Kondo Physics in Nanostructures. A.Abdelrahman Department of Physics University of Basel Date: 27th Nov. 2006/Monday meeting

Transcription

1 Kondo Physics in Nanostructures A.Abdelrahman Department of Physics University of Basel Date: 27th Nov. 2006/Monday meeting

2 Kondo Physics in Nanostructures Kondo Effects in Metals: magnetic impurities Artificial Atoms: Quantum Dots in lateral/vertical GaAs nanostructures, Carbon Nanotubes, Molecules, Quantum Point Contacts Due to various degeneracies Spin ½ degeneracy Singlet-Triplet degeneracy Orbital degeneracy Combined degeneracies 2 Channel Kondo effect

3 Metals at Low Temperature Experiments:1930s, 50s metals with magnetic impurities metals superconductors Kouwenhoven et al., Physics Today, 2002

4 Metals at Low Temperature Increase in the resistivity at low T impurities phonons observed experimentally D. Goldhaber-Gordon, Ph. D. Thesis

5 Kondo Effect New energy scale: Kondo Temperature T K Kondo cloud: spin- flip scattering screening impurity spin T<T K : effective spin-flip scattering (Kondo cloud) increased resistance S. Cronenwett, Ph. D. Thesis

6 Kondo Effect in Metals: Model free electrons (delocalized) localized electrons on site charging Localized delocalized Electrons coupling Kondo Temperature T K

7 Kondo Effect in Quantum Dots spin-flip co-tunneling process Odd Even Spin degenerate energy state Gate voltage control parameters Cotunneling: Virtual proces Effectively flip the spin of the dot Screening the dot spin Spin Singlet Formation ψ VT = ψ sfl1 + ψsfl ψdot ψ singlet

8 Kondo Effect in Quantum Dots Extra resosnance at Fermi Energy A narrow peak in the density of state (DOS): µ = L µ R DOS Kondo resonance enhances conductane. Kondo Temperature: T k UΓ exp πε o 2Γ

9 Kondo Effect in Quantum Dots: Signatures even odd even Even-odd structure Kondo DOS peak : enhancing vally conductance for odd Zero-Bias peak in odd valley Goldhaber-Gordon et al., Nature 1998 Zero-bias peak for odd N Cronenwett et al., Science 1998

10 Kondo Effect in Quantum Dots: Signatures Zero Magnetic Field Zero-Bias peak in odd valley Classical Kondo signature: Logarithmic T dependence of the maximum for g max ~ log T T k < ~ T width of peak =max(t,t K ) Cronenwett et al., Science 1998

11 Controlling Kondo Temperature Tk Decreasing the distance between the localized states and Fermi energy: ε o Fermi Energies: µ L = µ R ε o T k Cronenwett et al., Science 1998

12 Kondo Effect in Quantum Dots: Signatures Magnetic field B II Splits the spin degenerate states by Zeeman splitting: ε g * B 2 * II ± = ε o ± g µ B - the effective Lande factor Goldhaber-Gordon et al., Nature 1998

13 Kondo Effect in Quantum Dots: Signatures zero bias peak splits in magnetic field Spliting of the zerobias peak Cronenwett et al., Science 1998

14 Even Valleys? Even valleys: no Kondo effect seen given: two electrons, two orbital levels splitting -> states? singlet S 3 triplets, T singlet B singlet C 1e orbital states Coulomb interactions E singlet B, C >> E S, T J = E T E S << GS E T > E S for N=2, B=0 non interacting E T > E S : NO spin degeneracy, NO Kondo effect

15 Singlet-Triplet Kondo Effect Inducing singlet-triplet degeneracy leads to new Kondo effect S > T > Sasaki et al., Nature 2000

16 Singlet-Triplet Kondo Effect Magnetic Field Dependence S-T degeneracy ( N=6, B~0.25T ) Conductance inside the corresponding Coulomb gap Triplet-Singlet transition Conductance inside the Coulomb gap: T S Sasaki et al., Nature 2000

17 Singlet-Triplet Kondo Effect: Familiar Signatures Spin-triplet ground state (B=0.12T) Singlet-triplet degenerate (B=0.22T) Spin-singlet ground state (B=0.32T) Sasaki et al., Nature 2000

18 Singlet-Triplet Kondo Effect: Familiar Signatures Zero-Bias resonance and T- dependence of the conductance at the singlet-triplet degenenracy Kondo Resonance at Triplet-Singlet transition g max log T dependence Saturation at low T:due to the electronic noise! Sasaki et al., Nature 2000

19 S-T Kondo Effect: Bias-Induced Degeneracy T S -ev SD = J out of equilibrium S-T Kondo Zumbühl et al., PRL 2004

20 Kondo Effect in CNTs Spin ½, spin 1 Kondo effects also seen in Carbon Nanotubes Kondo resonance: coherent superposition of all orders of spin-flipping cotunneling processes J Nygard et al., Nature 2000

21 Kondo Effect in CNTs 0T CNT: additional orbital degeneracy -> four fold shell pattern 5T S-T states may be degenerate Kondo effect ZB peaks split in field (as expected) The Kondo ridges split in the applied magnetic field Babic et al., PRB 2004

22 Kondo Effect in Molecules ZB peak log T dependence splits in B Liang et al., Nature 2002 T K up to 25K

23 Kondo Effect Quantum Point Contacts zero bias peak temperature dependence Kondo scaling Cronenwett et al., PRL 2002

24 Orbital Degeneracy: Kondo Effect Tuned orbital degeneracy in a spin ½ QD Magnetic field induces orbital degeneracy (odd N, S= ½) Strong Kondo effect Sasaki et al., PRL 2004

25 Combined Orbital/Spin Degen. (CNTs) combined spin ½ + orbital degeneracy : SU(4) Kondo effect orbital Jarillo-Herrero et al, Nature 2005

26 Combined Orbital/Spin Degen. (CNTs) B = 0 B = 1.5 T four fold degeneracy splits in B Kondo peak in the centre of the CV Jarillo-Herrero et al, Nature 2005

27 2 Channel Kondo Effect So far: Coupling dot to two reservoirs (left / right) Reservoirs not independent, since electrons can be transferred between L and R, forming effectively one reservoir L R How couple to two INDEPENDENT reservoirs? Potok et al, cond-mat 2006

28 2 Channel Kondo Effect Use a coulomb blockaded dot as reservoir (red) Due to charging energy, electrons cannot leave dot, i.e. res. Decoupled Difficult: access to the symmetric 2CK state Kondo quantum dot two finite leads reservoir ONE Infinite Coulomb blockaded quantum dot reservoir TWO Potok et al, cond-mat 2006

29 2 Channel Kondo Effect delocalized localized 1CK Hamiltonian antiferromagnetic exchange J J J fr ir ir 2CK Hamiltonian 1CK with finite reservoir f J f J = J ir fr fr 1CK with infinite reservoir 2CK at the quantum critical point (symmetric 2CK state) localized reservoir 1 reservoir 2 Γ U J ~ ε o ( ε o + U ) Each reservoirs attempts to screen localized spin New ground state: Local impurity only partieally screened Non Fermi liquid ground state (e 0.5 quasi-particle lifetime) Potok et al, cond-mat 2006

30 2CK Signature: Scaling Plotting: hard to see in single plot. Combine the dependence of the differential conductance on both bias and temperature 2CK: characteristic exponent α = 0.5 g(0, T ) g( V α T Y ( x) = 1 F ds 2CK, T ) goπ 2T2 CK 3 ( x / π ) π 2 cx α ev Y ( x) kt x 1 x << 1 ds x >> 1 For various T, V ds : all collapse on a single universal curve!! SCALING similar for 1CK, but characteristic exponent α =2 Potok et al, cond-mat 2006

31 2CK Experiment Curves collapse ok but small range (power law) Large enough to be conclusive? same data with 1CK scaling clearly does not scale Potok et al, cond-mat 2006

32 Kondo Physics in Nanostructures: Summary Kondo Effects in Metals Quantum Dots in: lateral/vertical GaAs nanostructures, Carbon Nanotubes, Molecules, Quantum Point Contacts Due to various degeneracies spin ½ degeneracy Singlet-Triplet degeneracy Orbital degeneracy combined degeneracies 2 Channel Kondo effect

33 Thanks for your attention