Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems

Outline: The Two-channel Kondo effect Quantum boxes Charge two-channel Kondo scenario in quantum-box systems T K enhancement

One-channel Kondo effect T >>T K T <<T K Impurity spin is progressively screened below A (local) Fermi liquid is formed for T<<T K

Two-channel Kondo effect Impurity spin is overscreened by two identical channels A non-Fermi-liquid fixed point is approached for T<<T K

One- versus two-channel Kondo effect PropertyOne channelTwo channelNon-Fermi-liquid Residual entropy Diverging coefficient  Diverging susceptibility

Requirements for the realization of the two-channel Kondo effect No scattering of electrons between the bands Two independent conduction bands Equal coupling strength to the two bands No applied magnetic field acting on the impurity spin Is realization of the two-channel Kondo effect at all possible?

The Coulomb blockade in quantum box Quantum box: Small metallic grain or large semiconductor quantum dot with sizeable Charging energy E C but dense single-particle levels  Charging energy: Energy for charging box with one electron

Charging of a quantum box

Thermal smearing of charge curve (NRG)  t = 0.1 E. Lebanon, AS, and F.B. Anders, PRB 2003

Two-channel Kondo effect in charge sector (Matveev ‘91) Focus on E C >>k B T and on vicinity of a degeneracy point Introduce the charge isospin Lowering and raising isospin operatorsChannel index

Two-channel Kondo dictionary for the Charging of a quantum box Two-channel KondoCharging of a quantum box Spin index Channel index Exchange interaction Magnetic Field Bandwidth   H D Isospin index Physical spin Tunneling matrix element Deviation from deg. point Charging energy   2t2t eV ECEC

Smearing of the charge step and effective capacitance (NRG) Diverges logarithmically with decreasing T

Can one observe the two-channel Kondo effect? Observation of a fully developed two-channel Kondo effect requires Problem: In realistic quantum dots E C /  < 70, but Two-channel Kondo effect is unlikely to be observed in semiconductor devices (Zarand et al., 2000)

Question: Can one remedy Matveev’s scenario by increasing T K ? Can one avoid an exponentially small T K ? Proposal: Connect lead and box by tunneling through an ultrasmall quantum dot

Idea: Use small dot to tune the junction to perfect transmission at E F while maintaining a sharp staircase For  B,  L << E C there is a nearly perfect Coulomb staircase even if the transmission is one at the Fermi level [Gramespacher & Matveev, 2000]

Lead—Quantum dot—Quantum box setting (Courtesy of D. Goldhaber-Gordon) Leads Quantum box

Energy scales Charging energy of small dot: Charging energy of large dot: Level spacing of small dot: Level spacing of large dot:

The model for  B,  L << E C Coupling to quantum box Anderson impurity

Noninteracting dot at resonance with Fermi level Weak coupling RG for  B <<  L : The two-channel Kondo effect persists  d =U=0 Perturbative RG

Noninteracting dot at resonance with Fermi level  d =U=0 Wilson’s NRG: There is still a two-channel Kondo effect Intermediate coupling  B =  L

Enhancement of the Kondo scale T K /(  L +  B ) is maximal for Transmission coefficient through the level: