Fermi-Edge Singularity in Tunnel Junctions Jin Zhang, Y. Sherkunov, N. d’Ambrumenil, B....
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Transcript of Fermi-Edge Singularity in Tunnel Junctions Jin Zhang, Y. Sherkunov, N. d’Ambrumenil, B....
Fermi-Edge Singularityin Tunnel Junctions
Jin Zhang, Y. Sherkunov, N. d’Ambrumenil, B. Muzykantskii
University of Warwick, U.K.
APS March Meeting, Portland, 17th, March, 2010
00)( 10 ff tiHtiHf eetG
Fermi-Edge Singularity
,2
2
4
ff titG
Sudden change of potentialfelt by the Fermi sea:
At zero temperature in single lead
P. W. Anderson, PRL18, 1049 (1967)
10 HH
Orthogonality Catastrophein quantum point contact:
X-Ray Absorption:
Loop ClosedLineOpen
)()()( fff tGtLtS
Spectrum decomposition:
Scattering Matrix Approach
R
L
ti
ti
R
L
a
a
tS
tBetA
etAtB
b
b
)()(
)()()(
)(
t
dttVt ')'()(10 HH 10 SS Characterize by
000)( )( tif etG
( )i t t ie
t i
Choose with :
20
000)
2)( or,(
22
t
tV
Example: ;01
100
S
0
02
2
1
i
i
e
eS 1ftG ?
But how to connect the Hamiltonians?
Keeling Klich Levitov, PRL97, 116403 (2006)
Map onto Full Counting StatisticsFull Counting Statistics:
SfftG~
1det)( fRft 1det)(
00)(ˆˆ
11 QitiHQitiH
n
nin eeeeeP
00)( 10 tiHti eetG
Fermi-Edge Singularity:
ReT
eTRS
ti
ti
)(
)(~
iiti
itii
LiLi
eABeABe
eABeeAB
eSSeR
22)(
)(22
1
1
RS ~
Let
2
12 RB
2
12 RA
, with
00
01L
Example: Constant Phase Shift (I)
);( ft
otherwise ,0
0 ,)( 0 fttt
T=1 t T=1/2 t
)( ftG
22220
fttttV 0withe.g. Choose Lorentzian Pulses:
FES FCS
)()(0 fttttV dt
dtV
)( )()(0 tttt f
How to represent the delta functionHow to connect and0S 1S
Example: Constant Phase Shift (II)
JZ YS NdA BM, PRB80, 245308 (2009)
When , we have two independent Lorentzian Pulses:
2
0|)1)(1(4
1)(
ii ee
220 4
2 )( ff titG
)()()( 21 fff tGtGtG
)(1 ftG
2
)(t
ft0
ft
Conclusion
How to connect the two Hamiltonian matters
Map FES problem onto FCS
Thank You
The Effect of Opening & Closing
02
1 RRLLRLLRasym bababiabia00 asym
( ) Imt i
A tt i
Turn on the scattering as
YS JZ NdA BM, PRB 80, 041313 (R) (2009)
tAT 2
Outcome of the wave function:
Optimal Electronic Entangler
Fermi-edge Singularity in 2DEG
D. Cobden, BM, PRL75, 4274 (1995)
xlc HHHH
aaH c
NNc 1lN
..chbaWH x
',
''* 0|)()(|0)(
baWtaWtbtS fffab
Absorption Spectrum:
bbEH ll
aaH c
1NNc 0lN
',
'',
aaVaaH c
1NNc 0lN