Extremely Small Energy Gap in the Quasi-One-Dimensional Conducting Chain Compound SrNbO$_{3.41}$

4 Pages·0.44 MB·English

by  C. A. Kuntscher

Extremely Small Energy Gap in the Quasi-One-Dimensional
Conducting Chain Compound SrNbO
3.41
C. A. Kuntscher,1,2 S. Schuppler,1 P. Haas,2 B. Gorshunov,2,∗ M. Dressel,2 M. Grioni,3 F. Lichtenberg,4
4 4 4
A. Herrnberger, F. Mayr, and J. Mannhart
1 Forschungszentrum Karlsruhe, Institut fu¨r Festk¨orperphysik, D-76021 Karlsruhe, Germany
2 1. Physikalisches Institut, Universit¨at Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
3 3 Institut de Physique Appliqu´ee, Ecole Polytechnique F´ed´erale, CH-1015 Lausanne, Switzerland
0 4 Institut fu¨r Physik, EKM, Universit¨at Augsburg, Universit¨atsstr. 1, D-86135 Augsburg, Germany
0
(Received February 1, 2008)
2
Resistivity, optical, and angle-resolved photoemission experiments reveal unusual one-
n
a dimensional electronic properties of highly anisotropic SrNbO3.41. Along the conducting chain
J direction wefindan extremelysmallenergygap ofonlyafewmeVat theFermilevel. Adiscussion
in terms of typical 1D instabilities (Peierls, Mott-Hubbard) shows that neither seems to provide a
5
1 satisfactory explanation for the uniqueproperties of SrNbO3.41.

]
l
e
-
r Aone-dimensional(1D)interactingelectronsystemno 5.67 ˚A, and c=32.46 ˚A, in good agreement with earlier
t
s longer exhibits the quasiparticles known from Fermi liq- work [7]. The basic structural building blocks are NbO6
.
t uid theory and is instead a Tomonaga-Luttinger liquid octahedra [see Fig. 1(a)] grouped into slabs which ex-
a
m (TLL) whose properties also include spin-charge separa- tendparalleltothe (a,b)planeandforSrNbO3.4 arefive
tion and a power-law behavior of correlation functions octahedra wide along c. Only along the a axis the octa-
-
d [1]. This 1D theory does not, however, directly apply to hedraareconnectedcontinuouslyviatheirapicaloxygen
n real 1D materials since some coupling between the 1D atoms, forming 1D chains.
o entities(suchaschainsorsimilar)isalwayspresent,ren-
c The dc resistivity of SrNbO3.41 along the three axes
dering the systems quasi-1D and facilitating 2D and 3D
[ wasmeasuredusingafour-pointconfiguration[6]. Polar-
ordering effects. Real 1D materials are thus conducive
izedreflectionmeasurementsalongthe a and b axiswere
2
v to various instabilities masking the predicted TLL char- performedforfrequencies6-34000cm−1 byutilizingvar-
acteristics [2]. Electron-phonon coupling, for instance,
5 iousspectrometers;fordetailsseeRef.[8]. Toaccomplish
8 canleadtoagappedcharge-densitywave(CDW)ground the Kramers-Kronig analysis, we used a Hagen-Rubens
4 state (Peierls transition), and electron-electron interac- extrapolationforω→0andapowerlaw(ω−4)athighfre-
3 tion may cause the opening of a Mott-Hubbard (MH)
quencies. High-resolution (∆E=15 meV) ARPES data
0
gap at commensurate band filling.
1 were recorded with a Scienta ESCA-300 analyzer using
0 Recently, a new quasi-1D material was synthesized [3] the He Iα line of a discharge lamp. The samples were
t/ which belongs to the series SrNbO3.5−x of perovskite- cleaved at RT and a base pressure of 1 × 10−10 mbar to
a relatedtransition-metaloxides,withcharacteristicsspan- expose an (001) surface, and cooled down to 25 K. By
m ◦
ningawiderange: Depending ontheoxygenstoichiome- Laue diffraction the crystals were oriented to ±1 . The
- try,these niobium oxidesexhibitquasi-1Dmetallic char- angular resolution was set to ±0.5◦, and the Fermi level
d
acter(x≈0.1)[4]orferroelectricity(x=0)with veryhigh E was determined to 1 meV accuracy from the Fermi
n F
o transition temperature [5]. In this Letter we focus on cutoff of a freshly evaporated Au film recorded immedi-
c the unusual electronic properties of the quasi-1D metal- ately afterwards at the same experimental conditions.
:
v lic compound SrNbO3.41 which were determined by dc Fig. 1(b) shows the dc resistivity ρ versus temper-
i resistivity, optical spectroscopy, and angle-resolved pho-
X ature T of SrNbO3.41 along the three axes. It is
toemission (ARPES). Along the conducting chain direc-
highly anisotropic with very low, metal-like values along
r
a tion, an extremely small energy gap of only a few meV, the a direction (ρ (300K)=4.6×10−4 Ωcm) and a RT
a
much smaller than for other quasi-1Dcompounds, is ob- anisotropyofρ :ρ :ρ =1:102:104. Thevariationofρwith
a b c
served at the Fermi level. The gap is discussed in terms
temperature is smallerwithin the (a,b)plane thanalong
of a Peierls and a MH scenario.
c. In all directions a broadmaximum or shoulder is seen
SrNbO3.41 singlecrystalsoftypicalsize3×2×0.2mm3 between200and50K,andbelow50Kwefindanincrease
were grown [3,6] by the floating zone melting technique. of ρ, which in the range 20-40 K can be described by
Thepreciseoxygencontentwasdeterminedthermogravi- an activated behavior ρ∝exp{E /k T} with activation
a B
metrically. The analysis of the room temperature (RT) energies E =2-3 meV. In the range 60-130 K ρ (along
a a
x-ray powder diffraction pattern indicates single-phase the chains) has a metallic T dependence, whereas above
composition with lattice constants a = 3.99 ˚A, b = 130 K it slightly decreases with increasing temperature
1
(a) (b)103 Sr0.9La0.1NbO3.39 [4]as wellas for SrNbO3.41 [8]: A dis-
SrNbO
3.41 persingbandisfoundonlyalongonehigh-symmetryline,
102 Ea=1.8meV I U c Γ¯-X¯,paralleltothechaindirectiona,andseemstocross
E ; a second band near E does not show discernible
F F
dispersion. Neither band disperses along the transverse
101
direction Γ¯-Y¯. The Fermi surface (FS) is 1D [4], with
m) nesting vector 2k of about 1/3 of the Brillouin zone.
c 100 ||c F
W (
ry 10-3 10-2 10-1 100(eV)
vit 10-1 E=1.5meV
sti a 0.99
c esi ||b 6000 100 K 5 K R 5 K
R 10-2 b 50 K
UI a 300 K 0.9 300 K
a 10-3 Ea=3.3meV 4000
||a 0
101 102 103 104
10-4 -1m) n (cm-1)
0 50 100 150 200 250 300 c 2000 200 K E||a
Temperature (K) -1
cryFsItGal.s1t.ru(cat)urPe;roNjebctaitoonmasloanreghtihdedebnawxiisthoinf tthhee NSrbNOb6Oo3c.4- sWy (1 0 SrNbO 3.41
Dtacherdersaist(ilvigithyt ρgrevye)r.suWs hteitmep(egrraetyu)recirocfleSs:rNSbrO(O3.4)1ataolomnsg. t(hbe) uctivit 800 5 K 0R.9 9 E||b
three crystal axes, with the resp. measurement geometry. In nd 300 K 0.9
therange 20-40 K (grey bar) onefindsan activated behavior o 600
C
ρ∝exp{Ea/kBT} with Ea as indicated. 0
101 102 103 104
400
n (cm-1)
(thermallyactivatedhoppingbetweenmetallicstrands
may explain this). A similar temperature dependence is
200
observedforρ ,however,notasclearlydeveloped. There
b 300 K 5 K
are no signs of metallic behavior along c.
0
The anisotropy in the electrical properties of 101 102 103 104
SrNbO3.41 is also clearly seen in the optical response Frequency (cm-1)
(Fig. 2). The reflectivity R displayed in the insets of
FIG. 2. Frequency dependent conductivity of SrNbO3.41
Fig. 2 shows a sharp plasma edge for the polarization for different temperatures and the polarization E set par-
Eka with high values (R≈1) at low frequencies, indicat- allel to the a and b axes (insets: reflectivity R used for
ing metallic conductivity. In contrast, for Ekb the mate- Kramers-Kronig analysis). For E||a the low-temperature
rialisinsulatingandwemainlyseephononcontributions peakaround40cm−1indicatesexcitationsacrossagap2∆≈5
between 40 and 1000 cm−1 showing significant changes meV.
with temperature which will be discussed elsewhere [8].
Forbothpolarizationdirectionsthelowfrequency(ω→0) Furtherinsightisgainedbybandstructurecalculations
conductivityσ1agrees,ingeneral,wellwiththemeasured in the local density approximation [4,9] which demon-
dcdata(Fig.1),reproducingitsrathercomplicatedtem- strate that among the three inequivalent Nb sites per
peraturebehavior. AtRT theEkaconductivitycontains slab a predominant [9] contribution to the density of oc-
a Drude-like contribution at low frequencies followed by cupied states at E comes from the central Nb site; the
−1 F
several phonon lines between 100 and 1000 cm and a contributions of the other two Nb sites rapidly fall off
broad mid-infrared band around 1500 cm−1. Upon re- with distance away from the center. Distortion is small
ducing the temperature, σ1 exhibits substantial changes only for the NbO6 octahedra based on the central Nb
at frequencies lower than 100 cm−1, leading to the ap- sites, and one can thus clearly relate the quasi-1D char-
pearance of a peak around 40 cm−1, which is already acter of the dispersing band to these chains of almost
quitestrongat50K. At5K,thispeakhasshiftedslightly “perfect” octahedra in the middle of the slabs. The im-
to higher frequencies and has grown even stronger. We portance of the central chains is also demonstrated by
ascribe this feature to single-particle excitations across comparing ARPES results for SrNbO3.41 with those for
an energy gap in the electronic density of states with Sr0.8La0.2NbO3.50 [8], where the central chains are miss-
2∆(5 K)≈5 meV. ing since there the slabs are only four octahedra wide:
The momentum resolved electronic properties probed for the latter the 1D characterof the band structure has
by ARPES reveal a quasi-1D band structure for almost vanished.
2
The quasi-1D FS with almost complete nesting makes
D q = X D q =
SrNbO3.41 prone to instabilities opening a gap at EF,
and we thus concentrate on the region around k in or- 7° -0.5°
der to very sensitively detect such signatures. FiFg. 3 (a) 6.5° -00°.25°
showsthe correspondinghigh-resolutionARPESspectra 6.25° 00..255°°
along Γ¯-X¯ near E . At ∆θ =−1.5◦ the peak associated 6°
F
withthestronglydispersingbandislocatedat≈160meV y 5.5°kF* SrNbO3.41
binding energy and is rather broad, but sharpens up as nsit 5°
(it∆aθp≡p0r◦o)acahsetshEeFemainsdsioanppdeiarercsttiooncrfoorsswiht.icWhethdeelfienaediknFg n Inte 34°° (b) (Au)
edge midpoint of the spectrum is closest to EF. Due to ssio 2° Bi8n0ding E40nergy 0(meV-)40
a 2×1 superstructure [4] the peak reappears already at mi 1°
e
fkoF∗r=in5c.5r◦eaasinndgd∆isθp.erFseigs.t3ow(bar)ddsehpiigcthserthbeinAdRinPgEeSnesrpgeiecs- Photo 00.2.55°° k*F
tra around k for a narrow angular step size of 0.25◦ 0° kF
F
-0.25°
together with the Fermi cutoff of a Au film. Starting
◦ -0.5°
from −0.5 and going to higher ∆θ, the leading edge
-1°
omfidthpeoisnptecatprpar.oaActheks ,EtFhebsuptedctoreaslnwoetigrhetacaht itthefoFrearmnyi (a) -1.5G°G (c) kF
F
level is significantly suppressed (by ≈40%) compared to 0.3 0.2 0.1 0.0 -0.1 -0.2 0.3 0.2 0.1 0
the leading edge midpoint, and we find a gap between Binding Energy (eV) Binding Energy (eV)
the leading edge midpoint and EF of ∆(25 K)≈4 meV. FIG.3. ARPES spectra of SrNbO3.41 along Γ¯-X¯ near kF
Althoughthis“leadingedge”methodisknowntounder- atT=25K.Theangle∆θistheemissionanglewithrespectto
◦
estimate the gapsize somewhat for a peak-like structure kF (∆θ≡0 ). (a) Spectra between the two “crossing points”
a fit (not shown) of the kF spectrum, similar to Ref. (kF,kF∗) of the strongly dispersing band; peak po◦sitions are
[10] and accounting for the peak structure, gives only a marked by dots. (b) Spectra around kF in 0.25 steps. A
gap ∆≈5 meV is seen when compared to the Fermi cutoff
slightly larger result, ∆(25 K)≈(5±2) meV, corroborat-
of a gold film (thin solid line). (c) Intensity plot of spectra,
ingtheleadingedgeresult. Possibleextrinsiceffectssuch ∗ ◦
taken between kF and kF (step size 0.5 ) and normalized to
aschargingortoocoarseanangularstepsizecanalsobe
constant total intensity;a weak, dispersing shadowband can
excluded as a source of the gap [11]. The gap is thus beidentified.
clearly established and with a size of about 5 meV is, in
fact, the smallest one found in ARPES for any quasi-1D
compound. Mostsurprisingisthegap’sextremesmallness,making
ituniqueamongquasi-1Dmaterials;theunusualproper-
The intensity plot of high-resolution ARPES spectra
◦ ties of the gap, however, turn out to defy easy explana-
in 0.5 steps and normalizedfor clarity to constant total
tion: (i) A lattice superstructure with sufficiently small
intensity is shown in Fig. 3 (c). It indicates additional
∗ displacement amplitudes would of course be able to re-
states between k andk , where the stronglydispersing
F F produce the gap and its small size. It cannot, however,
bandis unoccupied: beyondk a “shadowband” is visi-
F plausibly explain why the gap should be situated right
ble which dispersesawayfromthe gapedge andexhibits
a symmetry consistent with the 2×1 superstructure. Its at EF, considering the large width (>∼2 eV [4,9]) of the
quasi-1Dband. Theinstabilitiesofquasi-1Dsystems,on
smallintensityiscompatiblewiththesmallgapsize[12].
the other hand, by their very nature cause a gap located
Asshadowbandsareratherweakingeneralacleariden-
at E and thus are more likely candidates for an expla-
tification in experiment has been possible only for very F
few quasi-1D materials [12,13]. nation of the gap properties observed for SrNbO3.41 –
suchas(ii) a MH-type insulating state with agapatE
F
The different experiments on SrNbO3.41 all yield clear due to electron-electron interaction; for this, the filling
evidence for an energy gap at E along the conducting level of the quasi-1D band would have to be commensu-
F
chains: a rise in the dc resisitivity, a strong peak in the rate, 1/3. This 1/3 filling, however, would require long-
optical conductivity, as well as a significant suppression range interaction and a TLL parameter K <1/3 for a
ρ
of spectral weight in ARPES. All results lead to char- MH gap to open [14], and the very strong correlation
acteristic energies of a few meV – agreeing well enough implied by the latter appears implausible for SrNbO3.41:
to demonstrate that the gap does exist and suggesting a correlationeffects are generally small for 4d systems like
commonorigin. Somespreadispresent,asexpected,due niobium oxides. The possibility of a MH gap is thus un-
to the different nature of the excitation for the various likely yet cannot be fully excluded based on our data
techniques (the optical gap, e. g., is somewhat smaller, as theoretical results for 1/3 filling are still scarce. (iii)
possibly due to excitonic effects). A Peierls instability caused by electron-phonon coupling
3
appears possible, too, leading to a CDW state for suffi- ∗ Permanentaddress: GeneralPhysicsInstitute,Academy
ciently low temperatures with a gap at E [15,16]. The of Sciences, Vavilov 38, Moscow 117942, Russia.
F
gapsizeisrelatedtothemean-field(MF)transitiontem- [1] J. Voit, Rep.Prog. Phys. 58, 977 (1995).
perature TMF, and in the weak-coupling limit 2∆(0) = [2] M. Grioni and J. Voit, in Electron spectroscopies applied
P
3.52k TMF; from the ARPES gap 2∆(25 K)≈10 meV tolow-dimensionalmaterials,editedbyH.P.Hughesand
B P
one can then estimate TMF≈40 K [17]. Only below this H. I. Starnberg(Kluwer, Dordrecht,2000).
P [3] F. Lichtenberg et al., Z. Phys. B 84, 369 (1991); T.
temperature the gap (or its precursor, the fluctuation-
Williams et al.,J. Solid StateChem. 103, 375 (1993).
induced pseudogap)canexist; inthis senseTPMF strictly [4] C. A.Kuntscher et al.,Phys. Rev.B 61, 1876 (2000).
limits the temperature range where any gap-related fea- [5] S. Nanamatsu et al., J. Phys. Soc. Jpn. 30, 300 (1971);
tures can possibly be observed. Yet for SrNbO3.41 one S. Nanamatsu, M. Kimura, and T. Kawamura, J. Phys.
clearly sees the upturn in ρa(T) (Fig. 1) to start at ≈55 Soc. Jpn.38, 817 (1975).
K, and the low-energy peak for Eka in optics (Fig. 2) [6] F. Lichtenberg et al., Prog. Solid State Chem. 29, 1
is almost fully developed already at 50 K, suggesting an (2001).
onsetwell abovethat temperature. A simple Peierls pic- [7] S. C. Abrahams et al., ActaCryst. B 54, 399 (1998).
ture therefore is also insufficient to provide an explana- [8] C. A.Kuntscher et al. (to bepublished).
[9] H. Winter, S.Schuppler,and C. A. Kuntscher,J. Phys.:
tion for the observed small gap [18]. Inconsistencies be-
Cond. Matt. 12, 1735 (2000).
tweentheexperimentalresultsandtheoricalmodelshave
[10] N. P. Armitage et al., Phys.Rev.Lett. 86, 1126 (2001).
been found for other quasi-1D systems as well, like the
[11] Charging: Withρa,b,c(25K)fromFig.1,estimatesofpos-
paradigmatic(NbSe4)3I, (TaSe4)2I, and K0.3MoO3. The siblechargingeffectsinducedbythetotalphotoemission
latter two are CDW systems yet show clear discrepan-
current turn out to be 3 orders of magnitude smaller
cies to the Peierls picture (e. g., ARPES line shape and thanthegapsizeobserved.Angularstepsize: Simulated
Fermi cutoff above TP), which were attributed to corre- ARPESspectrawithintheFermiliquidmodelforaband
lationeffects [2,19]. Incontrast,quasi-1DSrNbO3.41 has with the experimental dispersion near kF and account-
no obvious Peierls transition, little tendency to correla- ing for the experimental angular and energy broadening
tion, and the relevant energy scale is drastically smaller. show that (i) the gap indeed closes at kF, and that (ii)
◦
Itseemstobe asystemwithcharacteristicsdistinctly its a step size of 0.25 (implying that the actual kF can be
◦
”missed“ by 0.125 at most) is clearly sufficient to rule
own, thus expanding the parameter space where real 1D
outthatagapwith∆>1meVcouldbeduetothiseffect.
systems remain to be fully understood.
[12] J. Voit et al., Science 290, 501 (2000).
[13] V. Vescoli et al., Phys. Rev. Lett. 84, 1272 (2000); J.
Sch¨afer et al.,ibid. 87, 196403 (2001).
Insummary,weconsistentlyobserveinARPES,dcre-
[14] H. J. Schulz, in Strongly correlated electronic materials,
sistivity, and optics that SrNbO3.41 is a compound with edited by K. S. Bedell et al. (Addison-Wesley, Reading,
1D electronic characteristics around E ; as expected for
F MA, 1994).
such a system, instabilities lead to an energy gap at E .
F [15] R. Peierls, Quantum theory of solids (Oxford University
Most surprising is its small gap size: only a few meV
Press, London, 1955).
by all techniques and thus much smaller than for other [16] The fact that no signatures for a transition are obvious
quasi-1D compounds. Further analysis shows the ex- in resistivity (Fig. 1) or detectable in thermal expansion
perimental findings to appear inconsistent with validity (P.Nagel,V.Pasler,andC.Meingast,unpublished)may
ranges for both the Peierls and Mott-Hubbard picture. beduetothelownumberofelectronsinvolvedinthe1D
These aspects promise more general implications for the characterofSrNbO3.41;itdoesnotbyitself meanthata
understanding of real 1D systems. Peierls transition does not occur.
[17] A BCS-type approximation for ∆(T) was used for the
estimate.
We thank B. G¨otz, G. Hammerl, A. Loidl, L. Per- [18] The structural affinity of SrNbO3.41 to ferroelectric
fetti, C. Rojas, C. Schneider, R. Schulz, I. Vobornik, J. SrNbO3.50 may be of importance: the central chains
responsible for the 1D electronic character are coupled
Voit, and H. Winter for valuable help and fruitful dis-
toanetwork of polarizable NbO6 octahedra structurally
cussions. This work was supported by the DAAD, the
equivalent tothosegiving riseto thehigh dielectric con-
BMBF (project No. 13N6918/1),and the DFG.
stant in the ferroelectric, and a certain influence on the
electronic properties of thechains is conceivable.
[19] L. Perfetti et al.,Phys. Rev.Lett. 87, 216404 (2001).
4