Point contact spectroscopy Point contact spectroscopy Point contact spectroscopy Point contact spectroscopy

�Ballistic point contact Ballistic point contact Ballistic point contact Ballistic point contact �PointPointPointPoint----contact spectroscopy of electroncontact spectroscopy of electroncontact spectroscopy of electroncontact spectroscopy of electron----phonon interaction phonon interaction phonon interaction phonon interaction �PointPointPointPoint----contact spectroscopy of electroncontact spectroscopy of electroncontact spectroscopy of electroncontact spectroscopy of electron----boson interaction boson interaction boson interaction boson interaction �Point Point Point Point ––––contact Andreev reflection spectroscopy of superconducting contact Andreev reflection spectroscopy of superconducting contact Andreev reflection spectroscopy of superconducting contact Andreev reflection spectroscopy of superconducting energy gap energy gap energy gap energy gap

----BTK model for arbitrary barrier and sBTK model for arbitrary barrier and sBTK model for arbitrary barrier and sBTK model for arbitrary barrier and s----wave superconductivitywave superconductivitywave superconductivitywave superconductivity----Tanaka extension of BTK to anisotropic order parametersTanaka extension of BTK to anisotropic order parametersTanaka extension of BTK to anisotropic order parametersTanaka extension of BTK to anisotropic order parameters----MultigapMultigapMultigapMultigap superconductivity, MgBsuperconductivity, MgBsuperconductivity, MgBsuperconductivity, MgB2222 & & & & pnictidespnictidespnictidespnictides----Spin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopy

�Andreev reflection versus tunnelingAndreev reflection versus tunnelingAndreev reflection versus tunnelingAndreev reflection versus tunneling

Peter SamuelyPeter SamuelyPeter SamuelyPeter Samuely****

* In * In * In * In collaborationcollaborationcollaborationcollaboration withwithwithwith P. P. P. P. SzabóSzabóSzabóSzabó, J. , J. , J. , J. KaKaKaKačmarmarmarmarčíkíkíkík, Z. , Z. , Z. , Z. PribulováPribulováPribulováPribulová

V

kF,, EF

+V/2

-V/2

• bulk sample, characteristic size >> electron mean free path llll

• applied voltage => gradient of VVVV across whole sample

• electrons accelerated by fraction of eVeVeVeV• increasing VVVV => Joule heating of the sample over the ‘bath’ temperature

-V/2 +V/2

Bulk conductor in electric field

eV

V

EF

+V/2

-V/2

eV

• standard electrical contact between two wires with contact diameter d d d d >> l l l l , electron mean free path =>> RM = ρρρρ/d (Maxwell)

• let the orifice diameter dddd << llll => point contact (~ 10-100 nm) made e.g. by tip pressed on a bulk sample (Sharvin, Sov.Phys. JETP, 1965)

• applied voltage =>gradient of el. field only in area close to PC

• Fermi surface splits into two parts – energy separation between any two states of electrons at Fermi surface is equal to eVeVeVeV or zero

-V/2 +V/2

Ballistic point contactBallistic point contactBallistic point contactBallistic point contact

Electron accelerated by applied voltage V to drift velocity ∆v = eV/pF , pF – Fermi momentum

Current I=π(d/2)2ne∆v & from Drude model ρle = pF / ne2

=> Sharvin resistance

20

210

2222

)(

2/

)()(

2.

3

16

dkGG

heGR

dk

R

dke

h

d

lR

FS

Q

F

Q

Fs

=

==

=≈=

−

ρπ

Q. conductance x No. of q. channelsNo = (kF ~ π/a)2d 2

Different regimes of electron motion through point contact

Ratio between point contact radius a and electron mean free path lwhere le – elastic mean free pathdue to changing momentum but unchanged energy

l i – inelastic mean free path where electron can change both energy and momentum

If point contact diameter d ~ de Broglie wave length of electron λ λ λ λ (0.1 – 0.2 nm)⇒1. quantum regime

with point-contact conductance dI/dV being a sum of several conducting channels each with quantum conductance G0 = 2e2/h

l i, le>> a >> a>>le l i, le << a eill

2. ballistic regime 3. diffusive regime 4. thermal regime

STM experiment

Excess energy of electrons controlled by applied voltage like in tunnel junctions

with the voltage drop on insulating barrier

Excess energy lost by generating phonons=>

backscatterring of electrons at orifice (Umklapp processes)via generating of phonons

=> enhance slightly PC resistance at the characteristic phonon energy E=eV

Born by I.K. Yanson, ZhETP 1974

PPPPoint contactoint contactoint contactoint contact spectroscopy spectroscopy spectroscopy spectroscopy of electronof electronof electronof electron----phonon interactionphonon interactionphonon interactionphonon interaction

Point contact spectroscopy of electron-phonon interaction

Strictly, Sharvin resistance is independent on resistivity and on energy since: ρρρρl = const.But for the contacts with finite ratio l/a point-contact resistance RPC have a little correction Γ <1 coming from Maxwell resistance RM:

)16

31()

16

31(

.

3

162 τ

ππρρπ F

SSe

PC v

dR

l

dR

dd

lR Γ+=Γ+=Γ+=

)/1exp( λω −∝cTP. Samuely, 1986

)()(2

)(0

21 εεαπτ Fh

eVeV

phel ∫=−−

αααα2F(ε) (ε) (ε) (ε) is important characteristics:

)()()(/)( 222 εεα FgVdIVdVdVdR

PCPCPC =≈≈

∫= εε

εεαλ dF )()(2

Point-contact spectra of LaB6

Theory by Kulik, Omelyanchuk, Shekhter, 1977:Iterative solution of Boltzmann eq., gPC differs from EliashbergEPI function by special form factor which prefers backscattering

Different experimental realisations of point contacts

– Mechanically ControlableBreak junctions

Measurement• dV/dI(V), d2V/dI2(V)• modulation technique• dc current I and small ac current i

...))2cos(1(4

1)cos()(...)(cos

2

1)cos()())cos(( 2

2

222

2

2

++++=+++=+ tidI

Vdti

dI

dVIVti

dI

Vdti

dI

dVIVtiIV ωωωωω

Point contact spectroscopyEffect of temperature & modulation

[ ] 2/12211 )44.5())0(22.1(),( TkeVTkeV BB +=δ

A.G.M. Jansen, GrenobleI.K. Yanson, Charkiv

Point contact spectroscopy .Point contact spectroscopy .Point contact spectroscopy .Point contact spectroscopy .Electron interaction with other scatterersElectron interaction with other scatterersElectron interaction with other scatterersElectron interaction with other scatterers

Conduction electrons scattered on crystal electric field levels splitted in magnetic field

In superconducting state: Electrons (fermions) freeze out ⇒energy gap appears in electrons’ distribution

instead Cooper pairs (“bosons”) are createdenergy gap ~ binding energy of CP

Electrons are fermions satisfying Pauli exclusion principleMetal is a system with Fermi surface in momentum space

Superconductivity

is probability that CP state is occupied

is probability that CP state is empty

Point contact AndreevPoint contact AndreevPoint contact AndreevPoint contact Andreev----reflection spectroscopy reflection spectroscopy reflection spectroscopy reflection spectroscopy of superconducting energy gapof superconducting energy gapof superconducting energy gapof superconducting energy gap

Consider BALLISTIC point contact between normal N and superconducting S electrodesInside superconducting energy gap, i.e. for voltage /V/ < ∆ / e transfer of quasiparticles is forbidden

??? N/S junction has worse conductance than N/N ???NO! Because of Andreev reflection process => excess current inside gap

Normal

Superconducting

Electron-like qp

Hole-like qp

arbitrary strong

At T => 0 σσσσNS =dI/dV= C [1 + A(E) - B(E)]

Some improvements of BTK model

Plecenik, PRB 1994 , BdG equations with inelastic scattering:

Finite qp lifetime leads tobroadening of spectra Γ∼ Γ∼ Γ∼ Γ∼ h/τ τ τ τ

Γ/∆ Γ/∆ Γ/∆ Γ/∆ should be small

Then, coherence factors are:

Density of states is smeared:

Treating broadened spectra

2D/3D extension of BTK model

Electrons can approach PC at any angle θ θ θ θ Ν Ν Ν Ν with respect to the normal of PC interface

⇒ transparency or normal PC conductance is

⇒ directionality of PC depends on Z parameter

Tunnel junctions (Z >1)are more directional

In PC with Z = 0 all electrons within −−−−π/2 < π/2 < π/2 < π/2 < θ θ θ θ Ν Ν Ν Ν < π/2 < π/2 < π/2 < π/2 have unitary probability for transfer PC

22

2

+)cos(

)cos(K) (0

Zc

N

NNN θ

θσ =

∫

∫

−

−/2

/2

/2

/2

cos)(

cos),(=

)(:2D π

π

π

π

θθθσ

θθθσσ

σ

NNNNN

NNNNS

NN

NS

d

dEE

NS point-contact spectrum :

If gap is isotropic and Fermi surface spherical, 2 D=3D Daghero, Gonnelli, Arxive 2009

2D/3D affects only 2D/3D affects only 2D/3D affects only 2D/3D affects only Z Z Z Z parameterparameterparameterparameter

∆∆∆∆: : : : Energy gapΓΓΓΓ: : : : Quasiparticle smearingΖΖΖΖ: Τ: Τ: Τ: Τunnel barrier strength

∆∆∆∆====1.35 meVΓΓΓΓ==== 0.23 meVΖΖΖΖ= = = = 0.62

∆∆∆∆==== 6 meVΓΓΓΓ==== 0.12 meVΖΖΖΖ= = = = 2

Some examples

TanakaTanakaTanakaTanaka extensionextensionextensionextension ofofofof BTK to BTK to BTK to BTK to anisotropic energy gapanisotropic energy gapanisotropic energy gapanisotropic energy gapssss

E.g. in high-Tc cuprates order parameter has d-wave symmetry dx2-y2

Yukio Tanaka, PRL 1995, worked out BTK extension

* Size and sign of order parameterdepends on angle. of electron (θS) or hole (-θS) transmitted to superconductor* Cryst. a-axis is rotated at angleα with respect to PC X-axis* Electron and hole exeriences , resp.

NS point-contact spectrum for θ :where

Andreev refl. normal refl.

Total spectrum is

α is fixed

α α α α = π/4 = π/4 = π/4 = π/4 Point contact with normal parallel to a-axis

α α α α = 0 = 0 = 0 = 0

Order Parameter by Point-Contact Andreev Reflection Spectroscopy in HFS CeCoIn5 with Tc =2.6 K, W.K. Park, PRL 2008

In case of two band / two gap superconductor PC conductance is sum of two BTK conductances with weights α and (1-α)

dI/dV(V) = αααασσσσπ π π π ++++(1(1(1(1−−−−αααα))))ΣΣΣΣσσσσ = = = = f(∆∆∆∆π π π π , ∆, ∆, ∆, ∆σ σ σ σ , Γ, Γ, Γ, Γπ π π π , Γ, Γ, Γ, Γσ σ σ σ , Ζ, Ζ, Ζ, Ζπ π π π , Ζ, Ζ, Ζ, Ζσ σ σ σ , α, α, α, α)))) but ΓΓΓΓπ π π π , Γ, Γ, Γ, Γσ σ σ σ => => => => 0000=>> two energy gaps

@ Szabo et al, PRL 2001

MultigapMultigapMultigapMultigap superconductivitysuperconductivitysuperconductivitysuperconductivity , MgB, MgB, MgB, MgB2222 & & & & pnictidespnictidespnictidespnictides

-20 -10 0 10 20

1.0

1.5

2.0N

orm

aliz

ed c

ondu

ctan

ce Experiment σ

π

BTK

σσ

BTK

0.7 σπ

BTK + 0.3 σσ

BTK

Voltage (mV)

High Tc superconductivity in MgB2 @ 40 K

« Trick is two gaps », Mazinbased on H.Suhl, B.T. Matthias, and L.R. Walker, Phys. Rev. Lett. 3, 552 (1959)

cover Yildrim

� Akimitsu et al., Nature 410, 63 (2001)

� Significant isotop effect for boronphonon mediated interaction mechanism

kTc = ωD e−1/λ

1. High ωD due light element/boron

2. High λ: but this holds only for part of electrons

Anisotropic strong coupling of 2D σ electronsvia E2g phonons: λσσ is large

How can two gaps help ?

)/1exp( effDckT λω −≈

2/])(4[ 2ππσσπσσπππσσ λλλλλλλ −+++=eff

λeff ~ max λii

E.g. λσσ=1 & λππ =λσπ =λπσ=0.1 =>> λeff~1

Mazin, 2001

In system with 2 groups of Cooper pairs (σ−band & π−band)with different coupling=> λ is a matrix2x2

Point-contact spectra of MgB2, with two gaps

@ P. Szabo, P. Samuely, J. Kacmarcik et al., Phys. Rev. Lett. 87, 137005 (2001)

-20 -10 0 10 20

0,0

0,5

1,0

1,5

5

4

3

2

1

IPC

// c

IPC

// ab

T = 4.2 K

Nor

mal

ized

con

duct

ance

Voltage (mV)

I // c

I // ab

c T. Dahm

dI/dV(V) = αΣπ +(1−α)Σσ = f(∆π , ∆σ , Ζπ , Ζσ , α)=>> two energy gaps∆σ = 6.8 +/- 0.3 meV or 2∆σ /kTc ~ 4∆π = 2.7 +/- 0.1 meV or 2∆σ /kTc ~ 1.6α = 0.65 - 0.95 (Brinkmann, PRB 2002: α=0.65 for i||ab, α=0.99 for i||c)

Cu tip

Momentum space vs. real space .

Two gaps, effect of temperature

-20 -10 0 10 20

1.0

1.1

1.2

1.3

1.4

1.5 Experiment: T = 4.2 K T = 10 K T = 20 K T = 25 K T = 30 K T = 35 K T = 38 K T = 40 K

BTK fit

Voltage (mV)

Nor

mal

ized

con

duct

ance

0 10 20 30 400

2

4

6

8 ∆(T) BCS theory∆

L(T)

∆S(T)

Ene

rgy

gap

(meV

)

Temperature (K)

Both gaps close at the same critical temperature

...but∆π pretends to close at lowerTc

π

Point contact spectrum

Electronic specific heat, Bouquet, 2001

Tcπ ∼ 13 Κ Tcπ ∼ 13 Κ

Two gaps, effect of magnetic field

T13.0/;2 2

2

,220

,2 ≅∆∝=>∆∝Φ=F

cFc vBvB π

ππππ

π ξπξ

Small gap features gone at very low fields

But Bc2 determined by ∆2σ

-20 -10 0 10 20

1.0

1.1

1.2

1.3

1.4

Con

duct

ance

T = 4.2 K

Voltage (mV)

0 T 0.2 T 0.5 T 1T 3 T 9 T 12 T 20 T

Point contact spectrum Vortex imaging , Eskildsen, ‘01@ 50 mT & 2 K

ξ ab= 50 nm => Bc2 = 0.13 T

Βut real Bc2 ||c= 3T => ξab = 10 nm !!!ξ is extremely dependent on fieldAt low fields ξ = ξπ , at high fields ξ = ξσ

Undoped iron pnictides are non superconducting

Undergo structural & magnetic transition(tetragonal => orthorhombic & paramagnetic => antiferromagnetic)

Under doping (electron or hole) or pressure => appears superconductivity

Structural & magnetic transition are partly suppressed in doped region

coexistence of AFM & SC or phase separation ?

Iron pnictides, new high-Tc ‘s

Ni Ni et al., PRB 2009

-30 -20 -10 0 10 20 300.90

0.95

1.00

1.05

1.10

1.15

0 10 2002468

-50 -25 0 25 501.0

1.1

1.2

T = 4.4, 6, 8, 10, 12, 15, 17, 20, 22K

ab- plane

Nor

mal

ized

con

duct

ance

Voltage (mV)

∆ (

meV

)

27 K

T = 4.4 K

Two s-wave gaps2∆s /kTc ~ 2.72∆s /kTc ~ 9

@ P. Szabo, Z. Pribulová, G. Pristaš, P. Samuely, Phys. Rev. B. 79 (2009), 012503

PCAR on single xtals of (Ba 0.55K0.45)Fe2As2

ARPES mesurements on FS’s & s/c order parameters

H. Ding, Europhys. Lett (2008)Three FS sheetson (Ba,K)Fe2As2 with Tc = 37 K inner αand outer β hole FS pocket around Γ& small γ electron-like FS at M-point

laterK. Nakayama, Europhys. Lett (2009) found 4th δ electron pocket at M-point

Two nodeless gaps6 meV on outer hole FS pocket β& 12 meV on two small FS’s (hole α & electron γ)

& about the same on δ electron pocket

FS sheets with very strong coupling 2∆/kTc ~ 8connected by (π,0) SDW vector in parent comp.=>interband interaction between nested FS’s

Iron pnictides, 4 bands/2 gaps

superconductivity is inducedbythe nesting-related antiferromagnetic

spin fluctuationsnearthe wave vectors connecting the

electron and hole pockets

“… first example ofmultigap superconductivity with a discontinuous sign changein order parameter between the bands, which is principally

different from the multi-band s-wave superconductivitydiscovered in MgB2.”

Theoretical proposal of Mazin et al.

Iron pnictides

Spin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopySpin polarized Andreev reflection spectroscopy

Andreev reflection versus tunnelingAndreev reflection versus tunnelingAndreev reflection versus tunnelingAndreev reflection versus tunneling

IN IN IN IN HTHTHTHTcccc CUPRATES PSEUDOGAP EXISTS ABOVE CUPRATES PSEUDOGAP EXISTS ABOVE CUPRATES PSEUDOGAP EXISTS ABOVE CUPRATES PSEUDOGAP EXISTS ABOVE TTTTcccc

G. Deutscher, Nature 1999

G. Deutscher, Nature 1999: „Tunneling scans SC DOS gap as a single-particle excitation energy—the energy (per particle) required to split the paired charge-carriers that are required for superconductivity“

„Andreev reflection experiments reflect coherence energy range of the superconducting state—the macroscopic quantum condensate of the paired charges“.

PCAR spectra in contrast to tunneling do not show pseudogapbut only SC gap below Tc, smaller than pseudogap in underdoped regime

ConclusionsConclusionsConclusionsConclusions

Point contact spectroscopy has been effective tool to study

� various interactions of conduction electrons with otherquasiparticles as phonons, magnons, magnetic excitations ,CEF levels, etc.

� superconducting order parameter (size, symmetry, etc.)

� spin polarization in metals, semimetals

� quantum transport

� ....

1. Yu.G. Naidyuk, I.K. Yanson: Point contact spectroscopy, Springer, 2003.2. E.L. Wolf: Principles of electron tunneling spectroscopy, Exford

university press, 1989.3. G.E. Blonder, M. Tinkham, T.M. Klapwijk: Transition from metallicto

tunneling regimes in superconducting microconstrictions, Physical Review B 25, 4515 (1982).

4. Y. Tanaka and Satoshi Kishiwaya: Theory of tunnelling spectroscopy in d-wave superconductors, Physical Review Letters 74, 3451 (1995).

5. D. Daghero and R.S. Gonnelli, Probing multiband superconductivity by point-contact spectroscopy, Arxive 0912.4858.

Recommended references

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