Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems
Jan 15, 2016
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