1. Introduction to the Kondo Effect in Mesoscopic Systems

2. T(K) Resistivity minimum: The Kondo effect De Haas & ven den Berg, 1936 Franck et al., 1961 Fe in Cu Enhanced scattering at low T

3. Intermediate-valence and heavy fermion systems: Enhancement of thermodynamic and dynamic properties Strongly enhanced thermodynamics Single-ion scaling up to x=0.5 On-set of lattice coherence at high concentration of Ce Ce x La 1-x Cu 6 [from Onuki &Komatsubara, 1987]

4. Photoemission spectra Energy (meV) CeSi 2 CeCu 2 Si 2 Patthey et al., PRL 1987 Reinert et al., PRL 2001 Occupied DOS A(  )f  DOS A(  )

5. Planner tunnel junction with magnetic impurities V (mV) T(K)  G(0)/G 0 (0) Wyatt, PRL (1964) log(T) enhancement of the conductance Zero-bias anomaly

6. Kondo-assisted tunneling through a single charge trap Ralph & Buhrman, PRL 1994 dI/dV has image of Anderson impurity spectrum Zero-bias anomaly splits with magnetic field

7. Kondo-assisted tunneling in ultrasmall quantum dots Goldhaber-Gordon et al., Nature 1998 Quantum dot Plunger gate Temperature depedence Field dependence

8. Cobalt atoms deposited onto Au(111) at 4K (400A x 400A) Madhavan et al., Science 280 (1998)

9. STM spectroscopy on and off a Co atom Madhavan et al., Science 280 (1998)

10. The Kondo Effect: Impurity moment in a metal A nonperturbative energy scale emerges Below T K impurity spin is progressively screened Universal scaling with T/T K for T<T K Conduction electrons acquire a  /2 phase shift at the Fermi level All initial AFM couplings flow to a single strong-coupling fixed point

11. Local-moment formation: The Anderson model  d |  d + U hybridization with conduction electrons V

12. Energy scales: Inter-configurational energies  d and U+  d Hybridization width  =  V 2 Condition for formation of local moment: T TKTK 0 Charge fluctuations Free local moment Kondo screening Schrieffer & Wolff 1966

13. The Anderson model: spectral properties EFEF dd  d +U Kondo resonance A sharp resonance of width T K develops at E F for T<T K Unitary scattering for T=0 and =1

14. Bulk versus tunnel junction geometry Bulk geometry: Impurity blocks ballistic motion of conduction electrons Tunnel-junction geometry: Tunneling through impurity opens a new channel for conductance

15. dd U VLVL Q.D.Lead VRVR Ultrasmall quantum dots as artificial atoms

16. Anderson-model description of quantum dot IngredientMagnetic impurityQuantum dot Discrete single- particle levels 1.Atomic orbitalsLevel quantization On-site repulsion2.Direct Coulomb repulsion Charging energy E C =e 2 /C Hybridization3.With underlying band Tunneling to leads

17. Kondo resonance increases tunneling DOS, enhances conductance For  L =  R, unitary limit corresponds to perfect transmission G=2e 2 /h Tunneling through a quantum dot

18. Zeeman splitting with magnetic field HH eV Resonance condition for spin-flip-assisted tunneling:  B gH = eV eV Resonance in dI/dV for eV =  B gH

19. Electrostatically-defined semiconductor quantum dots Goldhaber-Gordon et al., Nature 1998 Quantum dot Plunger gate Temperature depedence Field dependence

20. More semiconductor quantum dots… van der Wiel et al., Science 2000 Conductance vs gate voltage Differential conductance vs bias dI/dV (e 2 /h) T varies in the range 15-800mK

21. Carbon nano-tube quantum dots Nygard et al., Nature 2000 Conductance vs gate voltage Nano-tube Lead T varies in the range 75-780mK

22. Magnetic-field-induced Kondo effect! Carbon nano-tube quantum dots Nygard et al., Nature 2000 Physical mechanism: tuning of Zeeman energy to level spacing  B gH Pustilnik et al., PRL 2000

23. Magnetic-field-induced Kondo effect! Carbon nano-tube quantum dots Nygard et al., Nature 2000 Physical mechanism: tuning of Zeeman energy to level spacing  B gH Pustilnik et al., PRL 2000

24. Phase-shift measurement in Kondo regime Ji et al., Science 2000  Two-slit formula: Relative transmission phase Aharonov-Bohm phase VpVp

25. Conductance of dot vs gate voltage Aharonov-Bohm oscillatory part Magnitude of oscillations & phase evolution Kondo valley Plateau in measured phase in Kondo valley ! Change in phase differs from  /2 But, no simple relation between  and transmission phase Entin-Wohlman et al., 2002

26. Nonequilibrium splitting of the Kondo resonance The Kondo resonance in the dot DOS splits with an applied bias into two peaks at  L and   R [Meir & Wingreen, 1994] Is this splitting measurable? Use a three-terminal device, with a probe terminal weakly connected to the dot YES! Sun & Guo, 2001; Lebanon & AS 2002

27. Measuring the splitting of the Kondo resonance de Franceschi et al., PRL (2002) Quantum wire Third lead Quantum dot Kondo peak splits and diminishes with bias Varying  V

28. Nonequilibrium DOS for asymmetric coupling to the leads de Franceschi et al., PRL (2002) Relative strength of coupling to left-and right-moving electrons is controlled by perpendicular magnetic field

29. Conclusions Mesoscopic systems offer an outstanding opportunity for controlled study of the Kondo effect In contrast to bulk systems, one can study an individual impurity instead of an ensemble of them New aspects of the Kondo effect emerge, e.g., the out-of- equilibrium Kondo effect and field-driven Kondo effect