Upload
miranda-lindsey
View
214
Download
0
Tags:
Embed Size (px)
Citation preview
Han PuRice University
Collaborators:
Lei Jiang (NIST/JQI)
Hui Hu, Xia-Ji Liu (Swinburne)
Yan Chen (Fudan U.)
2013 Hangzhou Workshop on Quantum Matter
Localized Impurity in Ultracold Fermi Gas
Useful impurities
• Impurities can be used to probe physical properties of their host.
Quasi-particle DOS
S.H. Pan, et al., Nature, 403, 746(2000)
Zn impurity in BSCCO
Impurities in cold atoms
• Cold atoms are intrinsically clean.• Impurities or disorders can be engineered.
Anderson localization of atomic BEC
Inguscio group, nature 453, 895 (2008) Aspect group, nature 453, 891 (2008)
A local impurity in fermionic superfluid
2 2
0 0
†
,
/
, : BCS mean-field Hamiltonian
( ) ( ) ( )
contact impurity: ( ) ( )
1extended impurity: ( )
:
:
imp
imp
x a
H H H H
H d U
U u
U u ea
u impurity strength
Non magnetic impurity u u
Magnetic impu
r r r r
r r
r
:rity u u
BdG and T-Matrix method
)()()()()()(
),()()()()()(
rvrUruirvkrEv
rurUrvirukrEuy
y
T-matrix is convenient for localized contact impurity without trap.
Contact potential: T-matrix only depends on energy.
BdG method gives numerical results for single impurity in harmonic trap.
);'()();()'();();',( 000 wkGwTwkGkkwkGwkkG
BdG solves self-consistently a set of coupled equations
Contact non-magnetic impurity
0
0
0
0.02 F TF
u u u
u E x
BdG results
with impurity
without impurity
LDOS at impurity site
Contact non-magnetic impurity
2220
0 22
muE
Bound state occurs when T-1(w)=0
T-matrix results
T-matrix
BdG
LDOS
x x
Contact magnetic impurity
00 uuu
200
200
0
00 )2/(1
)2/(1
Nu
NuE
Bound state energy inside the gap
BdG results
T-Matrix results
T-Matrix results
Yu-Shiba stateYu, Acta Phys. Sin. 21, 75 (1965)Shiba, Prog. Theor. Phys. 40, 435 (1968)
Extended magnetic impurity
Spin up Spin down
Impurity: Gaussian potential with width a
0 0.12, 0.4, 1.0
0.2F TF
TF
u E x
a x
Impurity strength
A strong magnetic impurity induces local spin imbalanceA controlled way of generating FFLO state
Jiang et al., PRA 83, 061604(R) (2011)
Impurity in Fermi gas with spin-orbit coupling
• 2D Fermi gas with Rashba spin-orbit coupling
Sau et al., PRL 104, 040502 (2010)
Topological superconducting state
Supports Majorana mode in the vortex excitation
Topological phase transition in Fermi gas with SOC
Liu et al., PRA 85, 021603(R) (2012)
Quasi-particle excitation spectrum in the presence of a single vortex
Non-topological Topological
Impurity in topological and non-topological host
Non-topological Topological
Incr
easi
ng im
purit
y st
reng
thLDOS near a contact magnetic impurity
Contact impurity in topological superfluid
Both magnetic and non-magnetic impurity induces mid-gap bound states.
Incr
easi
ng im
purit
y st
reng
th
As the impurity strength increases,the energy of the bound state approacha universal value: 2
0~ / FE
Gap profile
For sufficiently large impurity strength, the order parameter is suppressednear the impurity site.
Superfluid order parameter:
Mid-gap state at the edge
For sufficiently large impurity strength, the order parameter is suppressednear the impurity site.
Topological superfluid
0
20 0
/
/ /
F
F F
v
E k E
Alicea, Rep. Prog. Phys. 75, 076501 (2012)
Bound states induced by extended impurity
Incr
easi
ng im
purit
y st
reng
th
Hu et al., PRL 110, 020401 (2013)
Measuring LDOS
3
RF-spectroscopy
†3 3
3 3
( ) ( ) ( )
' ( , '; ) ( ', ; ) ( )
dI
dt
d d A A f
r r r
r r r r r
If state 3 has a flat dispersion:
3 3
3
( ', ; ) ( ' )
( ) ( , )
A
I
r r r r
r r