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Noncrossing Approximation for the Anisotropic Kondo Model: Charge Fluctuations in a Quantum Box

Eran Lebanon·Avraham Schiller·Vilen Zevin
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Abstract

The noncrossing approximation (NCA) is generalized to the multi-channel Kondo-spin Hamiltonian with arbitrary anisotropic exchange couplings and an external magnetic field, and applied -- in the framework of Matveev's mapping -- to the charge fluctuations in a single-electron box at the Coulomb blockade. The temperature dependences of the charge step and the capacitance are calculated for a narrow point contact. At low temperatures and close to the degeneracy point, the capacitance line shape exhibits an approximate scaling with U/\sqrt{T}, where U is the deviation in gate voltage from the degeneracy point. This scaling relation is proposed as a sharp experimental diagnostic for the non-Fermi-liquid physics of the system at low temperatures. Both the reliability and shortcomings of the Kondo NCA are discussed in detail. Through comparison with poor-man's scaling, we are able to pinpoint the omission of particle-particle processes as the origin of the NCA flaws. An extended diagrammatic scheme is devised to amend the NCA flaws.

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Eran Lebanon, Avraham Schiller, Vilen Zevin. 2001-10-17. Noncrossing Approximation for the Anisotropic Kondo Model: Charge Fluctuations in a Quantum Box. https://doi.org/10.1103/physrevb.64.245338

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