Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems

1. Exotic Kondo Effects andTK Enhancement inMesoscopic Systems

2. Outline: The Two-channel Kondo effect Quantum boxes Charge two-channel Kondo scenario in quantum-box systems TK enhancement

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

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

5. One- versus two-channel Kondo effect Property One channel Two channel Non-Fermi-liquid Residual entropy Divergingcoefficientg Diverging susceptibility

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

7. The Coulomb blockade in quantum box Small metallic grain or large semiconductor quantum dot with sizeable Charging energy EC but dense single-particle levelsD Quantum box: Charging energy: Energy for charging box with one electron

8. Charging of a quantum box

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

10. Two-channel Kondo effect in charge sector (Matveev ‘91) Focus on EC>>kBT and on vicinity of a degeneracy point Introduce the charge isospin Channel index Lowering and raising isospin operators

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

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

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

14. Question: Can one remedy Matveev’s scenario by increasing TK? Can one avoid an exponentially small TK? • Proposal: Connect lead and box by tunneling through an ultrasmall quantum dot

15. For GB , GL << EC there is a nearly perfect Coulomb staircase even if the transmission is one at the Fermi level [Gramespacher & Matveev, 2000] Use small dot to tune the junction to perfect transmission at EF while maintaining a sharp staircase Idea:

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

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

18. The model for GB, GL<< EC Anderson impurity Coupling to quantum box

19. Noninteracting dot at resonance with Fermi level ed=U=0 Weak coupling RG forGB << GL : The two-channel Kondo effect persists Perturbative RG

20. Noninteracting dot at resonance with Fermi level ed=U=0 Intermediate couplingGB = GL Wilson’s NRG: There is still a two-channel Kondo effect

21. Enhancement of the Kondo scale Transmission coefficient through the level: TK/(GL+GB)is maximal for