Nature of Correlated Motion of Electrons in the Parent Cobaltate Superconductors

0.29 MB·English

by  M. Z. Hasan

Nature of Correlated Motion of Electrons in the Parent Cobaltate Superconductors
M.Z. Hasan,1,∗ D. Qian,1 Y. Li,1 A.V. Fedorov,2 Y.-D. Chuang,2 A.P. Kuprin,2 M.L. Foo,3 and R.J. Cava3
1Department of Physics, Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
2Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, Ca 94305
3Department of Chemistry, Princeton University, Princeton, NJ 08544
(Dated: February 2, 2008)
5
0 Recently discovered class of cobaltate superconductors (Na0.3CoO2.nH2O) is a novel realization
ofinteractingquantumelectronsystemsinatriangularnetworkwithlow-energydegreesoffreedom.
0
Weemployangle-resolvedphotoemissionspectroscopytouncoverthenatureofmicroscopicelectron
2
motionintheparentsuperconductorsforthefirsttime. Resultsrevealalargehole-likeFermisurface

n (consistent with Luttinger theorem) generated by the crossing of super-heavy quasiparticles. The
a measured quasiparticle parameters collectively suggest a two orders of magnitude departure from
J
the conventional Bardeen-Cooper-Schrieffer electron dynamics paradigm and unveils cobaltates as

0 a ratherhidden class of relatively high temperature superconductors.
3
PACSnumbers: 71.20.b,73.20.At,74.70.b,74.90.+n

]
l
e
- Research on strongly correlated electron systems has precise control of sodium concentration[2, 5]. Cleaving
r
t led to the discovery of many unconventional states of the samples in situ at 20 K (or 100K) resulted in shiny
s
. matter as such realized in the high temperature su- flat surfaces, characterized by diffraction methods to be
t
a perconductors, quantum Hall systems or in the charge- clean and well ordered with the same symmetry as the
m orbital ordering magnetic compounds. Recently, atten- bulk. No Ruthanate-like surface state behavior was ob-
- tionhasfocusedonlayeredcobaltoxidesNaxCoO2·nH2O served in high quality samples and all the data taken at
d
- a new class of doped Mott insulator which in ad- 20K although cleaved at 100K in a few cases for careful
n
dition to being strongly correlated are also frustrated cross-checking.
o
c in their magnetic interactions. Depending on the car-
Fig-1(a-d)showsrepresentativesingleelectronremoval
[ rier concentrations, cobaltates exhibit colossal ther-
spectra as a function of energy and momentum in
moelectric power, dome-shaped superconductivity and
2
Na CoO . Abroadquasiparticle(electrondressedwith
v charge-density-wave phenomena[1]-[5]. They carry cer- 0.3 2
interactions)featureisseentodispersefromhighbinding
0 tainsimilaritiessuchasthe twodimensionalcharacterof
3 non-Fermi-liquidelectrontransport,spin-1/2magnetism energies at high momentum values near the corner (K)
5 or the face (M) of the crystal reciprocal space (Brillouin
and dome-shaped superconductivity as observed in the
1 zone, BZ) to the Fermi level (zero binding energy). This
cuprate superconductors[1]-[7]. Unlike cuprates, cobal-
0
electron-featuregrowsinintensity(yellowemergingfrom
5 tates can be carrier doped over a much wider range and
red)beforecrossingtheFermilevel. Thisisthequasipar-
0 allowtostudyemergentbehaviorinaveryheavilydoped
/ Mott insulator. Previous ARPES studies have focused ticlebandinthissystem. Itisahole-like[8,9]bandsince
t
a on the high doping regime (x=70%, TE-doping) where the bottom of the band is located near the zone bound-
m ary (K or M) as opposed to the zone center. We trace
colossal thermopower is observed [8]. Transport, mag-
- netic and thermodynamics measurements suggest that themomentumvalues(k)oftheelectron(quasiparticle)’s
d zero-bindingenergycrossingpointoveralargepartofthe
n the electron behavior is dramatically different in low
Brillouin zone. This allows us to generate a momentum
o sodiumdoping(x=30%,SC-doping)wheresuperconduc-
space density of states ”n(k)” plot (Fig.2(a)). The inner
c tivity is observed [5, 9]. We have carried out (for the
: edgeofthisdensityplotistheFermisurface. Itisalarge
v firsttime)adetailedmicroscopicstudyofthesingleelec-
rounded hole around the zone center. The Fermi sur-
i tronmotioninthe parentcobaltatesuperconductor(low
X face of the parent superconductor (x=30%, SC-doping)
doping regime) class which reveals the novel many-body
r aswereporthereexhibitsmorehexagonalcharacterthan
a state of matter realized in this system.
the related thermoelectric compound (x=70-75%, TE-
Spectroscopic measurements were performed at the doping)[8]. ThisshapeissimilartotheLocalDensityAp-
Advanced Light Source. Most of the data were collected proximationcalculation[10]. However,nosatellitepocket
with 90 eV or 30 eV photons with better than 30 or 15 is observed. This could be due to strong correlation
meV energy resolution, and an angular resolution better effects, which can push the minority bands away from
than 1% of the Brillouin zone at ALS Beamlines 12.0.1 the Fermi level deep below in binding energies and wash
and 7.0.1 using Scienta analyzers with chamber pressure out their relative intensity. A large Hubbard-U (∼ 4
better than 8×10−11 torr. A key aspect of the success eV) can be extracted by fitting the valence excitations
of our spectroscopic studies has been a careful growth with a cluster model [8]. The size of the Fermi surface,
and characterization of high quality single crystals and k ∼ 0.8 ˚A−1, for the SC-doping studied here is larger
f
2
a K b K
1.0 1.0
-1A) 0.0 G M -1A) 0.0 G M
k(y k(y
-1.0 -1.0
x=0.3
x=0.7
-1.0 0.0 1.0 -1.0 0.0 1.0
kx(A-1) kx(A-1)
FIG. 2: Fermi Surface of Parent Superconductor: a,
Momentum-space density of states (n(k)) plot shows a large
hole-pocket centered around the Γ-point. The inner edge of
thepocketistheFermisurfacewhichexhibitssomehexagonal
anisotropy. b,Comparison of theFermisurface between par-
FIG.1: Single-Particle Dispersion: Zonefacetothezone
ent superconductor (x=0.3) and the thermoelectric (x=0.7)
center (M→ Γ): a, Spectral intensity. b, Energy dispersion
host compound.
curves; Zone corner to the zone center (K→ Γ): c, Spectral
intensity. d, Energy dispersion curves. Color red/blue corre-
sponds tohigh/low intensity. e, Valenceband. f, Quasiparti-
cles. g, Dispersion relation, E vs. k along M→ Γ (extracted which does not consider electron correlationeffects. The
after background correction and symmetrized around the M
bandwidth measured here is consistent with that ex-
point). The bandwidth (”W” ∼ 200 meV) is estimated by
tracted/estimated from the bulk thermal measurements
tracing/extrapolating the band to the zone boundary shown
on the hydrated superconducting samples[7]. The spe-
in (g). h, The raw dispersion (background not subtracted)
along the K→Γ cut shows a kink (also seen in the raw data cific dispersion behavior (band having maximum at the
(c). All thedata were taken at 20K. zone boundary or emanating from the zone boundary to
cross Fermi level in moving towards the zone center) in-
dicatesanegativesign[12]-[14]ofeffectivesingle-particle
than the size observed in the TE-doping[8] suggesting a hopping (t<0). This sign is crucial in describing the
hole doping picture of these compounds (since x=30% physics in a triangular network. The possibility of su-
samples have more holes)(Fig.2(b)). The Fermi surface perconductivity and its doping dependence in triangular
area suggests that about 64% of the Brillouin Zone is many-bodymodels suchasHubbardmodel ort-J model
electron-occupied. This is consistent with the conven- crucially depend on the sign of t [12]-[15]. Hence, our
tional electron count in the x=30% compound. Hence unambiguous determination of a negative sign of t in
Luttinger theorem is satisfied in a conventional sense. the SC-doping compound has implications for the pos-
For the SC-doping, the carrier sign of thermopower or sibilities of superconducting order parameters (such as
Hall transport[4, 5] being positive at all temperatures dx2−y2) it can sustain: dx2−y2 superconductivity is frag-
suggests that it is the holes that carry the current - a ileforanegativet modelwhereasitisrobustforpositive
fact consistent with our finding of a hole-like Fermi sur- t. Furthermore, a negative t rules out the possibility of
face. Nagaoka-type ferromagnetic instability[13] in these sys-
tems. However, next neighbor Coulomb interaction can
In order to estimate the total bandwidth we need to
stabilize superconductivity in the presence of a negative
obtain the complete dispersion relation (energy vs. mo-
t and restore Resonating Valence Bond mechanism of
mentum) overthe full Brillouinzone. To achieve this we
superconductivity[15].
extrapolate the quasiparticle band to the zone bound-
ary (Fig.1(g)). This gives a value of the total energy We then estimate an effective Fermi velocity, which is
dispersion, or bandwidth, of about 180 meV ± 20 meV roughlytheslopeofthedispersionrelationorthederiva-
(∼ 0.2 eV). This bandwidth is about a factor of two tive of the band[9] evaluated very close to the Fermi
larger than the bandwidth observed in the thermoelec- level, by analyzing the dispersion curves in Fig.1(a-d).
tric (TE-doping, x ∼ 70%) cobaltates[8] suggesting a The Fermi velocity, averaged over the entire Fermi sur-
more delocalization (electron-wavefunctions spread out face is found to be about 0.15 ± 0.05 eV·˚A(about 0.2
more) of carriers in the parent superconductor. Larger eV·˚A). This is quite small comparedto most known cor-
bandwidth may be responsible for weaker thermopower related layered oxides. The velocity is about a factor of
observed near superconducting doping because within a 10smallerthanthesuperconductingcuprates[16]. Given
Fermi liquid picture thermopower is inversely related to thesizeoftheFermisurfaceweestimatethecarriermass,
the bandwidth[3, 9]. However, the observed bandwidth m* ∼ ¯hk /|v | ∼ 60 m . This is a rather large carrier
f f e
is still much smaller than the value calculated (∼1.5 massforahigh-conductivitytransitionmetaloxide. Sim-
eV)using the LocalDensity Approximationmethods[10] ilarly large carrier mass has recently been reported by
3
suggeststhat the system canbe thought of as a strongly
renormalized heavy-Fermi liquid. This scaling behavior
a b ~w2 isinsignificantcontrastwith ourfindings inthe thermo-
E -w= 0.25
) (mFeV) kf ~w1.53 electric cobaltates (x=70%) [8].
nt. (Rel. Units 11250050 article Width/0.20 ttcihooenTndo,cuowgcbaetaionlnrtsoafuwtaernstchdowemcritopihnnavsroieetgnhhttehtirosenicbnalaatlossBsicteChseeSloenfscautlatrpuoyenrerericceoodnpfdaeolruxeacicdmttoererotssneur(pmsTeaoor---f
m. I 2350 asip bnloete1)t.haBtatsheedcoonbaoltuartefisndhianvge oaf lealregcetroonn-sbietehaevlieocrt,rowne-
Nor 35 Qu x=30% electron interaction energy (U, measured in a similar
G->M 40 0.15 SC-Doping manner described in Ref. [8]) comparable to the super-
conducting cuprate family[16] but both the bandwidth
0.6 0.8 1.0 0 20 40 60 and the Fermi velocity are several fold smaller and the
k(A-1) E -w(meV)
F nodal carrier mass is orders of magnitude larger (Table
1). To compare superconducting properties, we define a
FIG.3: Self-energy Behavior: a,Momentumdistribution
curves along M→ Γ shows changes of lineshapes away from parameter kBTmc ax/W which compares two fundamen-
tal energy scales in an electronic system. The quan-
theFermilevel(0meV).b,Quasiparticle(lineshape)widthin
x=30% sample (superconducting doping) plotted as a func- tity kBTc (Tc is the transition temperature and kB is
tion of binding energy, which shows nearly ω2 (quadratic) thethermalBoltzmannconstant)describesthesupercon-
Fermi-liquid-likebehavior. ductingcondensationtemperature/energyscaleandWis
the total effective bandwidth that describes the total ki-
netic energy available to the electron system. We make
muon spin rotation measurements[18]. Such large car- a plot, shown in Fig.4(A), of the quantity, transition
rier masses are typically seen in the heavy-fermion com- temperature as a fraction of quasiparticle bandwidth,
pounds (∼ 100 me), where the low-energy physics arises kBTmc ax/WARPES (maximum transition temperature is
from two hybridized bands including an atomic-like f- considered in doped systems) for several major classes
electron band, but are rarely observed in the transition oflayered(quasi-2-Dmaterials)superconductors[16, 17].
metaloxides. Howcobaltatesexhibitsuchalargecarrier Wethenlocatethecobaltateclassbasedonourdata. Itis
masswhereonlyasingled-bandisatplayremainstobe evident fromFig.-4(a)that the ratio,k Tmax/W
B c ARPES
understood. (∼k *5Kelvin/0.2 eV·˚A∼ 0.002) for the cobaltate sys-
B
We further observe that electron velocity changes tem is about two orders of magnitude larger than the
beyond 50-70 meV binding energy range and a kink strong coupling BCS superconductors such as tin (Sn)
(Fig.1(c))isobservedinthedispersionrelationalongthe or lead (Pb)[21]. The cobaltate value is rather close to
Γ→K direction in that energy range. This could be due that observed in the cuprate superconductors or doped
to coupling to bosonic collective modes such as phonons fullerenes[22] where both strong electron-electron and
ormagneticfluctuations(kinkinFig.1(c)and1(g)). The electron-boson (or phonon) interactions are observed.
energy scale of the kink - the velocity cross-over - di- A two-orders-of-magnitude departure from the conven-
rectly corresponds to the optical phonon (Raman-active tional phonon-only BCS-like value in the cobaltates is a
lattice vibrations 55-75 meV) energies in the cobaltates signature for its electron dynamics to be of unconven-
[19]. Basedon the kink parameters (ratio of high-energy tional origin in the sense that phonons alone can not be
velocityandlow-energyvelocity)inourdatatheeffective accountedforsuperconductivity. Electron-electroninter-
coupling is on the order of unity which is very similar to actionleadstoareductionorrenormalizationofWwhich
what is observed in the cuprates[16]. A similar kink was isamanifestationofthe strongcorrelation(Mott) effect.
also reported in the high doping regime [8]. Its observa- This strong electron-electron (Mott effect) interaction
tion indicates the existence of strong bosonic interaction leadstotheenhancementofthequantityT /W.Inorder
c
or coupling in the single-particle dynamics of the cobal- to further test its relevance to superconductivity in the
tates. It would be interesting to look for such modes sense that T /W reflects a measure of relative effective
c
using inelastic x-ray [20] or neutron scattering. interactionstrength(fromoneclasstotheother)weplot
We study the scaling behavior of the electron self- this quantity against a known independently measured
energy based on the momentum distribution curves parameter - the inverse coherence length (1/ξ) which is
shown in Fig.3(a). The quasiparticle line widths which an inverse measure of the size of the superconducting
provide a measure of electron self-energy or scattering electron-pair wavefunction hence a measure of the over-
rate, as a function of electron binding energy (ω) can be all coupling strength (interactions) from one materials
fitted with a quadratic-like (ω ∼ 2) form (Fig.3(b)) with class to the other. In Fig-4(b) we plot Tmax/W
c ARPES
a large prefactor than conventional metals [9, 11]. This vs. ξ−1 and observe that this is true for most classes
4
TABLE I:ARPES Quasiparticle parameters for major classes of superconductors
Class Tc(K) Bandwidth Fermi velocity Mass Hubbard Ref.
WAPRES(eV) vf[ARPES](eV·˚A) m/me U(eV)
Cobaltates(NaCoO) 5 0.18±0.04 0.15±0.10 60±20 >4.0 Present work
p-Cuprates(LSCO) 38 ∼0.4 1.8 2 (nodal) 3 - 5 [16]
n-Cuprates(NCCO) 22 ∼0.5 2.0 2.4 (nodal) ∼3 [17]
Ruthanates(SrRuO) 1 0.5 0.4 (avg) ∼9 (avg) 1 [16]
BCS-typeSCs(Pb) 7.2 9.5 12 2 [21]
of modern (unconventional) superconductors as well as
wowfhouaehrvrimcitTohhaueckr/is.eBWCfaGonS(ui∼vnesemdun0pp.t0etiorr0hic2ecbo)aenslddlaoeausbptctaoeitmuoootranfst(tesc0huo.o0egbf0gal21eilnt//sat0eξit.ne0f(ogs∼2rmant0mehu.a0ens2i∼ucvorneebr0mdsa.1a)lht)laaebtirnneeeds--, Bandwidth)1100--32 a YBNNKLBS3SCaCCCCCC6u0ouCuOOOOuO Bandwidth)111000---312 b NNaCKCL3oBCYCSOSuB6COC0CuCuOuOO .-1cm)W11000 c SrRuOMgB2
vemseetriasmesuanrteeamsnoeomnftesctoewhri.etrheiTnnchteihseleasngagrmetheesobrraedsmeerda-rokofa-nmblmayganwginittuehtdiecr[e6fic,ee7nld]t. maxT/(QP-c10-4 SPSnbrRuO maxT/(QP-c10-4 SnPbSrRuO (msNaC1oO LBYNSSBCCCCCuCuuOOuOO
10-5
We further plot dc conductivity[5, 16, 22, 23] as a func- 10-5 Al Al K3C60(fullerene)
tion of quasiparticle bandwidth in conventional and un- 0.1
10-3 10-2 10-1 100 101 0 1 2
conventional superconducting materials, which suggests x-1ab(nm-1) QPBandwidth(eV)
that cobaltates (Fig.-4(c)) fall closer to the cuprates or
ruthanates but in a different regime where magnesium FIG. 4: Quasiparticle-Bandwidth and Superconduc-
diboride belongs to. tivity: a,Transition temperature(Tc)asafraction ofband-
The fact that the cobaltate system has a relatively width (Tmc ax/bandwidth) for several classes of superconduc-
largetransitiontemperatureasafractionofquasiparticle tors. b, Tc/(ARPES-bandwidth) is found to scale with the
inverse ab-plane coherence length. Coherence length data is
bandwidthandsmallFermivelocityisratherremarkable.
taken from Ref. [24]. c. Electrical (dc) conductivity is plot-
This suggests thatgiventhe totalbandwidth or totalki-
ted as a function of (ARPES) bandwidth for conventional
netic energy, the system has achieved superconductivity andunconventionalsuperconductorclasses. Ingeneral,cobal-
at a relatively high temperature although the actual Tc tate class is found to cluster with the unconventional super-
is rather low in absolute numbers. In this sense it is a conductorsthantheBCStypeconventionalsuperconductors.
hidden ”high temperature superconductor” even though Acharacteristictwo-orders-of-magnitudedeparturefromcon-
ventionalBCS-like behavior is evident in (a), (b) and (c).
it may have a very different order parameter symmetry
than the cuprates.
Our results provide the fundamental electron parame-
recorded at ALS which is operated by the DOE Office
ters (Fermi surface topology, sign of hopping, Fermi ve-
ofBasicEnergyScience. MZHacknowledgespartialsup-
locity, quasiparticle mass, bandwidth etc.) to construct
port through NSF-MRSEC (DMR-0213706) grant. Ma-
a model hamiltonian for the cobaltate class. The un-
terials synthesis and ARPES characterization was sup-
usual character of the microscopic electron dynamics in
portedby DMR-0213706andthe DOE,grantDE-FG02-
the cobaltates observed here suggests that any compre-
98-ER45706.
hensive theory of these materials needs to account for
the fact that a relatively large value of transition tem-
peratureisachievedinanextremelynarrowbandparent
material with unusually heavy and slow moving carriers
whereatwo-orders-of-magnitudedeparturefromconven- ∗ To whom correspondence should be addressed:
tionalphonon-onlyBCS paradigmis observedin the mi- [email protected]
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