Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface Wan Kyu Park and Laura H....

Andreev reflection at the CeCoIn5 Heavy Fermion Superconductor Interface

Wan Kyu Park and Laura H. Greene UIUCJohn L. Sarrao and Joe D. Thompson LANL

Theoretical support:Justin E. Elenewski UIUC, Greene groupVladimir Lukic UIUC, Leggett groupAnthony J. Leggett UIUCDavid Pines LANL & UIUC

Experimental supportKaren Parkinson UIUC, Undergraduate Thesis StudentCaitlin Jo Ramsey UIUC, UndergraduateB. Florian Wilken UIUC, German exchange student, 03-04Alex N. Thaler UIUC, REU 2003Patrick J. Hentges UIUC, PhD, 2004, now at IntelWilliam L. Feldman UIUC, Lab Tech, retired 2003

Funding support: US DoE, DEFG02-91ER45439 through FSMRL and CMM

RTS Workshop, June 10-11, 2005, Notre Dame, IN

Conditions ~10ms after Big Bang:

•10 GeV/fm3 or ~1016gm/cm3

•T ~ 170 MeV or ~ 2 x 1012 K

Same physics as superconductivity, (strongly-correlated electron systems) but 1016 different in energy !

I. Definition of Issues• Andreev reflection between a heavy-fermion

superconductor (HFS) and a normal (N) metal: • Point Contact Spectroscopy (PCS):

II. The HF superconductor CeCoIn5

III. Some Basics of Andreev Reflection and PCS

IV. Experiment: Cantilever-Andreev-Tunneling (CAT)

V. Data & Analysis (extended BTK model)• Known theories cannot explain AR at the

N/HFS interface: • Some analysis consistent with d-wave and

strong-coupling• New data on (110) may show spectroscopic

evidence for d-wave

VI. Conclusions

Outline

Definition of the issues

1. Understanding charge transport across HF interface Existing models cannot account for

Andreev reflection at the HFS/N interface

2. Spectroscopic studies of CeCoIn5 (OP symmetry, mechanism, etc.,…)

-2.0 -1.0 0.0 1.0 2.0

1.0

1.2

1.4

1.6

1.8

2.0

exp. data s-wave BTK d-wave BTK

Nor

mal

ized

Con

duct

ance

Voltage (mV)

-2 -1 0 1 2

0.9

1.0

1.1

400 mK 2.6K

dI/d

V /

dI/d

V| V

= -

2mV

Voltage (mV)

The Heavy-Fermion Superconductor CeCoIn5

C. Petrovic et al., J. Phys.: Condens. Matter 13, L337 (2001)

Tc = 2.3K (record high for HFS) 0

ab = 82Å, 0c = 53Å, ab ~ 1900Å, c ~ 2700Å,

Hc2ab(0) = 12T, Hc2

c(0) = 5T

Superconductivity in clean limit (l >> 0, l = 810Å)

Non-Fermi liquid: ~ T 1.0 ± 0.1, Cen / T ~ -lnT, 1 / T1T ~ T –3/4

Heavy-fermion liquid- n = Cen / T = 0.35J/mol K2, meff = 83m0 “heavy-fermion”

- (0) ~ 10 -2 emu/mol

- ( - 0) / T 2 ~ 0.1cm/K2 (under high pressure)

- Transition from Kondo impurity fluid to coherent heavy electron fluid at T *

TK ~ 1.7K (single ion Kondo temperature)

T * ~ 45K (intersite coupling energy of Kondo lattice) CEF splitting~120K (Nakatsuji, Pines, Fisk, PRL 92, 016401 (2004))

Anisotropic type-II superconductor d-wave pairing symmetry? (Spectroscopic evidence is still lacking) FFLO phase transition? - Power-law dependence: Cen / T ~ T, ~ T 3.37, 1/T1 ~ T 3+, ~ T 1.5

Layered-tetragonal Crystal Structure Quasi-2D Fermi Surfaces

a = 4.62Å, c = 7.55Å, c/a = 1.63

T = Co, Rh, Ir

H. Shishido et al., JPSJ. 71, 162 (2002)

Ce

e

N S

h+

N S

Pair Breaking

Probability of finding Cooper Pairs

ANDREEV REFLECTION (no insulator): Normal Metal/Superconductor (N/S)

In N: Electrons retro-reflected as holes

In S: Cooper

Pairs Broken

near interface

EF (few V)

E

k

Energy Scales for Andreev Reflection

SN

Particle conversion process that conserves charge, energy and

momentum!

Δ (few mV)

≈≈

A : Andreev reflectionB : Normal reflectionC : Transmission without branch- crossing (electron-like)D : Transmission with branch- crossing (hole-like)A(E)+B(E)+C(E)+D(E)=1

Probabilities

Blonder-Tinkham-Klapwijk (BTK) Model for charge transport across the N/S interface PRB 25, 4515 (1982)

Assumes (among other things) Ballistic transport

s-wave BTK Conductance

• Describes transitional behavior from AR to tunneling• Effective barrier strength

22 (1 )

, 4

FNeff

FS

r vZ Z r vr

-4 -2 0 2 40

1

2

E/DE/D

E/D

RNd

I/d

V

Z=0.0

RNd

I/d

V

E/D-4 -2 0 2 4

0

1

2

Z=0.5

-4 -2 0 2 40

2

4

Z=1.5

RNd

I/d

V

RNd

I/d

V

-4 -2 0 2 40

2

4

6

8

Z=5

S. Kashiwaya et al., PRB 53, 2667 (1996) Extended BTK theory

22

+

, cos 2

, ,

The con

c-axis junction of d-wave superco

ductance is given

the integration over the half space of momentu

ndu

y

m

c

b

tor

T T

E E

2 2

2 2

22

0 0

0

2

1

1

, , k exp

cos = , , sin sin

cos

, c

1

1 1 e

os

xp

S

FS FS

S FSFS S FN N

N FN

N

N NN

N

E a E b E

EE k i

kk k

k

ZZ

i i

Z

0 2

2 2

4

1 4

FN

N

mH

k

Z

' , =E E i

d-wave BTK Conductance

along c-axis

-4 -2 0 2 40

1

2

E/DE/D

E/D

RNd

I/d

VZ=0.0

RNd

I/d

V

E/D-4 -2 0 2 4

0

1

2

Z=0.5

-4 -2 0 2 40

1

2

Z=1.5R

Nd

I/d

V

RNd

I/d

V

-4 -2 0 2 40

2

Z=5

BTK model has worked well for a wide range of materials, but NOT for HFS/N interfaces:

22 (1 )

, 4

FNeff

FS

r vZ Z r vr

Recall the effective barrier

strength:

The Fermi velocity mismatch is so great at the HFS/N interface that

Andreev reflection (AR) should never occur

(Z>5, extreme tunneling limit).

However, AR is routinely measured at the N/HFS interface (many reports), albeit

suppressed.

Gold tip - sharpened by electrochemical etchingCeCoIn5 single crystal - c-axis oriented - etch-cleaned using H3PO4

Coarse approach - done before inserting probeFine approach - done during cool down - piezo driven by computer control Operation range - Temperature : down to 300mK - Magnetic Field : up to 12T

B e-C u

S c re w(C o a rse a p p ro a c h )

P ie zo e le c tricB im o rp h s(F in e a p p ro a c h )

T ip h o ld e r

G o ld tip

S am p le h o ld e r

S am p le

3 H e pot

Our Experiment: Cantilever-Andreev-Tunneling (CAT) rig

0

0 2

0 2

Wexler's Formula ( )

, , Knudsen ratio

) 1, ( ) 0.694

4 , Sharvin (Ballistic) limit

3) 0

Proc. Phys. Soc. 89, 927

, 1

,

(196

4 31

3 8

)

2

6

M

e

eSharvin

Maxwell

e K l a

i K K

lR R

aii

lR K

a

K K

Ra

K

R

axwell (Diffusive) limit

2aI I

Basics of PCS: Contact Regimes

Length scales2a: contact sizelel: elastic mean free pathlin: inelastic mean free pathx: coherence length

Therefore, our experiments are in the ballistic, Sharvin Limit, required for good spectroscopy

For our experiment:

* Upper limit of 2a = 46 nm

* lel at Tc= is 81 nm (from thermal conductivity), and

increases with decreasing T, to 4-5 µm at 400mK.

-2 -1 0 1 2

1.0

1.5

2.0

0.400.600.80

0.981.12

1.311.521.631.751.861.972.07

T(K)

60.050.0

40.0

30.0

20.0

10.0

5.0

2.602.242.15

Nor

mal

ized

Con

duct

ance

Voltage (mV)

DATA: Dynamic Conductance of Au/CeCoIn5

T*

Tc

Background develops an asymmetry at the heavy-fermion liquid coherence temperature, T* ~ 45 K, gradually increasing with decreasing temperature to the onset of superconducting coherence, Tc =2.3 K.

Normalization by dividing each G-V data by normal state (2.6K) G-V data

-2 -1 0 1 2

0.9

1.0

1.1

2.60

0.40

N

orm

aliz

ed C

ondu

ctan

ce

Voltage (mV)

T (K)

0.60 0.80 0.98 1.12 1.31 1.52 1.63 1.75 1.86 1.97 2.07 2.15 2.24

Background Normalization

-2 -1 0 1 2

1.00

1.05

1.10

1.15

Nor

mal

ized

Con

duct

ance

Voltage (mV)

T(K) 0.40 0.60 0.80 0.98 1.12 1.31 1.52 1.63 1.75 1.86 1.97 2.07 2.15 2.24 2.60

B

(0) 404μeV

2 (0)4.08

k cT

Strong Coupling

BUT: Decreasing with decreasing T: Not physically meaningful

-2 -1 0 1 2

2.60K

13

.3%

2.24K

2.15K

2.07K

1.97K

1.86K

1.75K

1.63K

1.52K

1.31K

1.12K

0.98K

0.80K

0.60K

0.40K

No

rma

lize

d C

on

du

cta

nce

(a

rb. u

nit)

Voltage (mV)

s-wave fit

0.0 0.5 1.0 1.5 2.0 2.50

100

200

300

400

D (

T),

G (

T)

(m

eV

)

Temperature (K)

D(T)

G(T)

BCS energy gap

G=349(1-t3) meV

Z=0.346

Γ(T)Δ(T)

s-wave d-wave

Z 0.346 0.215

(eV) 384 460

(eV) 305 220

Fitting Parameters

24.64

B ck T

strong coupling

d-wave fit

-2 -1 0 1 2

1.00

1.04

1.08

1.12 Exp. s-wave d

x2-y2-wave

d-wave vs. s-wave fitting

T=400mKH=0G

G(V

) / G

(-2m

V)

Voltage (mV)

BUT AGAIN, decreasing with decreasing T (like s-wave case): So again, Not physically meaningful

Zero-bias Conductance Fit (one point)

Constant Γ : Supportive of d-wave pairing symmetry, consistent with literature

218 eV(t) = 0.86(0) x (1-t3/3)

(T, ) =(T)cos(2), (T) = 2.35kBTc x tanh(2.06(Tc/T-1)1/2)

(0) = 349 eV, (T): BCS energy gap

0.3650.346Z

d-waves-wave

Fitting Parameters

0.0 0.2 0.4 0.6 0.8 1.01.00

1.05

1.10

1.15

Nor

mal

ized

ZB

C

T / Tc

exp. data s-wave fit d-wave fit

Similar AR magnitudes: Common in N/HFS

G. Goll et al., PRL 70, 2008 (1993)

Yu. G. Naidyukv et al., Europhys Lett. 33, 557 (95).

URu2Si2-Pt

-4 -2 0 2 40.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

T = 0.41 KH = 0 G

Conductance of [110]CeCoIn5-Au point contact

d

I/dV

(-1

)

Voltage (mV)

VERY NEW DATA: PCS on 110-orientation: Spectroscopic proof of d-wave ??? (work in progress):

-4 -2 0 2 4

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

2.58 K

2.16 K

2.03 K

1.93 K

1.76 K

1.57 K

1.38 K

1.17 K

1.02 K

0.88 K

0.65 K

0.41 K

Normalized conductance of [110]CeCoIn5-Au point contact

G(V

) / G

(-5

mV

)

Voltage (mV)

-4 -2 0 2 4

1.0

1.1

1.2

1.3

1.4

1.5

1.6

2.58 K

2.16 K

2.03 K

1.93 K

1.76 K

1.57 K

1.38 K

1.17 K

1.02 K

0.88 K

0.65 K

0.41 K


G(V

) / G

(-5

mV

)

Voltage (mV)

Temperature Dependence: Can normalize as the c-axis data

-4 -2 0 2 40.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

T = 0.41 KH = 0 G


N

orm

aliz

ed

Co

nd

uct

an

ce

Voltage (mV)

Note magnitude of Andreev signal is the SAME as for the (001) PCS!

This supports:A) Intrinsic property (reproducibility indicates not a “barrier” effect)

B) Sharvin limit

Shape supports d-wave: May be 1st spectroscopic evidence.

BTK Conductance: s-wave vs. d-wave

work in progress…

-4.0 -2.0 0.0 2.0 4.00

1

2

3

4

5

RNd

I/dV

E /

Z=0 Z=0.5 Z=1 Z=5

d-wave: ab-plane

-4 -2 0 2 4

0

1

2

E/E/

E/

RNdI

/dVZ=0.0

RNdI

/dV

E/-4 -2 0 2 4

0

1

2

Z=0.5

-4 -2 0 2 40

1

2

Z=1.5

RNdI

/dV

RNdI

/dV

-4 -2 0 2 40

2

Z=5

d-wave: c-axis

-4 -2 0 2 40

1

2

E/E/

E/

RNdI

/dVZ=0.0

RNdI

/dV

E/-4 -2 0 2 4

0

1

2

Z=0.5

-4 -2 0 2 40

2

4

Z=1.5

RNdI

/dV

RNdI

/dV

-4 -2 0 2 40

2

4

6

8

Z=5

s-wave

Models which address the observation of AR at HFS/N Interface

1. Deutscher and Nozières, PRB 50, 13577 (1994)

From PCS of N/HFS, it has been common to obtain conductance curves corresponding to low Zeff value.

Deutscher and Nozières’ argument: “The boundary condition at the interface involves Fermi velocities without mass-enhancement factors.”

2. N. A. Mortensen et al., PRB 59, 10176 (2000)

Mismatch of Fermi Momenta combined with the two-fluid model of Nakatsuji, Pines & Fisk causes strong effect on tunneling cone. Zeff must be calculated for each component.

This effect can explain ZBC normalized to normal state conductance, but not to high-bias conductance.

3-Dimensional System

Breakdown of the Andreev Approximation

Retro-reflection whenever D << EF (Andreev approximation).

If D/EF is non-negligible, the hole does not trace back the electron trajectory exactly (breakdown of Andreev approx.).

3. A. Golubov and F. Tafuri, PRB 62, 15200 (2000)

2 2, , 1 in N 1 in S e h FN F FS Fk k k Ek E EE

0 1 2 3 45

6 A

B CD

N S

-q - q -

Dq +-q + k +k --k --k +

Energy-Dependent QP Lifetime

4. F. B. Anders and K. Gloos, Physica B 230-232 437 (1997)

Causes a reduction in gap energy (renormalization due to the strongly reduced QP spectral weight) Causes asymmetry: with the emergence of coherent heavy quasi-particles

2eV

N S

HL HR

HT

1. Clean dynamic conductance data are measured between 60 K and 400 mK across HFS/N (CeCoIn5/Au) nano-scale junctions

2. Careful investigations show the contact is in the Sharvin limit.

3. Existing models cannot adequately describe the particle-hole Andreev conversion process at the HFS/N interface.

4. The low-temperature (400mK) conductance curve is consistent with strong coupling and the temperature-dependence of a single point, the zero-bias conductance, is consistent with a d-wave order parameter symmetry, both conclusions consistent with the literature for CeCoIn5.

5. We propose that systematic corrections to the BTK model that go beyond the breakdown of the Andreev approximation and re-normalized Fermi momenta may provide a framework for our future understanding of Andreev reflection at the N/HFS interface.

6. Recent (110) data may be spectroscopic evidence for d-wave

Conclusions

Biscuits

2

2

/

n

F

TT

Tl v

l T

Is the Contact in Sharvin Limit?

Thermal Conductivity

R. Movshovich et al., PRL 86, 5152 (2001)

• Contact Size, d O ~ 500 Å using Wexler’s formula with RN=R0(1+Z2), RN ~ 1 , Z ~ 0.35, Tc ~ 3.1 cm• 0 ~ 82Å• lel ~ 4-5 mm, lin ~0.65 mm @400mK• 0 < d << lel, lin Contact is ballistic, even if considering reduced l in point contact

Scattering Rate from Microwave Conductivity

R. Ormeno et al., PRL 88, 047005 (2002)

/ ~ 0.6 @45 μ 00 mKm inelasticl

0 1 2

0.1

1

10

Mea

n F

ree

Pat

h (m

m)

Temperature (K)

How can we explain the background conductance?

Nakatsuji, Pines, Fisk, PRL 92, 016401 (2004)

Relative weight of HF fluid f(T) = f(0)(1-T/T*), T* ~ 45 K Kondo impurity fluid Coherent heavy-fermion fluid Saturating to 0.9 below ~ 2K

Enhanced asymmetry due to DOS change (shift of spectral weight toward Fermi energy) with increasing HF fluid?

Particle-hole asymmetry due to different kinetic energies in HFL?

“The pseudo-gap at T*, arising from the formation of the heavy quasi-particles in the coherent state, asymmetrically increases the resistance of the contact.” (K. Gloos et al., JLTP 105,37 (1996))

2q m E

-4 -2 0 2 4

0.85

0.90

0.95

1.00

1.05

1.10

1.15 0.41 K0.65 K0.88 K1.02 K1.17 K1.38 K1.57 K1.76 K1.93 K2.03 K2.16 K2.58 K


G(V

) / G

(-5

mV

)

Voltage (mV)

-4 -2 0 2 4

0.9

1.0

1.1

1.2

1.3

1.4

1.5

T = 0.42 K

9 T

8 T

7 T

6 T

5 T

4 T

3 T

2 T

1 T

0 T

Field dependence of normalized conductance in [110] CeCoIn

5-Au point contact

G(V

) / G

(-m

V)

Voltage (mV)

0 1 2 3 4

0.160

0.165

0.170

0.175

0.180

Zero-bias conductance of [110]CeCoIn5-Au point contact

Ze

ro-b

ias

Co

nd

uct

an

ce

Temperature (K)

0.0 0.2 0.4 0.6 0.8 1.01.00

1.02

1.04

1.06

1.08

1.10

1.12

Normalized zero-bias conductance of [110]CeCoIn5-Au point contact

No

rma

lize

d Z

BC

T / Tc

Heating Effect?

-2 -1 0 1 2

0.9

1.0

1.1

-1 0 1 2

after normalizationbefore normalization

400 mK 2.6K

Nor

ma

lized

Co

ndu

cta

nce

Voltage (mV)

400 mK 2.6K

• Local minima not intrinsic but caused due to incomplete match of BC

• No minima in un-normalized data

• No heating effect due to non-ballistic contact Sharvin contact!

Non-Ballistic Point Contact

K. Gloos et al., JLTP 105, 37 (1996)

R = RA + RMAX

In N/HFS point contact, Maxwell resistance dominates since the resistivity of HFS is large.

CeCoIn5 has relatively small resistivity ( ~ 3.1 cm) and extremely long electron mean free path at low temperatures. Sharvin(ballistic) point contact could be formed

82//a,b 53//c

90

77

190

120//a,b 140//c

95

75//a, 130//c

(Å)

~ 10

3

~ 10

~ 2

~ 13

~ 2

~ 6

l/

810

270

720

470

1600

165

440

l (Å)

2.3

0.5

2

1

0.48

0.87

1.20

Tc(K)

3.5, 36.366UPd2Al3

1.5-65380CeCu2Si2

3.183CeCoIn5

3048UNi2Al3

0.27//c 0.45//b

180UPt3

43260UBe13

11140URu2Si2

0 (cm)m*/m0HFS

Properties of Heavy-Fermion Superconductors

The Four Questions

1. Is the contact ballistic, diffusive, or thermal? (A: Ballistic: we have shown the Sharvin Limit)

2. How can we explain the background conductance shape? We observe a change in asymmetry at T*

3. What is the Pairing symmetry? (s-wave or d-wave) fit the data using extended BTK models

4. Why is the enhancement of sub-gap conductance so small? (~13.3% @ 400mK, NOT 100% as in conventional SCs) explore various possibilities…

Models to account for observaion of AR at HFS/’N Interface

50

7

0

9.74 10 , 83

1 8.08 1083,

1.

1 1, , (1 )

73

1

0.28

F F ef

F eff

F

F

FS

f

N

f

ef

v cm s m m

z v cm s

vr

v v zz

v

m m

Z

: effective

:

qu

ve

asip

loci

article velocity

: renormalization fact

t

or

y

F F

F

F

v v z

v

z

v

Deutscher and Nozières, PRB 50, 13577 (1994)

2 2 1/ 2

8

55

,

[ (1 ) / 4 ] , /

1.40 10 / , for Au

9.7

Ac

4 10 / , for CeCoIn

.

cording to BTK model

6, tunneling regi

No AR expected to be observed in N/HFS contacts

meeff

eff FN FS

FN

FS

Z

Z Z r r r v v

v cm s

v cm s

From PCS of N/HFS, it has been common to obtain conductance curves corresponding to low Zeff value.

Deutscher and Nozières’ argument: “The boundary condition at the interface involves Fermi velocities without mass-enhancement factors.”

Quantum Critical Point & Phase Diagram

V. A. Sidorov et al., PRL 89, 157004 (2002)

P. G. Pagliuso et al., Physica B 312-313, 129 (2002)

• Coexistence of AFM & SC

• Similar to cuprates

Ce(Co,Rh,Ir)In5

PCS in Sharvin limit

- contact resistance independent of materials’ resistivities

- in practical situation, heterogeneous contact

d l1, l2

2

2

16 31

16

3

3

8e

e

PC

lR K

d K

l

d d

Yu. G. Naidyuk and I. K. Yanson, J. Phys.: Condens. Matter 10, 8905 (1998)

Calculated Resistance of Point-Contact

2

2

/

n

F

TT

Tl v

l T

Is the Contact in Sharvin Limit?

Thermal Conductivity

R. Movshovich et al., PRL 86, 5152 (2001)

• Contact Size, d O ~ 500 Å using Wexler’s formula with RN=R0(1+Z2), RN ~ 1 , Z ~ 0.35, Tc ~ 3.1 cm• 0 ~ 82Å• lel ~ 4-5 mm, lin ~0.65 mm @400mK• 0 < d << lel, lin Contact is ballistic, even if considering reduced l in point contact

Scattering Rate from Microwave Conductivity

R. Ormeno et al., PRL 88, 047005 (2002)

/ ~ 0.6 @45 μ 00 mKm inelasticl

0 1 2

0.1

1

10

Mea

n F

ree

Pat

h (m

m)

Temperature (K)

Andreev Reflection

A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964)

0 0

2

2

ˆ ˆ

For energies of the order of , the medium is

compl with an accuracyetely homogeneous ( )

Then, set

,

w

( / 2 ) ( ) ,

( / 2 ) ( )

( ), (

e

h re

)

F

ip n r i t ip r

F

n i t

i f t m f i r

i t m i r f

f e

E

E

r e r

0

1 2

1 2 30 0

1

0

ˆ

2

is the Fermi momentum and and are slowly

varing functions compared with .

, ( ) 0

,

where

(2 )

1 0

0 1

ˆ ˆ,

(

)

ik r ik r

ip n r

p

e

z r

R

A e B e

k n v k n v

f p T d e

,

where 2 1.

T

cH H

Thermal resistance of Sn in intermediate state

/

/

ikx iEt

ikx iEt

f ue

g ve

Assume x)=V(x)=0, D(x)=D

Plane wave solutions

2 2

2 2

2

2

k

m u uE

v vk

m

Bogoliubov-de Gennes Equations

2 for N ( =0)q m E

22 22 2

2

kE

m

2 2

2 1E

k m

Solving for E, u, v

2 22 21

1 12

Eu v

E

2 22 20 0

11 1

2

Eu v

E

(u0 > v0)

22

22

( ) ( ) ( , ) ( ) ( , )2

( ) ( ) ( , ) ( ) ( , )2

fi x V x f x t x g x t

t m

gi x V x g x t x f x t

t m

Excitations in a superconductor

Four types of QP waves for given E

0 0

0 0

( )Defining ,

( )

, ik x ik x

k k

f x

g x

u ve e

v u

Suggestions For Theoretical Study

The following issues need to be investigated carefully.

Mismatch in Fermi parameters: effective mass, momentum, velocity

Anisotropy: order parameter, layered structure, Fermi surface

Emergent heavy quasiparticles, two fluid model

Quasiparticle scattering rate in AR process across N/HFS interface

Length scales for electrostatic potential, order parameter, effective mass, etc., in terms of coherence lengths both in a normal metal and in a superconductor

Successful model should explain the following experimental features.

Concomitance of asymmetry in background conductance with emergent heavy-fermion liquid

Suppressed Andreev reflection to quantify the full conductance curve

Possible shrinking(?) of the conductance curve

2

2 22

2 2

2

2 2

2

cos1

1 sincos4coscos1

( 1), original BTK thoery

4

sin1 sin

v

keff

k v

k

veff

v

rZ Z

r

rrZ

Zr r

r

S1

conserv. of parallel momenta

,

sin sin ,

, 2

1sin , critical angle

FN FNk v

FS FS

FN N FS S

N ck

k vr r

k v

k k

ifr

Mismatch of Fermi Momenta

N. A. Mortensen et al., PRB 59, 10176 (2000)

3-Dimensional System

This effect can explain the suppression of ZBC normalized to normal state conductance, but not to high-bias conductance.

If the superconductor is inhomogeneous as in the two-fluid model (Nakatsuji, Pines & Fisk), we can define different Zeff for each component. We’re exploring this possibility.

Breakdown of Andreev Approximation

Retroreflection whenever << EF (Andreev approximation).

If /EF is non-negligible, the hole does not trace back the electron trajectory exactly (breakdown of Andreev approx.).

This happens in layered structures, too.

A. Golubov and F. Tafuri, PRB 62, 15200 (2000)

2 2, , 1 in N 1 in S e h FN F FS Fk k k Ek E EE

0 1 2 3 45

6 A

B CD

N S

-q - q -

Dq +-q + k +k --k --k +

0.285.321.59.25Nb

~ 2.0~ 12090YBCOCuprate

2.3

39

7.20

1.18

Tc(K)

0.5

1.2 – 1.8

5

0.4-0.62.4

7.0

MgB2

Two-band

0.149.471.35Pb

~ 2.1~ 0.0220.46CeCoIn5HFS

0.01511.70.175AlElemental

/EF (%)EF(eV)(meV)ExampleSC type

Ratio of Gap Energy to Fermi Energy of Superconductors

Layered N / isotropic S

d-wave BTK Conductance

along c-axis

-4 -2 0 2 40

1

2

E/DE/D

E/D

RNdI

/dVZ=0.0

RNdI

/dV

E/D-4 -2 0 2 4

0

1

2

Z=0.5

-4 -2 0 2 40

1

2

Z=1.5

RNdI

/dV

RNdI

/dV

-4 -2 0 2 40

2

Z=5

-4.0 -2.0 0.0 2.0 4.00

1

2

3

4

5

RNdI

/dV

E / D

Z=0 Z=0.5 Z=1 Z=5

along ab-plane

MgB2 PCS

-25 -20 -15 -10 -5 0 5 10 15 20 250.25

0.30

0.35

0.40

0.45

0.50

0.55

T = 1.52 K

MgB2- #9 (ASU)-3rd contact

M04020 (STI)

Conductance of ion-irradiated MgB2-Au point contact

May 25, 2005

dI/d

V (-1

)

Voltage (mV)

-25 -20 -15 -10 -5 0 5 10 15 20 250.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

T = 1.52 K

MgB2- #9 (ASU)-3rd contact

M04020 (STI)

Normalized conductance of ion-irradiated MgB2-Au point contact

May 25, 2005

G(V

) / G

(-2

5m

V)

Voltage (mV)

-10 -5 0 5 10 150.00

0.05

0.10

0.15

0.20

0.25

T = 1.50 K

MgB2-9 (ASU)-5th contact (initial)

M04020 (STI)


May 25, 2005

dI /

dV

(-1

)

Voltage (mV)

-20 -15 -10 -5 0 5 10 15 200.09

0.10

0.11

0.12

0.13

T = 1.51 K

MgB2- #9 (ASU)-5th contact (final)

M04020 (STI)


May 25, 2005

G(V

) / G

(-2

0m

V)

Voltage (mV)

-20 -15 -10 -5 0 5 10 15 20

1.0

1.1

1.2

1.3

1.4

T = 1.51 K


M04020 (STI)


May 25, 2005

G(V

) /

G(-

20

mV

)

Voltage (mV)

-20 -15 -10 -5 0 5 10 15 20

1.0

1.1

1.2

1.3

1.4 MgB2- #9 (ASU)-5th contact (final)

M04020 (STI)

1.51 K 6.41 K 11.10 K 16.49 K 21.67 K 26.69 K 31.72 K 36.70 K 39.30 K


May 25, 2005

G(V

) / G

(-2

0m

V)

Voltage (mV)

0 5 10 15 20 25 30 35 400.085

0.090

0.095

0.100

0.105

0.110

0.115

Zero-bias conductance of MgB2-Au point contact


M04020 (STI)May 25, 2005

Ze

ro-b

ias

con

du

cta

nce

(

)

Temperature (K)

Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface Wan Kyu Park and Laura H....

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Transcript of Andreev reflection at the CeCoIn 5 Heavy Fermion Superconductor Interface Wan Kyu Park and Laura H....