1

Core-level photoemission measurements of the chemical potential shift asa probe of correlated electron systems*

A. Fujimoria, A. Inob, J. Matsunoa∗, T. Yoshidaa, K. Tanakaa, T. Mizokawaa

aDepartment of Complexity Science and Engineering and Department of Physics, University of Tokyo,Bunkyo-ku, Tokyo 113-0033, Japan

bHiroshima Synchrotron Radiation Research Center, Hiroshima University, Higashi-Hiroshima739-0046, Japan

The shift of the chemical potential as a function of band filling provides useful insight into the electronicstructure of solids. In this article, we describe how the chemical potential shift can be measured using core-levelphotoemission spectroscopy and what information can be obtained from the measured chemical potential shift,in particular on strongly correlated systems. We present results on various transition-metal oxides, which includematerials showing typical Fermi-liquid behavior, pseudogap behavior, charge-density-wave formation, “stripe”formation, etc.

KEYWORDS: core-level photoemission, chemical potential shift, Mott transition, stripe, pseudogap

1. INTRODUCTION

Since strongly correlated electron systems arecharacterized by their unusual magnetic andcharge responses [1], the measurements of theseresponses are of utmost importance to under-stand their complex behaviors. While the energy-and momentum-dependent magnetic susceptibil-ity χ(q, ω) has been extensively studied by inelas-tic neutron scattering, and its static limit by nu-clear magnetic resonance and magnetic suscepti-bility measurements, the corresponding informa-tion about the charge susceptibility χc(q, ω) hasbeen rather limited. The dynamical susceptibilityχc(q, ω) can in principle be measured by electron-energy-loss spectroscopy or inelastic x-ray scat-tering. The static (ω = 0), uniform (q = 0)limit of χc(q, ω) is the charge susceptibility χc ≡∂n/∂µ, where n is the electron density and µ isthe electron chemical potential or the Fermi level(EF ), but few experimental studies have been re-ported so far on χc. The corresponding quan-tity in the magnetic response channel is the uni-

∗Present address: JRCAT, Tsukuba 305-8562, Japan.*Published in J. Electron Spectrosc. Relat. Phenom.124, 127 (2002)

form magnetic susceptibility χ ≡ ∂M/∂H, whereM is the magnetization and H is the magneticfield. Because charge responses certainly playroles equally important to magnetic responses instrongly correlated systems, it is highly desired todevelop a practical method to study the chargesusceptibility.

In compounds where the band filling can bechanged by chemically doping charge carriers,i.e., in filling-control systems, the uniform chargesusceptibility can be determined by the rate ofthe chemical potential shift ∂µ/∂n through χc =(∂µ/∂n)−1. Because binding energies in pho-toemission spectra are measured referenced tothe chemical potential µ, characteristic featuresin photoemission spectra should be shifted whenthe chemical potential is shifted. If there isno electron-electron interaction, the rate of thechemical potential shift ∂µ/∂n is simply given bythe inverse of the bare electronic density of statesNb(µ) at the chemical potential:

∂µ

∂n=

1Nb(µ)

. (1)

In an insulator, ∂n/∂µ vanishes unless states at µare localized due to disorder. As one moves from

2

p-type (hole) doping to n-type (electron) dopingacross the undoped insulator, µ should show ajump of the magnitude of the band gap.

The chemical potential shift in interacting elec-tron systems, on the other hand, is not triv-ial, especially near a metal-insulator transition orwhen the system has peculiar charge responsessuch as charge-density wave formation and charge“stripe” formation, as described below. In suchcases, studies of the chemical potential shift givesparticularly useful information about the elec-tronic structures of interacting electron systems.In this article, we describe how one can deducethe chemical potential shift largely from mea-sured core-level photoemission data and what onecan learn from the chemical potential shift aboutthe physics of strongly correlated systems.

2. MEASUREMENTS OF THE CHEMI-CAL POTENTIAL SHIFT

2.1. Chemical potential shift in filling-control systems

The chemical potential of a many-electron sys-tem is defined as the increase of the Gibbs freeenergy density g per unit increase of the elec-tron density: µ = ∂g/∂n. Here, the neutralizingpositive background charges, namely, the positivecharges of ion cores, should increase by the sameamount as the increase of the electronic charges tomaintain the charge neutrality. If the charge neu-trality is violated, a strong electrostatic field hasto be applied from outside of the sample in orderto confine the added charge carriers to the sam-ple. In real systems, when the electron density isvaried by chemical doping, the background pos-itive charges of ion cores are varied by the sameamount and the charge neutrality is maintained.

One should bear in mind that long-rangeCoulomb interaction and hence resulting macro-scopic electric fields are usually neglected in mi-croscopic models such as the Hubbard model andthe t-J model. This situation well corresponds toreal filling-control systems, where the charge neu-trality is maintained. Thus the results of chemi-cal potential shift measurements on filling-controlsystems can be compared with calculations basedon those microscopic models.

2.2. Deducing the chemical potential shiftfrom core-level shifts

The shift ∆E of the energy of a core level mea-sured relative to the chemical potential µ, whenthe band filling is varied, is given by [2]

∆E = −∆µ + K∆Q−∆VM + ∆ER, (2)

where ∆µ is the change in the chemical potential,∆Q is the change in the number of valence elec-trons on the atom, K is a constant, ∆VM is thechange in the Madelung potential and ∆ER is thechange in the extra-atomic relaxation energy ofthe core-hole state. Here, ∆Q produces changesin the electrostatic potential at the core-hole siteas well as in the intra-atomic relaxation energy ofthe core-hole final state, thereby producing a shiftwhich is dependent on the valence of that atom,i.e., the so-called chemical shift. ∆ER is due tochanges in the screening of the core hole potentialby metallic conduction electrons and/or dielectricpolarization of surrounding media. Thus ∆µ canbe extracted from the measured core-level shifts∆E only if the other terms in Eq. (2) are neg-ligibly small or can be estimated from other in-formation. In particular, the Madelung potentialscalculated using the point-charge model are of theorder of 20 eV, and its change ∆VM is also of theorder of 1 eV when the electron density changesby a few tenths of an electron per transition-metalatom. In real materials, this value is expected tobe considerably reduced by covalency, dielectricscreening and metallic screening. Whether ∆VM

is indeed negligible or not compared to ∆µ has tobe tested experimentally. Madelung potential cal-culations using the point charge model would helpus to see whether the observed core-level shifts re-flect changes in the Madelung potentials or not.

In order to demonstrate how one can de-duce the chemical potential shift ∆µ from mea-sured ∆E’s using Eq. (2), we show an illustra-tive example of a high-Tc superconductor systemLa2−xSrxCuO4, where Sr substitution for La (thesubstitution of Sr2+ ions for the La3+ ions) intro-duces holes in the otherwise antiferromagnetic in-sulating CuO2 plane [3]. Cu is in the Cu2+ statewith the S = 1/2 local spin in La2CuO4, and thedoped hole density per Cu is given by x. Figure1 show the x-ray photoemission (XPS) spectra of

3

-530 -525

x = 0

0.1

0.15

0.2

0.3

O 1s (a)

-840 -835 -830

x� = 0

0.1

0.15

0.2

0.3

La 3d5/2

(b)

-940 -935 -930

x� = 0

0.1

0.15

0.2

0.3

Cu 2p3/2 (c)

105

0.15

0.2

0.3

La 4f(BIS)

(d)

x=0.074

Energy relative to EF (eV)

Inte

nsity

(ar

b.un

its)

Figure 1. Core-level photoemission (O 1s, La 3d,Cu 2p) and La 4f inverse-photoemission (BIS)spectra of La2−xSrxCuO4 [3].

some core levels in La2−xSrxCuO4 for various x’s.Here, data from the empty La 4f (semi-core) levelmeasured by inverse-photoemission spectroscopy(BIS) are also shown.

The observed energy shifts shown in Fig. 2 arenearly the same between the O 1s, La 3d andLa 4f levels while the Cu 2p core level exhibits aquite different shift. The rather complicated shiftof the Cu 2p core level could be decomposed intotwo simple components, as shown in Fig. 2: oneis the shift which is almost linear in x and theother is the shift common to all the core levels.The ‘linear’ component of the Cu 2p core-levelshift can be attributed to the increase in the Cuvalence with hole doping (∝ −x∆Q) from Cu2+

towards Cu3+, i.e., to the chemical shift. Then,the shift common to all the four levels may reflectthe chemical potential shift ∆µ. ∆VM is differentbetween the core levels of cations and anions andcannot be the origin of the common shifts. Infact, the calculated Madelung potentials shown

0.4

0.3

0.2

0.1

0.0

-0.1

-0.2

-0.3

Rel

ativ

e E

nerg

y (e

V)

0.30.20.10.0x

O 1s La 3d La 4f (BIS)

La2-xSrxCuO4

Cu 2p

Core-level shifts in

Figure 2. Energy shifts in La2−xSrxCuO4 rela-tive to the undoped (x = 0) compound plottedagainst hole concentration x [3]. Crosses give thedifference between the shift of the Cu 2p core leveland the average of the shifts of the O 1s, La 3dand La 4f levels, and thus represent the chemicalshift of the Cu 2p core level.

in Fig. 3 show quite different behaviors from theexperimental shifts shown in Fig. 2. Also, thecalculated difference in the shifts of the La andO core levels is absent in experiment, indicatingthat ∆VM is reduced sufficiently to be neglectedin the real materials. ∆ER would shift filled andempty levels towards the opposite directions andcannot explain the common shifts. Also, Cu andoxygen core levels may be influenced by metallicscreening while the La core levels are not becausehole carriers are known to enter the CuO2 plane.Furthermore, the line shapes of the oxygen corelevels do not show asymmetric broadening char-acteristic of metallic screening [4] for all the com-positions, indicating negligible contributions frommetallic core-hole screening.

The chemical potential shift in La2−xSrxCuO4

thus deduced is displayed in Fig. 4. In the figure,the chemical potential shifts in other systems are

4

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

Rel

ativ

e E

nerg

y (e

V)

0.30.20.10.0

x, Sr concentration

Cu Op Oa La

Figure 3. Changes in the Madelung potentials−∆VM for La2−xSrxCuO4 relative to the un-doped (x = 0) case plotted against hole concen-tration x. Op and Oa denote the oxygen sites inthe CuO2 plane and the LaO plane, respectively.Here, the crystal structural data have been takenfrom Ref.[5]

also shown and shall be discussed below.

2.3. Experimental accuracyIt is not trivial to measure the shifts of core

levels with sufficient accuracy for several reasons.First, shifts can be accurately determined onlywhen the spectral line shape of the core leveldoes not change. There are both intrinsic andextrinsic causes which may make the line shapedependent on the chemical composition. Changesin the number of carriers may change the metal-lic screening and hence the peak asymmetry, al-though this effect was found to be weak in thecase of La2−xSrxCuO4 as described above, as wellas in other filling-controlled systems. Changes inthe valence of a transition-metal atom will changethe core-level line shape of the transition-metalatom, mostly due to the overlap of different com-ponents from different valence states (Cu2+ andCu3+ in the case of La2−xSrxCuO4) with varyingspectral weight, Cu2+ : Cu3+ = 1-x : x. This also

-0.4

-0.2

0.0

1.00.80.60.40.20.0

Hole concentration δ

Ba1-xKxBiO3 (δ = x)

-0.2

0.0

La1-xSrxTiO3+y/2 (δ = x+y)

-0.4

-0.2

0La2-xSrxNiO4+y/2 (δ = x+y)

-0.2

0.0La1-xSrxFeO3 (δ = x - 0.67)

-0.2

0.0

La2-xSrxCuO4 (δ = x)

Che

mic

al p

oten

tial s

hift

∆µ (

eV)

Figure 4. Chemical potential shifts ∆µ in var-ious filling-control transition-metal oxides [3,8–11]. For La1−xSrxTiO3 and La1−xSrxFeO3,valence-band photoemission data have also beenused.

leads to an apparent shift of the peak position be-cause each component is usually unresolved, as inthe case of the Cu 2p core level described above.In some cases, however, each component has anarrow width and is therefore discernible as twocomponents, as shown in Fig. 5 in the case ofY1−xSrxTiO3. Here, the intensity ratio of thetwo components is found to vary as Ti4+ : Ti3+

= x : 1-x [6].As for an extrinsic cause for changes in the

line shape, surface contamination or degradationsometimes takes place. In such a case, the lineshape is not reproducible between different sam-ples and an accurate determination of the shiftsbecomes difficult.

5

Energy relative to EF (eV)

Figure 5. Ti 2p core-level photoemission spec-tra of Y1−xCaxTiO3 and their decomposition intothe Ti4+ and Ti3+ doublets at higher and lowerbinding energies, respectively, shifted by ∼1 eV[6].

An accurate determination of the shifts fromthe peak positions alone is in fact difficult becausethe peak position cannot be defined so accuratelyfrom experimental data. The mid point of theslope on the lower binding energy side of the peakis generally more accurate. The lower binding en-ergy side rather than the higher binding energyside is usually reliable because the high bindingenergy side is often influenced by contaminationor by the arbitrariness of the background. Over-laying different spectra as shown in Fig. 6 enablesus to make a more accurate determination of theshifts and to check whether changes in the lineshape are absent or not.

The accuracy of the spectrometer to determineenergies also affects the accuracy of core-level

Inte

nsity

(ar

b. u

nits

)

-834 -833 -832 -831 -830 -829

Energy Relative to EF (eV)

x=0 x=0.1 x=0.15 x=0.2 x=0.3

La2-xSrxCuO4

La 3d

3d5/2

Inte

nsity

(ar

b. u

nits

)

-533 -532 -531 -530 -529 -528 -527 -526

Energy Relative to EF (eV)

hν=1253.6eV

La2-xSrxCuO4 O 1s

x=0 x=0.1 x=0.15 x=0.2 x=0.3

Figure 6. O 1s and La 3d core-level photoemis-sion spectra of La2−xSrxCuO4. The same data asthose in Fig. 1 are plotted overlayed. Horizontalarrows indicate the mid point of the low bindingenergy slope, where the shifts can be more accu-rately measured than at the peak positions.

shifts. Binding energies measured by an x-rayphotoemission spectroscopy (XPS) spectrometerare usually reproducible to only within 0.1 eV,largely due to the limited stability of the highvoltage (> 1 kV) power supply. Figure 7 showsthe time-dependent fluctuations of the measuredAu 4f7/2 core-level energy, indicating that the re-tarding voltage of the commercial hemisphericalanalyzer fluctuates by as much as 100 meV in sev-eral hours. To correct for such fluctuations, theretarding voltage was directly measured. Thuswe were able to reduce the fluctuations to within10 meV, which is much smaller than errors intro-duced by the arbitrariness caused by subtle line-shape differences between different samples.

6

100

8�

0

6�

0

4�

0

20

0�

Rel

ativ

e E

nerg

y (m

eV)

108�

6�

420�

Time (hour)

without correction with correction

Au 4f7/2

Figure 7. Time dependent fluctuations of themeasured Au 4f7/2 core-level energy (filled cir-cle). If the energy is corrected using the directlymeasured retarding voltage, the fluctuations canbe reduced by an order of magnitude (open cir-cles).

3. APPLICATIONS TO CORRELATEDELECTRON SYSTEMS

In the remainder of this article, we describehow the chemical potential shift measurementshave been applied to filling-control systems,mostly transition-metal oxides, and how useful in-formation can be obtained to understand strongcorrelation phenomena.

3.1. Normal Fermi-liquid and nearly rigid-band behavior

The most conventional behavior of a filling-control system is a rigid-band behavior, where the(renormalized) electronic band structure, namely,the band structure of a quasi-particle (QP),ε∗(k), rather than that of a bare electron andthe (renormalized) density of QP’s, N∗(ω), donot change with band filling or electron densityn. Here, ε∗(k) is different from the bare bandstructure εb(k), which yields Nb(ω). In such acase, the rate of the chemical potential shift isgiven by substituting N∗(µ) for Nb(µ) in Eq. (1).In addition, because of the repulsive interactionbetween QP’s, the chemical potential shift occursfaster than predicted by the non-interacting rigid-band model (1), as schematically shown in Fig. 8.

µ

µ+∆µ

ωω

∆n/Ν (µ)

∆n

Ν (ω)

n� n� +∆n

∗

∗

F ∆n/Ν (µ)s0

∗

Figure 8. Schematic presentation of the chemicalpotential shift in a filling-control system wherea rigid-band behavior is observed. From the leftto the right, the carrier density n is increased by∆n and the chemical potential rises by ∆µ. ∆µis given by F 0

s ∆n/N∗(µ) + ∆n/N∗(µ).

Thus the rigid-band model should be modified byincorporating the QP-QP repulsion representedby a Landau parameter F 0

s (> 0) as [7]:

∂µ

∂n=

1 + F 0s

N∗(µ)≡

(mb

m∗

) 1 + F 0s

Nb(µ), (3)

where mb is the band mass and m∗ is the renor-malized effective mass at the chemical potential,therefore, m∗/mb being the so-called mass renor-malization factor. F 0

s is a Landau parameter rep-resenting the isotropic spin-symmetric part of theQP-QP repulsion.

N∗(µ) can be deduced from the electronic spe-cific heat coefficient γ through

γ =π2k2

B

3N∗(µ), (4)

and hence

∂µ

∂n=

π2k2B

3γ(1 + F 0

s ). (5)

Therefore, one can estimate the QP-QP repul-sion parameter F 0

s from the measured values of

7

Table 1QP-QP repulsion F s

0 and the mass renormaliza-tion factor m∗/mb in normal Fermi-liquid sys-tems. For La2−xSrxCuO4 and La1−xSrxCuO2.5,data in the overdoped (x > 0.15) region, wherethe system behaves as a normal Fermi liquid, arelisted. Similarly, values at x <∼ 1 are listed forLa1−xSrxVO3.

F s0 m∗/mb Ref.

La2−xSrxCuO4 ∼7 2–3 [3]La1−xSrxCuO2.5 ∼4 1.5 [12]La1−xSrxVO3 ∼6 2–3 [8]liquid 3He 9.2 2.8 [13]Ba1−xKxBiO3 ¿1 1.2 [11]

∂µ/∂n and γ using Eq. (5). The result of suchanalyses for filling-control systems showing nor-mal Fermi-liquid behavior is listed in Table 1. Forthe 3d transition-metal oxides [3,8,12], in whichelectron-electron interaction is rather strong be-cause of the spatially localized 3d orbitals, F s

0

is rather large and is comparable to the typ-ical Fermi-liquid system, liquid 3He [13]. ForBa1−xKxBiO3, where only sp-derived states arelocated around the chemical potential, F 0

s is in-deed small.

If F 0s is largely determined by the spatial ex-

tent of the relevant atomic orbitals, F 0s would not

strongly depend on the band filling in a filling-control system, and the rate of the chemical po-tential shift would reflect changes in the effec-tive mass m∗ at µ. In the filling-control systemLa1−xSrxTiO3+y/2 showing a typical Fermi-liquidbehavior [14], m∗ is known to be divergently en-hanced as the hole concentration δ = x + y isdecreased and the Mott insulating state is ap-proached (as long as the system remains in thePauli-paramagnetic metallic phase: δ > 0.08)[14]. As shown in Fig. 4, ∆µ is in fact flattened,i.e., ∂µ/∂n ∝ 1/m∗ is suppressed as δ is decreased[8].

n� n� +∆n

µ

ωω

Ν (ω)∗

µ+∆µ

Spectral weight transfer

Figure 9. Schematic presentation of the chemicalpotential shift in a filling-control system where apseudogap behavior is observed. From the left tothe right, the carrier density n is increased by ∆nand the chemical potential rises by ∆µ, although∆µ is small.

3.2. Pseudogap behavior and spectralweight transfer across the chemicalpotential

The rigid-band picture breaks down when theQP band structure ε∗(k) and the density of QP’sN∗(ω) change with band filling. In such a case,there is no such simple relationship as Eq. (3)between ∂µ/∂n and N∗(µ). Nevertheless, thenumber of states should be transferred across thechemical potential according to the change in theband filling. Figure 9 illustrates an example ofnon-rigid band behavior where a pseudogap isopened at the chemical potential and spectralweight is transferred from above to below it asthe band filling is increased.

When a pseudogap is opened and spectralweight transfer occurs with band filling, thechemical potential shift ∂µ/∂n becomes smallerthan that predicted by Eq. (5). If one still ap-plies Eq. (5) to such a case, a negative F 0

s wouldbe obtained. Therefore, one may use the condi-

8

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0.0

Experiment

∆µ ∝ δ2

(a)

La2-xSrxCuO4

-0.3

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-0.1

0.0

0.1

0.30.20.10.0

(b)

Experiment from γ from band calc.

La2-xSrxCuO4

Che

mic

al p

oten

tial s

hift

∆µ

(eV

)

Hole concentration δ

Figure 10. Chemical potential shift ∆µ inLa2−xSrxCuO4 [3]. (a) Comparison with predic-tions by band theory [Eq. (1)] and electronic spe-cific heats [Eq. (5) with F 0

s ]. (b) Fit to the theo-retical prediction ∆µ ∝ −δ2 [7].

tion

∂µ

∂n<

π2k2B

3γ, (6)

as an indication of the opening of a pseudogap atµ. For example, in the high-Tc cuprates in theunderdoped region, the electronic specific heatγ decreases with decreasing hole concentrationδ, almost linearly with δ [15]. This has beentaken as evidence for the opening of a pseudogapin the underdoped samples, in contrast with theFermi-liquid system La1−xSrxTiO3+y/2, where γincreases with decreasing x. For La2−xSrxCuO4,as shown by the solid curve in Fig. 10(a), ∂µ/∂nincreases with decreasing δ, whereas in the samefigure the chemical potential shift deduced fromthe core level shifts is suppressed in the under-doped region δ < 0.12. This indeed satisfies con-dition (6), the fingerprint for the opening of apseudogap [3]. A suppression of the chemical po-

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-0.2

-0.1

0�

0�

.1

0�

.200�

.150�

.100�

.050�

Experiment

∆µ ∝ − δ 2

BSCCO

Hole Concentration / Cu

Che

mic

al P

oten

tial S

hift

∆µ (e

V)

Figure 11. Chemical potential shift ∆µ in Er- andPr-substituted Bi2Sr2CaCu2O8 as a function ofdoped hole concentration δ [16]. A fit of ∆µ ∝ δ2

is shown by a dashed curve.

tential shift has also been identified in heavily un-derdoped rare-earth-substituted Bi2Sr2CaCu2O8

[16], as shown in Fig. 11. The doped “ladder”compound La1−xSrxCuO2.5 also shows a suppres-sion of the chemical potential shift for small x[12].

Suppression of the chemical potential shift withdecreasing hole concentration has been theoreti-cally predicted for the two-dimensional Hubbardmodel [7,17] and the t-J model [18]. In partic-ular, ∆µ ∝ −δ2 has been predicted by Monte-Carlo simulations for the two-dimensional Hub-bard model [7]. That is, the charge susceptibilityis predicted to diverge as δ → 0. In Figs. 10 and11, comparison is made between the experimen-tal results and the theoretical prediction, show-ing rather good agreement. There seems to exist,however, a subtle but systematic discrepancy be-tween theory and experiment for small δ: partic-ularly, the measured ∆µ for La2−xSrxCuO4 ap-pears too flat compared to ∆µ ∝ −δ2 in the re-gion δ < 0.15. This may be due to the effect ofcharge stripes and shall be discussed below.

Theoretically the divergence of the charge sus-ceptibility in the limit δ → 0 occurs because ofthe disappearance of the long-range antiferromag-

9

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0�

.2

0�

.0

-0.2

0�

.12

0�

.08

0�

.04

0�

.00

0�

.12

0�

.08

0�

.04

0�

.00

0�

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0�

.08

0�

.04

0�

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0�

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0�

.00

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-0.4

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0�

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Inco

mm

ensu

rabi

lity

εC

hem

icla

l Pot

entia

l Shi

ft ∆µ

( eV

)

NCCO LSCO

Doping Level / Cu

(a)

(b)

0�

.00�

.1 0�

.1 0�

.20�

.2 0�

.30�

.3

Figure 12. Chemical potential shift ∆µ inNd2−xCexCuO4 (NCCO) [19], together with thatof La2−xSrxCuO4 (LSCO) (a). (b): Incommen-surability of the neutron peak near q = (π, π)[22].

netic order of the parent Mott insulator for avery small number of hole doping [7]. In fact,the antiferromagnetic order in La2−xSrxCuO4 isdestroyed for x as small as 0.03, while in theelectron-doped superconductor Nd2−xCexCuO4,where the antiferromagnetic ordering persists upto doped electron concentrations of δ ∼ 0.15,there is no suppression of the chemical potentialshift [19] as shown in Fig. 12.

3.3. Effects of charge density waves, chargeordering and charge stripes

Since the chemical potential shift is expected tobe a sensitive probe of charge response, it is inter-esting to see how the chemical potential behaveswhen a charge-density wave (CDW) is formed.For a “conventional” CDW, where a certain pe-riodicity is stable against a small change in theband filling, the charge density in real space isexpected to change with band filling nearly uni-formly. The chemical potential is therefore ex-pected to show an appreciable shift according tothe rigid-band picture.

As shown in Fig. 4, La1−xSrxFeO3 around x =0.67 and Ba1−xKxBiO3 show monotonous shiftsas functions of band filling. La1/3Sr2/3FeO3 isknown to show ordering of the Fe3+ and Fe5+

charge states (Fe3+ : Fe5+ = 2 : 1) with the peri-odicity of three lattice spacings along the (111) di-rection [20]. This periodicity is robust for a smallchange in x, resulting in the rigid band-like chem-ical potential shift. If the charge-ordered statehas a gap, the chemical potential would show ajump when it crosses the gap. Unfortunately,the data points are too few to identify such ajump in the La1−xSrxFeO3 data in Fig. 4. Asfor Ba1−xKxBiO3, the x = 0 material is knownto show a breathing-type lattice distortion (corre-sponding to a charge modulation with wave vec-tor q = (π, π, π)). The distortion gradually dis-appears as holes are doped into BaBiO3, but theperiodicity does not change with x, again result-ing in the rigid-band-like chemical potential shift.

Another type of CDW is an unconventionalone, called “stripes”. Stripes change their peri-odicity with band filling, so that the local chargedensity does not change. That is, when the holeconcentration increases, the hole rich region ex-pands and the hole-poor region shrinks on a mi-croscopic scale. Thus the hole density in eachregion remains nearly unchanged. If this can beviewed as a phase separation into hole-rich andhole-poor regions on a nanometer scale, thermo-dynamics requires the chemical potential to befixed at a constant value as long as the stripesexist. Indeed, Fig. 4 shows that the chemical po-tential of La2−xSrxNiO4 is fixed between x = 0and x ' 1/3, i.e., in the region where chargestripes change their periodicity with hole doping.Nd-doped La2−xSrxCuO4 also shows stripes be-tween x = 0 and x ' 1/8 [21]. Without Nd,La2−xSrxCuO4 is thought to show charge fluctua-tions of stripe type [22]. The pinning of the chem-ical potential in La2−xSrxCuO4 between x = 0and x ' 1/8 (Fig. 3 and 10) is therefore mostlikely due to the stripe fluctuations.

3.4. Electronic phase separation ?As stated above, charge stripes are a kind of mi-

croscopic electronic phase separation. If an elec-tronic phase separation occurs on a larger scale

10

(e.g., on a micron scale), too, the chemical po-tential is expected to show a pinning behavior. Itis therefore interesting to apply chemical poten-tial shift measurements to those systems wherean electronic phase separation may occur. It hasbeen frequently argued that an electronic phaseseparation occurs in hole-doped Mn oxides andthat such a phase separation may be the originof the colossal magneto-resistance (CMR) oxides[23]. Electron microscopy studies have indicatedinhomogeneous spatial images [24], but it has notbeen clear whether they are driven by (extrinsic)chemical inhomogeneity or (intrinsic) electronicinhomogeneity. This can be tested by the chem-ical potential shift because the chemical poten-tial shift is sensitive only to the electronic phaseseparation. Figure 13 shows that the chemical po-tential in La1−xSrxMnO3 is shifted monotonouslywithout indication of chemical potential pinning,especially around x ∼ 0.3 where the CMR effect isthe strongest [25]. More systematic studies on re-lated materials (such as Pr1−xCaxMnO3, layeredMn oxides, etc.) are needed to establish whetheran electronic phase separation plays a role in theCMR phenomena of the hole-doped Mn oxides.

-0.5

-0.4

-0.3

-0.2

-0.1

0�

Che

mic

al p

oten

tial s

hift

∆µ (

eV)

0�

.60�

.50�

.40�

.30�

.20�

.10�

x, Sr concentration

La 1-x Sr x� MnO3�

from XPS from γ

Figure 13. Chemical potential shift ∆µ inLa1−xSrxMnO3 [25].

3.5. Chemical potential jump across theband gap

In the simple rigid-band picture, when thechemical potential crosses a band gap as a func-tion of band filling, it should show a jump of finitemagnitude. The magnitude of the jump should beidentical to the minimum gap, i.e., the gap for in-trinsic charge transport, and is generally smallerthan the optical gap.

In strongly correlated systems, the situation isessentially unaltered because for an insulator, thechemical potential should move to the first ioniza-tion level for an infinitely small number of holedoping and to the first affinity level for an in-finitely small number of electron doping. How-ever, in cases where doped carriers are segregatedin space though attractive interaction betweenthem, the chemical potential may not move tothe band edges but stay within the band gap,separated from the band edge by the magnitudeof the attractive interaction. A recent angle-resolved photoemission study of La2−xSrxCuO4

has indeed shown that the chemical potential inheavily underdoped samples is located ∼0.4 eVabove the top of the valence band [26].

The chemical potential jump between the hole-doped and electron-doped high-Tc superconduc-tors, La2−xSrxCuO4 and Nd2−xCexCuO4, hasbeen a controversial issue for a long time. Thejump estimated from valence-band photoemis-sion studies was at most ∼0.5 eV [27,28], whichis much smaller than the optical gaps, 1.5-2.0 eV, of the parent insulators La2CuO4 andNd2CuO4. It is difficult to estimate the chemi-cal potential jump between La2−xSrxCuO4 andNd2−xCexCuO4 even from core-level photoemis-sion because La2SrCuO4 and Nd2CuO4 have dif-ferent chemical compositions and different crystalstructures. Nevertheless, one can conclude fromthe small magnitude of the jumps of the O 1s andCu 2p core levels (0.15 and 0.40 eV, respectively)that the chemical potential jump is at most ∼0.5eV and is much smaller than the optical gaps.A recent resonant inelastic x-ray scattering studyhas shown that the band gap is indirect and thatthe minimum gap is smaller than the optical gapby ∼0.5 eV [29]. Combining this finding and thechemical potential pinning ∼0.4 eV above the top

11

of the valence band [26], the ∼1 eV discrepancybetween the optical gaps and the chemical poten-tial jump can be explained.

Figure 14. Chemical potential shift ∆µ inLa1.17−xPbxVS3.17 [30]. x = 0.17 correspondsto the undoped (δ = 0) case.

Figure 14 shows the chemical potential shift inLa1.17−xPbxVS3.17, a system in which both holedoping (x > 0.17) and electron doping (x < 0.17)are possible. The result shows a chemical poten-tial jump of ∼0.1 eV at x = 0.17, where the Mottgap is considered to open. Unfortunately, no op-tical studies have been reported for this systemand the optical gap of the x = 0.17 compound isnot known.

Finally, a jump of the chemical potential of∼0.15 eV may be recognized for La2−xSrxNiO4

around x ' 0.33 (Fig. 4), where a stable chargeordering with the periodicity of three lattice spac-ings has been reported [10]. This gap is similar tobut somewhat smaller than the reported opticalgap of the x = 0.33 compound, 0.26 eV [31].

4. CONCLUSION

We have shown that the chemical potentialshift as a function of band filling provides use-ful information about the electronic structure of

filling-control systems. We have described howthe chemical potential shift can be deduced fromthe measured shifts of core-level photoemissionspectra and what information can be obtainedfrom the chemical potential shift. Results arepresented and discussed for cases where a rigid-band behavior, conventional CDW or charge or-dering and charge stripe formation is observed.Although the chemical potential shift is a rela-tively simple quantity, it gives deep insight intothe electronic properties of strongly correlatedsystems.

ACKNOWLEDGMENT

This work was supported by a Grant-in-Aidfor Scientific Research for a Priority Area “NovelQuantum Phenomena in Transition Metal Ox-ides”, a Grant-in-Aid for Scientific ResearchA12304018 and a Special Coordination Fund forthe Promotion of Science and Technology fromthe Ministry of Education, Culture, Sports, Sci-ence and Technology.

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