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Nandini Trivedi The Ohio State University. Disorder and Zeeman Field-driven superconductor-insulator transition. Mohit Randeria. Yen Lee Loh. Karim Bouadim. See Poster. “Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010. SC. I. *. disorder.

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Nandini trivedi the ohio state university

Nandini Trivedi

The Ohio State University

Disorder and Zeeman Field-driven superconductor-insulator transition

Mohit

Randeria

Yen Lee

Loh

Karim

Bouadim

See Poster

“Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010


Disorder and zeeman field driven superconductor insulator transition

SC

I

*

disorder

SUPERCONDUCTOR-INSULATOR TRANSITION

QPT

amorphous quench

condensed films

T

I

“disorder”

What kind of insulator?

Exotic?

Unusual?

Trivial?

Band?

Anderson?

Mott?

Wigner?

Topological?

Quantum Hall?

Bose Glass?Fermi glass? Vortex glass?

SC

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)


Disorder and zeeman field driven superconductor insulator transition

  • 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


Disorder and zeeman field driven superconductor insulator transition

P(V)

-V

0

V

Model: Attractive Hubbard + disorder + field

Kinetic energy

2D

+

Attraction

(U controls size of Cooper pairs)

+

Random potential

Zeeman Field

V=0 s-wave SC

|U|=0 localization problem of non-interacting electrons

* Ignore Coulomb interactions


Disorder and zeeman field driven superconductor insulator transition

Methods

Bogoliubov-de Gennes-Hartree-Fock MFT

  • Local expectation values

  • Solve self consistently

BdG keeps only amplitude fluctuations

Determinantal Quantum Monte Carlo

No sign problem for any filling

Keeps both amplitude and phase fluctuations

Maximum entropy method for analytic continuation

DOS and LDOS


Part i superconducting film in zeeman field soft gaps in dos

Part I: Superconducting Film in Zeeman Field:Soft Gaps in DOS

Where do the states at

zero bias come from?

Magnetic impurities?

Orbital pair breaking?

??

states in gap

Experiment

Tunneling conductance into exchange-biased superconducting Al films

Catelani, Xiong, Wu, and Adams,

PRB 80, 054512 (2009)‏

Also Adams, private communication


Part i superconducting film in zeeman field soft gaps in dos1

Part I: Superconducting Film in Zeeman Field:Soft Gaps in DOS

states in gap

Theory

Disordered LO states provide spectral signatures at low energy

Loh and Trivedi, preprint

Experiment

Tunneling conductance into exchange-biased superconducting Al films

Catelani, Xiong, Wu, and Adams,

PRB 80, 054512 (2009)‏


Sc zeeman field

SC + Zeeman field

k

−k

BCS

FL

pairing Δ

Δ0

polarization m

Zeeman field

h

Chandrasekhar, Appl. Phys. Lett., 1, 7 (1962); Clogston, PRL 9, 266 (1962)‏


Modulated lo sc order parameter

Modulated (LO) SC order parameter

m

m

Δ

Δ

Δ

m

x

Δ

m

Weak LO

FL

BCS

Strong LO

Microscale phase separation =

polarized domain walls

pairingΔ

Δ0

polarization m

h

hc2

hc

hc1

Y-L. Loh and Trivedi, arxiv 0907.0679


Disorder and zeeman field driven superconductor insulator transition

Disorder + Zeeman field

h = 0.8

Local magnetization

Spin resolved DOS

Local

Pairing

amplitude

DOS

I. Paired unpolarized SC

In the next slide

Put a title sort of zeeman + disorder

Remove the h=1.75 panel

Give color bars

in each case plot the total dos

And most importantly

Have each set of panels for a given h come on

In a timed way at the push of “enter”


Disorder and zeeman field driven superconductor insulator transition

Disorder + Zeeman field

h = 0.95

+ and − domains

soft

gap

Disordered LO


Disorder and zeeman field driven superconductor insulator transition

m>0.05

F>0.05

F<−0.05

magnetization in domain walls

+ pairing

- pairing

Close-up view of a disordered LO state (h=1)‏


Disorder and zeeman field driven superconductor insulator transition

Disorder + Zeeman field

h = 1.5

+ and − domains

Non-superconducting


Disorder and zeeman field driven superconductor insulator transition

Spectrum

Magnetization

Pairing

hard gap

BCS

+ and - domains

Disordered

LO

soft

gap

gapless

Normalstate


Disorder and zeeman field driven superconductor insulator transition

Part II:

Local and Total Density of States


Disorder and zeeman field driven superconductor insulator transition

Previous Results:Self consistent mean field theory

Bogoliubov de-Gennes (BdG)

T=0

Pairing amplitude

DOS

Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)


Disorder and zeeman field driven superconductor insulator transition

Previous Results:Self consistent mean field theory

Bogoliubov de-Gennes (BdG)

Gap in single particle DOS

persists in insulator

Pairing amplitude

DOS

T=0

GAP

Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)


Disorder and zeeman field driven superconductor insulator transition

Why is the gap finite? Where do excitations live?

high hills: empty

D~0

D~0

Pairing

amplitude

map D(r)

deep valleys: trapped pairs

no number fluctuations

SC islands formed where

|V(r)-m| is small

Lowest excited states live

on SC blobs

Lowest excited states

GAP PERSISTS

Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)


Disorder and zeeman field driven superconductor insulator transition

What happens when phase fluctuations

are included?


Disorder and zeeman field driven superconductor insulator transition

Phase Diagram

U=-4t

n=0.88

Pairing scale

N

PG (generated

by disorder)

Coherence scale

INS

SC


Disorder and zeeman field driven superconductor insulator transition

Determining T*: peak in spin susceptibility

N

T

T*

SC

INS

Disorder


Disorder and zeeman field driven superconductor insulator transition

Determining Tc:

Vanishing of Superfluid stiffness

N

T

T*

Tc

SC

INS

Disorder

Twisted Boundary Condition


Spectral properties

Spectral properties


Disorder and zeeman field driven superconductor insulator transition

N

0.33

0.2

T

SC

INS

0

1.6

Disorder


Disorder and zeeman field driven superconductor insulator transition

N

0.33

0.2

T

SC

INS

0

1.6

Disorder


Disorder and zeeman field driven superconductor insulator transition

N

0.33

0.2

T

SC

INS

0

1.6

Disorder


Disorder and zeeman field driven superconductor insulator transition

N

0.33

0.2

T

SC

INS

0

1.6

Disorder


Disorder and zeeman field driven superconductor insulator transition

QMC DOS for SC: T dependence

N

U=-4t

V=1

Gapless

0.33

PG

T*(QMC) ~ 0.6

0.2

T

SC

Pseudogap

Coh peaks destroyed

INS

0

1.6

Disorder

T < Tc

T = Tc

Tc(QMC) ~ 0.12

SC gap

Coh peaks

T > Tc

28

Improve Schematic

With less jaggedy curve for SC

Indicate U, Vc, Tc(V=0)_QMC and T*(V=0) QMC

on the schematic fig

Δ < Eg

Δ0/Tc < 1.84


Disorder and zeeman field driven superconductor insulator transition

Temperature Dependence of DOS

Experiments:

Scanning tunneling spectroscopy(B. Sacépé et al.)‏

Theory:Bogoliubov-de Gennes-Hartree-Fock,

determinant quantum Monte Carlo

29


Qmc dos v dependence

QMC DOS: V dependence

N

U=-4t

T=0.1

Ins gap

No coh peaks

0.33

0.2

Vc~1.6t

T

SC

INS

0

1.6

Disorder

BdG gap

SC gap

Coh peaks


Dos summary

DOS: Summary

T

T

T

N

N

N

INS

SC

INS

SC

INS

SC

V

V

V

INS gap closes

No coh peaks

SC gap closes

Coh peaks die

Gap survives

Coh peaks die


Disorder and zeeman field driven superconductor insulator transition

Local Density of States


Disorder and zeeman field driven superconductor insulator transition

yes, we DO understand the weird behavior

Site (5, 4)‏

Pairing survives with V

Site (5, 1)‏

Pairing destroyed by V

Coherence peak destroyed;

incoherent weight builds up

Coherence peak survives

33


Local dos t dependence

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*.


Disorder and zeeman field driven superconductor insulator transition

Local DOS: T dependence

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

“Coherence peaks” disappear at every site at the same temperature

Pseudogaps still exist above Tc

35

More details about expt: are these at two different sites;

What is the Tc of these films; other exptl details;


Disorder and zeeman field driven superconductor insulator transition

Main Results:

1. Disordered LO states provide spectral signatures at low energy for Zeeman-field tuned superconductors

2. Coherence peaks disappear at

every site at the same T~Tc

Pseudogaps disappear at every site at T ~ T*

In disorder tuned transition the gap survives BUT coherence peaks die at V~Vc


Disorder and zeeman field driven superconductor insulator transition

Paired Insulator

Phase disordered

Disorder


The end

The End


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