Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.
-
date post
15-Jan-2016 -
Category
Documents
-
view
216 -
download
0
Transcript of Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.
![Page 1: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/1.jpg)
Exotic Kondo Effects and
TK Enhancement in
Mesoscopic Systems
![Page 2: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/2.jpg)
Outline:
The Two-channel Kondo effect
Quantum boxes
Charge two-channel Kondo scenario in quantum-box systems
TK enhancement
![Page 3: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/3.jpg)
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
![Page 4: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/4.jpg)
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
![Page 5: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/5.jpg)
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
![Page 6: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/6.jpg)
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?
![Page 7: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/7.jpg)
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
![Page 8: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/8.jpg)
Charging of a quantum box
![Page 9: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/9.jpg)
Thermal smearing of charge curve (NRG)
t = 0.1
E. Lebanon, AS, and F.B. Anders, PRB 2003
BB dV
QdTVC ),(
![Page 10: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/10.jpg)
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
![Page 11: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/11.jpg)
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
![Page 12: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/12.jpg)
Smearing of the charge step and effective capacitance (NRG)
BB dV
QdTVC ),(
Diverges logarithmically with decreasing T
![Page 13: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/13.jpg)
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)
![Page 14: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/14.jpg)
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
![Page 15: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/15.jpg)
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]
![Page 16: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/16.jpg)
Lead—Quantum dot—Quantum box setting
(Courtesy of D. Goldhaber-Gordon)
Leads
Quantumbox
![Page 17: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/17.jpg)
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
![Page 18: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/18.jpg)
The model for B , L << EC
dddUdddccH dBL k
kkk
, ,
Coupling to quantum box
Anderson impurity
eVdccdtdccdt zk
kBkBBk
kLkLL
,,
![Page 19: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/19.jpg)
Noninteracting dot at resonance with Fermi level
Weak coupling RG for B << L :
The two-channel Kondo effect persists
d=U=0
Perturbative RG
![Page 20: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/20.jpg)
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
![Page 21: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/21.jpg)
Enhancement of the Kondo scale
TK/(L+B) is maximal for 1T
Transmission coefficient through
the level: 2)(
4
BL
BLT
![Page 22: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/22.jpg)
![Page 23: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/23.jpg)
![Page 24: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/24.jpg)
![Page 25: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/25.jpg)
![Page 26: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/26.jpg)
![Page 27: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/27.jpg)
![Page 28: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/28.jpg)
![Page 29: Exotic Kondo Effects and T K Enhancement in Mesoscopic Systems.](https://reader031.fdocuments.in/reader031/viewer/2022020219/56649d6a5503460f94a48f93/html5/thumbnails/29.jpg)