Exotic Kondo Effects and

TK Enhancement in

Mesoscopic Systems

Outline:

The Two-channel Kondo effect

Quantum boxes

Charge two-channel Kondo scenario in quantum-box systems

TK enhancement

One-channel Kondo effect

T >>TK T <<TK

)0(,

sSJccΗ impk

kkk

Impurity spin is progressively screened below J

K eT /1

A (local) Fermi liquid is formed for T<<TK

Two-channel Kondo effect

2,12,1 ,

)0(

sSJccΗ impk

kkk

Impurity spin is overscreened by two identical channels

rT 0

A non-Fermi-liquid fixed point is approached for T<<TK

One- versus two-channel Kondo effect

Property One channel Two channel Non-Fermi-liquid

)0( TS

TC /

)0( T

0

KT/1

KT/1 )/log( TTK

)/log( TTK

)2log(2

1Residual entropy

Diverging coefficient

Diverging susceptibility

Requirements for the realizationof 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

EC but dense single-particle levels

Charging energy:

QVC

QQE B

0

2

2)(

0

2

2C

eEC

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

BB dV

QdTVC ),(

Two-channel Kondo effect in charge sector

(Matveev ‘91)

Focus on EC>>kBT and on

vicinity of a degeneracy point

Introduce the charge isospin

NNNNz 112

eVcccctccH zqk

kLqBqBkLBL k

kkk

,,, ,

Lowering and raising isospin operatorsChannel index

NN 1

Two-channel Kondo dictionary for theCharging of a quantum box

Two-channel Kondo Charging of a quantum box

Spin index

Channel index

Exchange interaction

Magnetic Field

Bandwidth

JDTK 2/exp

J

H

D

Isospin index

Physical spin

Tunneling matrix element

Deviation from deg. point

Charging energy

2t

eV

EC

tET CK 4/exp

Smearing of the charge step and effective capacitance (NRG)

BB dV

QdTVC ),(

Diverges logarithmically with decreasing T

Can one observe the two-channel Kondo effect?

Observation of a fully developed two-channel Kondo effect

requires CKB ETk

Problem: In realistic quantum dots EC/ < 70, but

CCKB EtETk 4/exp

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 TK?

Can one avoid an exponentially small TK?

Proposal:

Connect lead and box by tunneling through an ultrasmall

quantum dot

Idea: Use small dot to tune the junction to perfect transmission at

EF while maintaining a sharp staircase

For B , L << EC 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

Quantumbox

Energy scales

Charging energy of small dot:

Charging energy of large dot:

Level spacing of small dot:

Level spacing of large dot:

mev1U

mev4.0d

ev5

mev2.0CE

The model for B , L << EC

dddUdddccH dBL k

kkk

, ,

Coupling to quantum box

Anderson impurity

eVdccdtdccdt zk

kBkBBk

kLkLL

,,

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

)/ln(20

),0(2

TTTk

eTC K

KB

Intermediate coupling B = L

Enhancement of the Kondo scale

TK/(L+B) is maximal for 1T

Transmission coefficient through

the level: 2)(

4

BL

BLT