong-coupling fixed point in which the impurity is screened. In nanoscale systems such as quantum dots, the Kondo effect can produce unitary conductance at low temperatures, reflecting the formation of the correlated many-body state.

Experimentally, the Kondo effect has been observed in metals with dilute magnetic impurities, in heavy-fermion compounds where lattice versions occur, and in nanoscale devices where a single impurity can generate a pronounced zero-bias conductance peak. Variants include multi-channel and two-channel Kondo effects, which can exhibit non-Fermi-liquid behavior, and orbital Kondo phenomena, as well as Kondo insulators where hybridization gaps open at low temperatures.

See also: Kondo temperature, Anderson impurity model, heavy fermion, quantum dot.