high tc superconductors mark s. golden van der waals...

HighHigh--Temperature Superconductors: A View from KTemperature Superconductors: A View from K--SpaceSpace

Dr. Mark Golden, Amsterdam (KITP Correlated Electrons 10/09/02)Dr. Mark Golden, Amsterdam (KITP Correlated Electrons 10/09/02) 11

Mark S. GoldenMark S. Golden

LeibnitzLeibnitz Institute for Solid StateInstitute for Solid State andandMaterials Materials ResearchResearch DresdenDresden

VanVan der Waalsder Waals--ZeemanZeeman InstituteInstituteUniversity of AmsterdamUniversity of Amsterdam

© Mark S. Golden

HighHigh TTcc superconductorssuperconductors--

--

Condensed Matter Physics Group, University of AmsterdamCondensed Matter Physics Group, University of AmsterdamYingtaiYingtai HuangHuang

Spectroscopy Group, IFW DresdenSpectroscopy Group, IFW DresdenSergeySergey BorisenkoBorisenko AlexanderAlexander KordyukKordyukAndreasAndreas KoitzschKoitzsch Sibylle Legner Christian DürrMartin Knupfer Thomas Pichler Timur KimRoland Hübel Dieter Müller

Jörg Fink, Claus Schneider, Frank Matthes, Robert Frömter IFF, IFW Dresden

CrystalsCrystalsHelmuthHelmuth BergerBerger EPFL LausanneB. Liang, A. Maliouk, C. T. Lin, Bernhard Keimer MPI StuttgartGuang Yang Stuart Abell U. of Birmingham, UK

Experimental collaborationExperimental collaborationFred Schiller, Serguei Molodtsov, Clemens Laubschat TU Dresden IOMPRolf Follath BESSY Michael Sing, Ralph Claessen U AugsburgStefano Turchini, Stefano Zennaro ELETTRACesare Grazioli CNR Rome + ELETTRA

Crystal characterisationCrystal characterisationK. Nenkov, D. Eckert IMW, IFW Dresden

MoneyMoneyFOM, EU, BMBF, DFG, SMWK



OutlineOutline

ARPES as kARPES as k--space microscopyspace microscopy

results from the Biresults from the Bi22SrSr22CaCuCaCu22OO88 familyfamily

thethe FermiFermi surfacesurface-- topology, or: topology, or: "to"to PbPb or not toor not to PbPb""-- doping dependencedoping dependence

superconductingsuperconducting energy gapenergy gap

peaks, dips and humpspeaks, dips and humps

-- in thein the overdopedoverdoped regimeregime

-- in thein the underdopedunderdoped regimeregime

© Mark S. Golden

HTSC: a job for . . . . . . . spectroscopyHTSC: a job for . . . . . . . spectroscopy

the HTSC and parents are:the HTSC and parents are:-- not ordinary metalsnot ordinary metals-- not ordinary superconductorsnot ordinary superconductors

we need to understand the fundamentals of theirwe need to understand the fundamentals of theirelectron systemselectron systems

© Mark S. Golden

experimentexperimenttheorytheory

s p e c t r o s c o p ys p e c t r o s c o p yoffers a direct probe of the electronic states

is now a 'standard' test of any aspiring theories



SpectroscopiesSpectroscopies with electronswith electrons

PES XPS IPES XAS AES EEPES XPS IPES XAS AES EELSLS

NN--11 N, N, can becan be≈≈ N+1N+1

N N NN--11 N+1N+1 NN--22

© Mark S. Golden

Angle resolved photoemission Angle resolved photoemission spectroscopyspectroscopy

A R P E SA R P E S

© Mark S. Golden



ARPES and the HTSC: a love affair with a sticky start......ARPES and the HTSC: a love affair with a sticky start......

Na: 1 electron per atomCu: 1 electron per atomkF

The Fermi surface:is a constant energy surfacewith E = EFis the surface in k-sp ace enclosingall occupied statesis formed of points in k-space forwhich gap-less excitations between

at the outset:at the outset:

ARPES is somehow crankymeasures some kind of surface stuff.....high energy scale

now:now:

powerful, k-resolved tool to provide:- normal state e-structure, Fermi surface- gaps - normal state and superconducting state- interactions / lifetimes- low energy scale- one of the acid tests for theories

© Mark S. Golden

An ARPES experimentAn ARPES experiment

Θmonochromaticlight

photoelectrons

Sample

electron energyanalyser

Binding energy (eV)

Pho

toel

ectr

on c

urr

ent

En

erg

ie (

eV)

Wave vector, k

EF

band structure

θ1

θθ

θ

EF

2

3

4

θθ sin)(512.0sin2

|| eVEmE

k kinkin

==

© Mark S. Golden

single crystal

monochromatic light

ultra high vacuum

electron energy analyser

‘band mapping’‘band mapping’



AngleAngle--scanned photoemission with high (k,scanned photoemission with high (k,ω)ω)--resolutionresolution

© Mark S. Golden

low bandwidth, high intensitylow bandwidth, high intensityvariable energyvariable energyvariable polarisationvariable polarisation

synchrotron radiation

kk--space microscopyspace microscopy

hνν

θΦ

∆Etot = 2 meV

θ,Φ precision < 0.1 °

∆θ = 0.1 °

-90 ° < Φ < +160 ° -90 ° < θ < +160 °

5 < T sample < 300 K

4kBT at 5 K

< 1% of π/a

The nodal direction (0,0)The nodal direction (0,0)--((ππ,,ππ) as an illustration ) as an illustration

ΓΓ

Y

X Y

X

ΓΓ

XM

N =node

A =antinode

© Mark S. Golden



EDC: I(E) for approx. const. kMDC: I(k) for E = const.

ARPES with an angle multiplexing analyserARPES with an angle multiplexing analyser

0.00.20.4Binding energy (eV) Momentum (Å-1)

0.3 0.4 0.5 0.6 0.7

EEnergy nergy DDistribution istribution I (k,E)I (k,E) MMomentum omentum DDistribution istribution CCurves urves CCurvesurves

....this all lands on....this all lands onthe detector in 5the detector in 5 minsmins. !. !

© Mark S. Golden

What physical quantities are measured in photoemission ?What physical quantities are measured in photoemission ?

Fermifunction

spectralfunction

vec torpotential(pho tons)

momentum(pho toelectrons)

Spectral function:

the probablil ity of removing an electron of energy E andwavevector k from the interacting N-electron system BUT

the matrix element is always present:

dependence on photon energy, polarisation....

© Mark S. Golden



ReRepresenting presenting ARPESARPES data in 2Ddata in 2D

Energy0.4 0.0

kF

EF

EDM - I(kx,ky,ωω)EDC - I(k x,ky,ωω)

Binding energy (eV)

MomentumΓΓ XX

ZZ

M M

Y

MDM - I(kx,ky,ωω)MDC - I(kx,ky,ωω)

E = EF

BorisenkoBorisenko et al., PRBet al., PRB6464, 094513 (2001) , 094513 (2001) © Mark S. Golden

Divide raw signalDivide raw signal

BorisenkoBorisenko et al., PRBet al., PRB6464, 094513 (2001) , 094513 (2001) © Mark S. Golden



A full picture of IA full picture of IPESPES vs. the 3Dvs. the 3D kkxx,, kkyy, E, EBB spacespace

0.5

eV

(ππ,,ππ)(ππ,0,0)

EF

MX

min max

X

X

YM

M

Bin

ding

ene

rgy

(eV

)

Momentum (Å-1 )

ky

kx

2

EF

© Mark S. Golden

BorisenkoBorisenko et al., PRBet al., PRB6464, 094513 (2001) , 094513 (2001)

OutlineOutline








© Mark S. Golden



Determination of theDetermination of the

FermiFermi surface topologysurface topology

© Mark S. Golden

‘Experimental’‘Experimental’ FermiFermi surfaces of HTSCsurfaces of HTSC

ΓΓ

Y

X Y

X

ΓΓ

Y

X Y

X

ΓΓ

Y

X Y

X

ΓΓ

Y

X Y

Xwhich is correct is which is correct is notnota minor detail . . . . . a minor detail . . . . .

© Mark S. Golden

0.8(0.8(ππ,0),0)

HTSCHTSC FermiFermi surface:surface:

holehole--like ?like ?

electronelectron--like ?like ?

perfect nesting ?perfect nesting ?

stripeystripey ??



Why BiWhy Bi22SrSr22CaCuCaCu22OO88 ??

© Mark S. Golden

CuOCuO22 planesplanes

BiBi--O planesO planes

CuOCuO22 planesplanes

! modulated !! modulated !

cleave here !cleave here !CuO2

CuO2

BiO

SrO

Ca

primaryphotoelectron

diffractedelectrons

excellent excellent cleavage cleavage surfacesurface

diffraction diffraction replicasreplicas

suppressed bysuppressed byPbPb--dopingdoping

ΓΓ

YY

LEEDLEED

pristine Bi2212pristine Bi2212



Pristine BiPristine Bi--22122212 FermiFermi surface map surface map

Γ

Z

M Y

X

main FSmain FS

shadow FSshadow FS

diffraction diffraction replicasreplicas

high high intensity intensity ribbonsribbons

© Mark S. Golden

PbPb--doped Bi2212:doped Bi2212:

BiBi22--xxPbPbxxSrSr22CaCuCaCu22OO88

© Mark S. Golden



YY

ΓΓ

LEEDLEED

PbPb--dopeddopedBi2212Bi2212

TheThe FermiFermi surface ofsurface of PbPb--doped Bidoped Bi--22122212

Γ

M X

Z

T = 300 K (OD72K)T = 300 K (OD72K)

measured datameasured data

© Mark S. Golden



TheThe FermiFermi surface ofsurface of PbPb--doped Bidoped Bi--22122212

main FSmain FS

Γ

M X

Z shadow FSshadow FS

© Mark S. Golden

Constant energy surfaces: Constant energy surfaces: ωω dependence (OD69K)dependence (OD69K)

symmetric‘breathing’:

FS closesaround Γonly very late

KordyukKordyuk et al., 2000et al., 2000

300K,300K, hhνν = 21= 21 eVeV

© Mark S. Golden



What about the cWhat about the c--axisaxis

bibi--layer splitting ?layer splitting ?

© Mark S. Golden

……could this explain the ' sightings' of an ……could this explain the ' sightings' of an electronelectron--likelike FermiFermi surface in Bi2212 ?surface in Bi2212 ?

The role of the cThe role of the c--axisaxis bilayerbilayer splitting (BLS)splitting (BLS)

© Mark S. Golden

2CuO2 planes: close together

→ antibonding and bonding states

due to cc--axisaxis bilayerbilayer couplingcoupling

maximal near (π,0)

zero along (0,0)-(π,π)

((PbPb,Bi),Bi)22SrSr22CaCaCuCu22OO88

ΓΓ ππ,0,0

0,0,ππ ππ,,ππ

Could theCould the antibondingantibonding band band give an electrongive an electron--like FS?like FS?



! #"%$ & %& ')(*+! #,.- ! #"%$ & %& ')(*+! #,.-/0 1)2 3 4%563 7 3 8#9 :#2/0 1)2 3 4%563 7 3 8#9 :#2 ;=<>6?;=<>6?

@ A6BDC.EF#G HFJI K6LNM6O#P%Q P.R@ A6BDC.EF#G HFJI K6LNM6O#P%Q P.RS%A6Q F)TUVP#I KJF%AW KS%A6Q F)TUVP#I KJF%AW K XX Y Z [\Y Z [\

KordyukKordyuk,, BorisenkoBorisenko et al., 200et al., 20022

Bin

ding

ene

rgy

(B

indi

ng e

nerg

y ( e

VeV))

Momentum (Momentum (ÅÅ--11))

© Mark S. Golden

BB ABBB AB

]_^ `a6bdc^ e#f^ e#`+g ^ b_b h)b ai)jlkmn.opfq6b q]_^ `a6bdc^ e#f^ e#`+g ^ b_b h)b ai)jlkmn.opfq6b q

KordyukKordyuk et al., IFW Dresden,et al., IFW Dresden, condcond--mat 0mat 0208418208418



LEEDLEED

KordyukKordyuk,, BorisenkoBorisenko et al., 2001et al., 2001, , IFW Dresden IFW Dresden

νν

© Mark S. Golden

OutlineOutline








© Mark S. Golden



SuperconductingSuperconducting energy gapenergy gap

UD, biUD, bi--layer splitting resolvedlayer splitting resolved

© Mark S. Golden

SuperconductingSuperconducting energy gap: revisitedenergy gap: revisited

all ' old'all ' old'superconductingsuperconducting gap data was:gap data was:

analysedanalysed without taking the BLS into accountwithout taking the BLS into account

recorded from modulated, pristine 2212recorded from modulated, pristine 2212

© Mark S. Golden

……..a revisit is called for……..a revisit is called for



!" # %$'& ()+**,- !" # %$'& ()+**,-

© Mark S. Golden

AzimuthalAzimuthal cutcut

kk = 1.09 = 1.09 ÅÅ--11

zoomzoom

[by the way:[by the way:

clear BLS inclear BLS in

UD!]UD!]

40K40K

Borisenko et al., IFW Dresden, cond-mat 0208418, PRB(RC), in press

© Mark S. Golden

./0 12 3%41 5/76/0 1+/89%:;9<4 <=/1 /%4 0>: :./0 12 3%41 5/76/0 1+/89%:;9<4 <=/1 /%4 0>: :

Azimuthal MDC' sAzimuthal MDC' s

BB vs. AB can be BB vs. AB can be ' tuned' via' tuned' viahhνν ::

20' s: 20' s: approx =approx =38:38: BB > ABBB > AB50:50: AB > BBAB > BB

BB BB ABAB ABAB BBBB

BB BB ABAB ABAB BBBB

Borisenko et al., IFW Dresden,cond-mat 0208418, PRB(RC), in press



© Mark S. Golden

Leading edge gap (LEG)Leading edge gap (LEG)

-- only relative gaponly relative gapvalue possiblevalue possible

++ highly precisehighly precise

AB > BB is goodAB > BB is good

EDC fitEDC fit

++ absolute gapabsolute gap

-- model dependentmodel dependent

AB = BB is goodAB = BB is good

hhνννν = 25= 25 eVeV


!"#$ % '&(&'!%')*&'+, -"! . / !"#$ % '&(&'!%')*&'+, -"! . /

© Mark S. Golden

map ofmap of LEG' sLEG' s

BBBB

ABAB

ABAB

BBBB

minmumminmumgap locigap loci

LEG values along LEG values along minimum gap lociminimum gap loci

AB and BBAB and BB superconductingsuperconducting gaps gaps are essentially identicalare essentially identical




© Mark S. Golden

IIΣΣ50meV50meV at Eat EFF map ofmap of LEG' sLEG' s

minimum minimum gap locigap loci

azimuthal angle

pola

r an

gle

pola

r an

gle

azimuthal angle

hhνν = 21.2= 21.2 eVeV, He lamp, He lamp(low(low polarisationpolarisation))

plotplot LEG' sLEG' svs. FS vs. FS angle angle ϕϕ


! "$#%&'() ! "$#%&'()

© Mark S. Golden

UD 77KUD 77K

minmumminmumgap locusgap locus

00

9090

ϕϕ∆∆((ϕϕ)=)=∆∆maxmaxcoscos(2(2ϕϕ))

U--likelike





© Mark S. Golden

Flattening out of gap at nodes seen already in UDFlattening out of gap at nodes seen already in UD

MesotMesot PRL99 PRL99 (pristine Bi2212, not BLS(pristine Bi2212, not BLS--resolved)resolved)

Causes:Causes:

?? longer range pairing in UD due to longer range pairing in UD due to !! screeningscreening

standard dstandard d--wave: wave: ∆∆((ϕϕ)=)=∆∆maxmaxcoscos(2(2ϕϕ))higher gap harmonics: higher gap harmonics: ∆∆((ϕϕ)=)=∆∆11coscos(2(2ϕϕ)) + + ∆∆22coscos(6(6ϕϕ))

here = 27%here = 27% coscos(6(6ϕϕ))

?? other pairing symmetries ?other pairing symmetries ?

ddxx22--yy22 + is; d+ is; dxx22--yy22 ++ ididxyxy

OutlineOutline








© Mark S. Golden



The (The (ππ,0) peak,0) peak--dipdip--hump inhump in

o v e r d o p e d Bi2212o v e r d o p e d Bi2212

superconductingsuperconducting statestate

© Mark S. Golden

ππ !" !" #$% "& ')(* $ ' +#$% "& ')(* $ ' + # , "# , "

© Mark S. Golden

Ding et Ding et al.,al.,PRL1996PRL1996

LoeserLoeser et al., PRB1997et al., PRB1997

HwuHwu et al., et al., PRL1991PRL1991DessauDessau et al., et al.,

PRL1991PRL1991

Ding et al., Ding et al., PRL2001PRL2001

FedorovFedorov et al., PRL1999et al., PRL1999

FengFeng et al., et al., Science2000Science2000



ππ !#" !#"

© Mark S. Golden

((ππ,0),0) peakpeak--dipdip--humphump lineshapelineshape in Bi2212in Bi2212

PDH lineshape in ARPES:

coupling to bosonic modes

(π,π) resonant magnetic mode [INS]e.g. Campuzano PRL1999

phononse.g. Lanzara, Nature 2001

one of the seminal experimental results in HTSC canonone of the seminal experimental results in HTSC canon

$%& & '(*),+ - & %/. 01%2#& )'43$%& & '(*),+ - & %/. 01%2#& )'43ππ 5 6,798,:<;>= ?A@B= C,CBDC5 6,798,:<;>= ?A@B= C,CBDC EE FF

© Mark S. Golden

G#HI IJH KHI LM H JMN O P QR H9S LR/TG#HI IJH KHI LM H JMN O P QR H9S LR/T ππ UU ππ VV WW XZY[\9Y] ^ _^ `9Ya/b cd ef f ^ cbgh/iXZY[\9Y] ^ _^ `9Ya/b cd ef f ^ cbgh/ij kl jm n oZjp q rj kl jm n oZjp q r stuwvx y tz stuwvx y tz | xv| xv~ ~ , Z , Z , ,



Mode coupling Mode coupling peakpeak--dipdip--hump in ARPEShump in ARPES

© Mark S. Golden

Norman & Ding, PRB, 1998Norman & Ding, PRB, 1998

coupling to (coupling to (ππ,,ππ) mode ) mode seen in INS results in seen in INS results in

peakedpeaked ImImΣΣ

eats away spectral eats away spectral weight atweight at ∆∆ + + ΩΩ

dip! no BLS !! no BLS !

ππ ! " # #"$%# ! " # #"$%# && ' '' '

© Mark S. Golden

()+* *-,+).-)%* /%0),10+2 3 4 5+6 )87 /%69()+* *-,+).-)%* /%0),10+2 3 4 5+6 )87 /%69 ππ :: ππ ;; << = />,+)8/%6 2 ?2 @8/>7A 3-* B>C C 2 3-A+D+EF= />,+)8/%6 2 ?2 @8/>7A 3-* B>C C 2 3-A+D+EF)G>0)+6 2 = )+@4 H)G>0)+6 2 = )+@4 H I B = 0+5J B+@/I B = 0+5J B+@/ ?6 /%5+0?6 /%5+04 K)/%6 LH4 K)/%6 LH )M ? MN/%6 = B+@ :)M ? MN/%6 = B+@ : O P B+@/>.O P B+@/>. QQ I K+5 P 5+R />.I K+5 P 5+R />.

A 3-* B>C CS2 3-A+D+EF P )3 / = )>CB83 /%6 @)+6 C 4 /%@)8/>7 4 K)8)G0)+6 2 = )+@4 B+*A 3-* B>C CS2 3-A+D+EF P )3 / = )>CB83 /%6 @)+6 C 4 /%@)8/>7 4 K)8)G0)+6 2 = )+@4 B+*).>2 ,+)+@3 )87 /%6TC 0+2 @87 * 53 4 5B4 2 /%@UC 3 )+@B+6 2 /).>2 ,+)+@3 )87 /%6TC 0+2 @87 * 53 4 5B4 2 /%@UC 3 )+@B+6 2 /2 = 0/%6 4 B+@3 )8/>7 4 K)V92 = 0/%6 4 B+@3 )8/>7 4 K)V9 ππ :: ππ ;; << = />,+)8,+/%5 P 4 ), P L= />,+)8,+/%5 P 4 ), P L WXXWXX YY W+Z [-X+\ ] ^%_W+Z [-X+\ ] ^%_ YY` X+a+a+\ Z` X+a+a+\ Zb+c8d e f f>gh>h+gb+c8d e f f>gh>h+g ii j f f-kl>ck+m e nok+pd j f-q j d j8j pqrnos>q+k+f tuk+m k8uoe d vs%bdj f f-kl>ck+m e nok+pd j f-q j d j8j pqrnos>q+k+f tuk+m k8uoe d vs%bdww ii j l>e tj l>e t x e f jy k+mx e f jy k+m z +| ~ ~ z +| ~ ~ 8 >o z >z + - %8~ ~"+Vz ~ ~ + 8 ~ zo +8 >o z >z + - %8~ ~"+Vz ~ ~ + 8 ~ zo + | -+| -+z +| ~ ~ +"+ V -%| -z +| ~ ~ +"+ V -%| - + + >z z + >z z + %+ z +| ->z %+ z +| ->z



The The ' old' ' old' peakpeak--dipdip--hump edificehump edifice

© Mark S. Golden

But:But: no PDH in sc state 1L (e.g. Bi2201) ARPES !no PDH in sc state 1L (e.g. Bi2201) ARPES !

allall spectra published to date are withspectra published to date are with hhνν 1919--2222 eVeV

PDH seen near (π,0) ' only' in sc state :

T < Tc (Tc ca. 90K) in Bi-2212 based materials

PDH lineshape didn' t alter on modifying A(z) (via incidence angle)

Dip position vs. doping: fits with (π,π) mode from neutrons

Peak is non-dispersive along (0,0)-(π,0)-(2π,0)

© Mark S. Golden

All publishedAll published PDHsPDHs are recorded with 19<are recorded with 19<hhνν<22.5<22.5 eVeV

Ding et al., PRL1996Ding et al., PRL1996

LoeserLoeser et al., PRB1997et al., PRB1997

HwuHwu et al., PRL1991et al., PRL1991DessauDessau et al., PRL1991et al., PRL1991

Ding et al., PRL2001Ding et al., PRL2001

FedorovFedorov et al., PRL1999et al., PRL1999

FengFeng et al., Science2000et al., Science2000

22.422.4

19, 19, 2222

2121

2121

21212222

2222



The The ' old' ' old' peakpeak--dipdip--hump edificehump edifice

© Mark S. Golden

But:But: no PDH in sc state 1L (e.g. Bi2201) ARPES !no PDH in sc state 1L (e.g. Bi2201) ARPES !

allall spectra published to date are withspectra published to date are with hhνν 1919--2222 eVeV

the (the (ππ,0) point of modulated Bi2212 is dangerous !,0) point of modulated Bi2212 is dangerous !

→→ use modulationuse modulation--freefree PbBiPbBi--22122212

PDH seen near (π,0) ' only' in sc state :

T < Tc (Tc ca. 90K) in Bi-2212 based materials

PDH lineshape didn' t alter on modifying A(z) (via incidence angle)

Dip position vs. doping: fits with (π,π) mode from neutrons

Peak is non-dispersive along (0,0)-(π,0)-(2π,0)

LEEDLEED

KordyukKordyuk,, BorisenkoBorisenko et al., 2001et al., 2001, , IFW Dresden IFW Dresden

νν

© Mark S. Golden



© Mark S. Golden

ππ !"$#%& '(*) + %,.- !"$#%& '(*) + %,.- // 0 #123 ,41# 00 #123 ,41# 0,431 065 + 37,431 065 + 37 ππ !" !" 89*:<; =89*:<; = > ? @ACB DEGFH IHFJB KB E> ? @ACB DEGFH IHFJB KB EL MONQPRL MONQPR SS TUVWQXYQZ4X[\] ^_ ` XaTUVWQXYQZ4X[\] ^_ ` Xa bb Y c ddeY c dde fgfg h ij kmllnlh ij kmllnlop qrJs tu rop qrJs tu rvwyxGz|~ xvwyxGz|~ x νν ~ Q ~ Q ∆∆ Q Q

© Mark S. Golden

KordyukKordyuk et al., et al., PRL89, PRL89, 077003 (2002)077003 (2002)

νν ¡¢6¡£6 ¡£6¤J¡ ¡¢6¡£6 ¡£6¤J¡ ¥¥ ¦Q§¨©ª¦Q§¨©ª18 eV

65 eV

let' s pick out some let' s pick out some characteristic data…characteristic data…



! !

© Mark S. Golden

" ##$ %'& ()+* " * (,.---" ##$ %'& ()+* " * (,.---

/ #10* 2/ #10* 2

/ #10* 23 / #/ #10* 23 / #45)+245)+2

45)+245)+2# / " 6# / " 6

788788 9;:<9;:< =>=>?@ACBED?@ACBED FF G.HI JLKG.HI JLKMNOCPQMNOQRS PMNOCPQMNOQRS PTUVCWCXY WU.Z WTUVCWCXY WU.Z Wlineshapelineshape

depends on depends on photon energyphoton energy

KordyukKordyuk et al., et al., PRL89, 077003 (2002)PRL89, 077003 (2002)

[ \'] ^__` a[bLc;dfe.ghikjlmEi hC_mL] n'mLgmLo pqEmn n mai _sr[ \'] ^__` a[bLc;dfe.ghikjlmEi hC_mL] n'mLgmLo pqEmn n mai _sr

© Mark S. Golden

t u vwxyzwt u vwxyzw |~|+ |~|+ νν

→→ .|~|f Q .|~|f Q .|~|E .|~|E

νν→→ Q ¡ ¢ ¢ ¢ Q ¡ ¢ ¢ ¢ £¤'¥ £¤'¥

¦ §¨ © ª« ¬® ¯°±L®¨ ² ³´µ« ª¦ §¨ © ª« ¬® ¯°±L®¨ ² ³´µ« ª ¶¶ ·· ¸¹¸¹ ºº »+¼½¾ ¿sÀÁ»+¼½¾ ¿sÀÁ ÂÂνν ÃÄÅÄÆÃÄÆÇ ÈÃÄÅÄÆÃÄÆÇ È

picture: © Fenget al.

ÉÊË ËÌ ÍÎ ÏÐÎ Ñ ÏÒ ÓÐÑ Ì ÔÏÕÉÊË ËÌ ÍÎ ÏÐÎ Ñ ÏÒ ÓÐÑ Ì ÔÏÕÖ ×+ØÙ ÚÛÖ ÜÝ ÚÞßáàâãäQÛåæsç.èéfàÖ ×+ØÙ ÚÛÖ ÜÝ ÚÞßáàâãäQÛåæsç.èéfà×1êë ìêQÝ ÚÛì Ö.æLë Ù Ù ÚÝ ÚåÖ í îÖ Ø×1êë ìêQÝ ÚÛì Ö.æLë Ù Ù ÚÝ ÚåÖ í îÖ ØÛí Ö ÚÝ ë åïÛí Ö ÚÝ ë åï êê

νν



© Mark S. Golden

! "#$% &! "#$% &

'( $)+* , -%/. 01)2* 3 415'( $)+* , -%/. 01)2* 3 415

'( $)+* , -%/. 01)2* 3 4176'( $)+* , -%/. 01)2* 3 4176

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© Mark S. Golden

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© Mark S. Golden

antibonding

bonding

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© Mark S. Golden

LindroosLindroos et al.et al.,,PRBPRB6565, 054514 (2002), 054514 (2002)

OPOP


(π(π,0) OD,0) OD

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!" #%$&(' )!*' +),-)' .()$ " !" #%$&(' )!*' +),-)' .()$ " )/ +)$0)21 #%'3- $21 4" 4" #$20)$!' #)/ +)$0)21 #%'3- $21 4" 4" #$20)$!' #5%6%7985%6%798::ππ ;; ππ <>=(?@ACB D E AF GF A!E HE B ?%DCD?E3E A%DHIJ A2K ?%F3LNM<>=(?@ACB D E AF GF A!E HE B ?%DCD?E3E A%DHIJ A2K ?%F3LNMO P2Q RO P2Q R S RTUV TW%XU!TS RTUV TW%XU!TY Z U&[Q Y S!\ Y Q W%RCQ [Y Z U&[Q Y S!\ Y Q W%RCQ [[Q ]&Q ^ \ V Y WC_N`[Q ]&Q ^ \ V Y WC_N` aa bb

Feedback effects near (Feedback effects near (ππ,0) in,0) in

u n d e r d o p e d Bi2212u n d e r d o p e d Bi2212

normal &normal & superconductingsuperconducting statestate

© Mark S. Golden



νν ππ

© Mark S. Golden

! ! " #$%&#" #$%&# ' #&#( ' $*)( ' #&#( ' $*)( %% νν

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??

i) no spectrum without a dip or plateaui) no spectrum without a dip or plateau

ii) details ofii) details of hhνν dependence differdependence differ55

toy modeltoy model

NO! NO! subtle, yet crucial differences subtle, yet crucial differences

6879 ::<;=>+?=@:@A-B A =C>*=D:E B/F G A H6879 ::<;=>+?=@:@A-B A =C>*=D:E B/F G A H

© Mark S. GoldenBorisenkoBorisenko et al., IFW Dresden,et al., IFW Dresden, condcond--mat 0mat 0209435209435

thirdthird component clearly component clearly follows follows ABAB bandband

Idea:Idea:

selectselect hhνν that shows that shows

only AB band…..only AB band…..



© Mark S. Golden

νν

Bonding band has local minima atBonding band has local minima at hhνν 29 and 5029 and 50 eVeV

…..these…..these hhνν show ' pure' AB spectrumshow ' pure' AB spectrum

© Mark S. Golden

ππ


UDUD: : dip or plateaudip or plateau ODOD: : smoothsmooth

AntibondingAntibonding band has an ' intrinsic' peakband has an ' intrinsic' peak--dipdip--hump at (hump at (ππ,0),0)

Peak Peak ↔↔ dip separation = 38dip separation = 38--4040 meVmeV EEmodemode



© Mark S. Golden

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EEmodemode



ODOD

UDUD

T<T<TcTc

UDUD T>T>TcTc


T>T>TcTc


!" !"

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coupling to mode disappears abovecoupling to mode disappears above TcTc




ππ

UDUD

many body PDH many body PDH gone abovegone above TcTc

ODOD

band structure PDH band structure PDH remains aboveremains above TcTc

! " #%$&'")(+*,$-.,. ! " #%$&'")(+*,$-.,.

© Mark S. Golden

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ODOD optDoptD UDUD

* trying to make amends for the bashing the LDA* trying to make amends for the bashing the LDA--men got….men got….

doping doping dependence dependence ofof εεABAB andand εεBBBB

odd (odd (interbandinterband) ) character of character of

feedbackfeedback

materials' materials' dependence of dependence of band structureband structure

++ ++ ==

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© Mark S. Golden

T U V UW X Y XT U V UW X Y X Z [-\] ^ _4` a4bZ [-\] ^ _4` a4b c-dc-d e f g e e hi j e elk me f g e e hi j e elk m

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HTSCHTSC

nn oo pq rpq r

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OutlineOutline








the shadowthe shadow FermiFermi surfacesurface

© Mark S. Golden

next workshop….

next workshop….

interactions:interactions:lineshapeslineshapes, , kinks and kinks and self energiesself energies

FermiFermi surfacesurfaceshape, shape, topologytopology,,

gapsgaps

stripes ? stripes ? fractionalisationfractionalisationhidden orderhidden order

ddopingoping level, level, impuritiesimpurities

hhνν,,ppolarisationolarisation: :

linear, circularlinear, circular

ttemperatureemperature1010--300K300K

BiBi--2212, Bi2212, Bi--22012201LaLa--214, 214, TlTl--22012201



Condensed Matter Physics Group, University of AmsterdamCondensed Matter Physics Group, University of AmsterdamYingtaiYingtai HuangHuang

Spectroscopy Group, IFW DresdenSpectroscopy Group, IFW DresdenSergeySergey BorisenkoBorisenko AlexanderAlexander KordyukKordyukAndreasAndreas KoitzschKoitzsch Sibylle Legner Christian DürrMartin Knupfer Thomas Pichler Timur KimRoland Hübel Dieter Müller

Jörg Fink, Claus Schneider, Frank Matthes, Robert Frömter IFF, IFW Dresden

CrystalsCrystalsHelmuthHelmuth BergerBerger EPFL LausanneB. Liang, A. Maliouk, C. T. Lin, Bernhard Keimer MPI StuttgartGuang Yang Stuart Abell U. of Birmingham, UK

Experimental collaborationExperimental collaborationFred Schiller, Serguei Molodtsov, Clemens Laubschat TU Dresden IOMPRolf Follath BESSY Michael Sing, Ralph Claessen U AugsburgStefano Turchini, Stefano Zennaro ELETTRACesare Grazioli CNR Rome + ELETTRA

Crystal characterisationCrystal characterisationK. Nenkov, D. Eckert IMW, IFW Dresden

MoneyMoneyFOM, EU, BMBF, DFG, SMWK

high tc superconductors mark s. golden van der waals...

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