Post on 13-Dec-2015
1
Disorder and Zeeman Field-driven superconductor-insulator
transition
Nandini TrivediThe Ohio State University
“Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010
Karim Bouadim
Yen Lee Loh
Mohit Randeria
See Poster
SC
I “disorder”
*SC I
disorder
amorphous quench condensed films
Haviland et.al. PRL 62, 2180 (’89)Valles et.al. PRL 69, 3567 (’92)Hebard in “Strongly Correlated Electronic Systems”, ed. Bedell et. al. (’94)Goldman and Markovic, Phys. Today 51, 39 (1998)
SUPERCONDUCTOR-INSULATOR TRANSITION
What kind of insulator?Exotic?Unusual?Trivial?Band?Anderson?Mott?Wigner?Topological?Quantum Hall?Bose Glass?Fermi glass? Vortex glass?
QPT
T
Outline of talk:
Focus on three puzzling pieces of data:
Adams: Origin of low energy states in tunneling DOS in field-tuned SIT
Sacépé: Disappearance of coherence peaks in density of states above Tc
Armitage: Origin of states within the SC gap observed in €
h||
€
Reσ (ω)
H
€
−|U | ni↑ni↓
i
∑
€
+ (Vi − μ − hσ )ni
i
∑
..,
chcct jji
i
Kinetic energy
+Attraction
+
(U controls size of Cooper pairs)
Random potential
P(V)
-V 0 V
V=0 s-wave SC|U|=0 localization problem of non-interacting electrons
* Ignore Coulomb interactions
Zeeman Field
Model: Attractive Hubbard + disorder + field
2D
5
Determinantal Quantum Monte Carlo
No sign problem for any fillingKeeps both amplitude and phase fluctuations
Bogoliubov-de Gennes-Hartree-Fock MFT
Maximum entropy method for analytic continuation
€
nσ (r) ≡ crσ+ crσ
Δ(r) ≡|U | cr↑+ cr↓
+ ≡|U | F(r)
BdG keeps only amplitude fluctuations
Local expectation values Solve self consistently
),(1
)0()(),(
kAe
edcTckG kk
k
kAN
N ),(1
)(
Methods
DOS and LDOS
6
Part I: Superconducting Film in Zeeman Field:
Soft Gaps in DOS
ExperimentTunneling conductance into
exchange-biased superconducting Al films
states in gap
Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009)
Where do the states at zero bias come from?
Magnetic impurities?Orbital pair breaking???
Also Adams, private communication
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Part I: Superconducting Film in Zeeman Field:
Soft Gaps in DOS
ExperimentTunneling conductance into
exchange-biased superconducting Al films
TheoryDisordered LO states
provide spectral signatures at low
energy
Loh and Trivedi, preprint
states in gap
Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009)
€
N(E)
8
FLBCS
h
polarization mΔ0
pairing Δ
k−k ↑↑ ↓
SC + Zeeman field
Zeeman field
€
hc =1
2Δ0 = 0.707Δ0
Chandrasekhar, Appl. Phys. Lett., 1, 7 (1962); Clogston, PRL 9, 266 (1962)
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FLBCS Weak LOStrong LO
Δm
Δm Δ
m
xΔ
m
Modulated (LO) SC order parameter
hc
h
Δ0
hc1 hc2
polarization m
pairing Δ
Microscale phase separation = polarized domain walls
Y-L. Loh and Trivedi, arxiv 0907.0679
h = 0.8
I. Paired unpolarized SC
Local magnetization
Local Pairing amplitude
Spin resolved DOS
DOS
Disorder + Zeeman field
€
V = 2t
U = −4 t
€
Nσ (ω)
€
N(ω)
€
€
Disorder + Zeeman fieldh = 0.95
Disordered LO
+ and − domains
softgap
€
V = 2t
U = −4 t
€
Nσ (ω)
€
N(ω)
€
€
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Close-up view of a disordered LO state (h=1)
+ pairing
- pairing
magnetization in domain walls
F<−0.05F>0.05 m>0.05
€
V = 2t
Disorder + Zeeman fieldh = 1.5
Non-superconducting
+ and − domains
€
V = 2t
€
Nσ (ω)
€
N(ω)
€
€
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Magnetization Pairing Spectrum
softgap
BCS
DisorderedLO
+ and - domains
Normalstate
hard gap
gapless
€
N(ω)
€
Nσ (ω)
Part II:
Local and Total Density of States
Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)
Previous Results:Self consistent mean field theoryBogoliubov de-Gennes (BdG)
€
nσ (r) ≡ crσ+ crσ
Δ(r) ≡|U | cr↑+ cr↓
+ ≡|U | F(r)
Pairing amplitude DOST=0
Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)
Previous Results:Self consistent mean field theoryBogoliubov de-Gennes (BdG)
Gap in single particle DOS persists in insulator
T=0
€
nσ (r) ≡ crσ+ crσ
Δ(r) ≡|U | cr↑+ cr↓
+ ≡|U | F(r)
Pairing amplitude DOS
GAP
€
ρS
Pairing amplitude map r)
Why is the gap finite? Where do excitations live?
Low
est e
xcit
ed s
tate
s
high hills: empty
deep valleys: trapped pairs no number fluctuations
SC islands formed where |V(r)-| is small
Lowest excited states live on SC blobs
GAP PERSISTS
Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)
What happens when phase fluctuations are included?
U=-4tn=0.88
SC
N
PG (generated by disorder)
INS
Phase Diagram
Pairing scale
Coherence scale
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T
Disorder
€
V
SC
N
INS
Determining T*: peak in spin susceptibility
T*
22
T
Disorder
€
V
SC
N
INS
Twisted Boundary Condition
€
E =1
2ρ s(∇φ)2€
ρS
€
ρS
Determining Tc:Vanishing of Superfluid stiffness
T*
Tc
Spectral properties
T
Disorder
€
V
SC
N
INS0 1.6
0.2
0.33
T
Disorder
€
V
SC
N
INS0 1.6
0.2
0.33
T
Disorder
€
V
SC
N
INS0 1.6
0.2
0.33
T
Disorder
€
V
N
INS0 1.6
0.2
0.33
SC
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QMC DOS for SC: T dependence
Tc(QMC) ~ 0.12
T*(QMC) ~ 0.6
SC gapCoh peaks
PseudogapCoh peaks destroyed
Gapless
T < Tc
T > Tc
T = Tc
V=1
T
Disorder
€
V
SC
N
INS0 1.6
0.2
0.33
U=-4t
PG
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Temperature Dependence of DOS
Experiments:Scanning tunneling spectroscopy
(B. Sacépé et al.)
Theory:Bogoliubov-de Gennes-Hartree-Fock,determinant quantum Monte Carlo
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QMC DOS: V dependence
T=0.1Ins gap
No coh peaks
SC gapCoh peaks
BdG gap
Vc~1.6tT
Disorder
€
V
SC
N
INS0 1.6
0.2
0.33
U=-4t
€
V = 0
Egap,QMC ~ 0.7t
Egap,BdG ~ 1.4 t
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DOS: Summary
V
N
V
T
SC INS
N
V
T
SC INS
SC gap closesCoh peaks die
INS gap closesNo coh peaks
Gap survivesCoh peaks die
N
T
SC INS
Local Density of States
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Coherence peak destroyed;incoherent weight builds up
Coherence peak survives
Site (5, 4)Pairing survives with V
Site (5, 1)Pairing destroyed by V
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Local DOS: T dependence
Pairing FBdG(r, T) disappears at every site at the same temperature, T=TBdG.
“Coherence peaks” in LDOS NQMC(r, ω, T) disappear at every site at the same T ~ Tc.
Pseudogap remains on every site up to T*.
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c.f. Experiment (Sacépé):Scanning tunneling spectroscopy on an amorphous InOx film
(thickness 15 nm, on Si/SiO2 substrate)with Tc ~ 1.7 K, at two different locations at various T
Local DOS: T dependence
“Coherence peaks” disappear at every site at the same temperaturePseudogaps still exist above Tc
Main Results:
1. Disordered LO states provide spectral signatures at low energy for Zeeman-field tuned superconductors
In disorder tuned transition the gap survives BUT coherence peaks die at V~Vc
2. Coherence peaks disappear at every site at the same T~Tc
Pseudogaps disappear at every site at T ~ T*
Disorder Paired InsulatorPhase disordered
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The End