PHYSICAL REVIEW B 104, 195420 (2021)

Extraordinary alternating metal-insulator transitions in CaRuO3 ultrathin films
at integer multiples of 25 Å of thickness
M. Sakoda ,1,* H. Nobukane ,2,3 S. Shimoda,4 and S. Tanda1,3
1

Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Hokkaido, Japan2
Department of Physics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Hokkaido, Japan
3
Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo, 060-8628, Hokkaido, Japan
4
Institute for Catalysis, Hokkaido University, Sapporo 001-0021, Hokkaido, Japan(Received 10 March 2021; revised 25 October 2021; accepted 1 November 2021; published 17 November 2021)
Novel quantum phenomena, including high-temperature superconductivity, topological properties, andcharge/spin density waves, appear in low-dimensional conductive materials. It is possible to artificially create
low-dimensional systems by fabricating ultrathin films, quantum wires, or quantum dots with flat interfaces.
We show that extraordinary metal-insulator transitions that oscillate depending on the scale occur in CaRuO3
films with a thickness of around several unit cells. We grow high-crystalline CaRuO3 ultrathin films, whose
surface roughness is controlled at 199 pm, by molecular beam epitaxy. We observe that resistivity oscillates witha “magic” thickness of 25 Å, and changes by three and nine orders of magnitude at room temperature and at
low temperature, respectively. These changes are much larger than quantum size effects. We also confirm thesame periodicity with photoelectron spectroscopy by etching the ultrathin film. Considering the large energy,
periodicity, and anisotropy, we suggest that the oscillating transitions originate from the commensurability ofMott insulation triggered by Peierls instability.
DOI: 10.1103/PhysRevB.104.195420
I. INTRODUCTION

In ultrathin films with a thickness of several nanometers,
the degree of freedom of electrons is artificially enclosed
in two dimensions. For example, quantum size effects appear in single element ultrathin films whose thicknesses
are approximately of the order of de Broglie wavelengths[1–6]. Some experiments have been performed on ultrathincompounds of strongly correlated electron systems [7,8].
However, since it is technically difficult to control multiple elements precisely, most of the properties of artificiallyfabricated low-dimensional compounds fall into uncharted
territory. It is necessary to develop ultrathin films with clear
interfaces into compounds that have unique electronic states.
Ruthenium oxides based on the RuO6 octahedra layered structure contain a treasure chest of attractive physical properties
including an anisotropic superconductor Sr 2 RuO4 [9], andCa2 RuO4 , which exhibits pressure-induced superconductivity and high-Tc superconductivity in thin flakes [10,11]. In
addition, the layered compound Ca3 Ru2 O7 is suggested to
be a density wave state, and other combinations of RuO6
conduction layers exhibit a variety of properties derived fromthe pseudo-two-dimensional nature [12–15]. In this study, we
focus on CaRuO3 , which has the simplest structure in CaRu-O systems, as the target material for artificially fabricatedlow-dimensional electronic systems in ultrathin films.
CaRuO3 has a GaFeO3 -type crystalline structure consistingof a simple orthorhombic lattice (space group Pbnm) [16,17]*

Corresponding author: sakodam@eng.hokudai.ac.jp2469-9950/2021/104(19)/195420(8)[Fig. 1(a)]. Since it does not have a layered compound, itshows isotropic conduction in three dimensions. CaRuO3 isknown to behave as a non-Fermi liquid at low temperatures,as seen in its electrical resistivity, magnetic susceptibility, andspecific heat [18–25]. A narrow bandwidth of ∼20 meV anda large effective mass of ∼4 m0 have also been observed[24,26]. From the above, CaRuO3 is considered to be in thequantum critical region with strong electron correlation [22],and its physical properties are expected to change significantly
depending on various external fields and states. CaRuO3 hasa pole Fermi surface (FS) and is expected to exhibit quantum
phenomena based on two-dimensional (2D) electronic statesin microphysical properties. In this study, the degrees of freedom of electrons are limited in real space by fabrication ofultrathin films of the strongly correlated compound and lowdimensional electron systems artificially appears. Our purpose
is to explore the low-dimensional electronic properties thatarise from a dual restriction imposed on the dimensions inwavenumber space by using a pole-shaped FS and in real
space by using ultrathin films with clear interfaces. Since
the Fermi wavelength of CaRuO3 is as much as several
nanometers [26], it is expected that scale-dependent quantum
phenomena will appear in the ultrathin films.
Pure CaRuO3 single crystals with a high residual resistivity
ratio have been reported for bulk and thin films [27,28]. It
has been shown that CaRuO3 epitaxial thin films with few
lattice defects can be produced by supplying sufficient oxygen [28,29]. In this paper, we develop high-quality CaRuO3
ultrathin films with a stable supply of molecules by using
molecular beam epitaxy (MBE) [30,31] [Fig. 1(b)] to investigate the phenomena that occur in artificially fabricated 2D
electron systems.

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SAKODA, NOBUKANE, SHIMODA, AND TANDAPHYSICAL REVIEW B 104, 195420 (2021)

(a)

(b)

(c)

(d)

(e)

FIG. 1. (a) Crystal structure of CaRuO3 grown on NdGaO3 (110) substrate. (b) Schematic diagram of molecular beam epitaxy method.
(c) RHEED pattern of 8 Å thick CaRuO3 films. (d) Roughness of surface on 50 Å thick CaRuO3 ultrathin film observed with AFM. (e) EBSD
pattern of 50 Å thick CaRuO3 film.
II. EXPERIMENTAL METHODS
A. Samples

Ultrathin films are prepared in a customer-designed MBE
chamber (basal pressure of ∼5 × 10−6 Pa). Molecular beamsof Ru and Ca are controlled by electron impact emission
spectroscopy (EIES). The molecular beam of CaF2 is detected with a quartz crystal microbalance method in a constant
power mode. The target rates of the molecular beam are Ru
0.1 Å/s, Ca 0.3 Å/s, and CaF2 ∼ 1 Å/s, respectively. The
films are totally grown at rate of 25 Å/min. We determine
the film thickness from the deposition time. The oxygen is
supplied by O3 using a conventional ozonizer. (The ozone
concentration is about 14%.) The pressure of the O2 in thechamber is monitored with a quadrupole mass electrometer(Q-mass). The growth condition is ∼2 × 10−4 Torr for all
the films. The growth temperature is 800 °C. The home-madeMBE system is detailed elsewhere [30]. The substrate is
NdGaO3 (110) with a typical size of ∼3 mm × 6 mm. The
surface roughness of the NdGaO3 substrate is typically below
2.5 Å.

The CaRuO3 films grow along the same crystal orientation
as orthorhombic NdGaO3 substrates because the lattice constant is very close to that of NdGaO3 [31,32]. The high-quality
epitaxial films are grown by the MBE method because theexcess ruthenium supplied reevaporates as RuOx in an oxygen
atmosphere [30]. Since calcium has a high vapor pressure,the excess calcium supplied also re-evaporates from the substrate surface. Accordingly, both Ca and Ru are autoregulating
constituent elements on epitaxial growth. We reproducibly
fabricate pure and highly crystalline CaRuO3 ultrathin films
using a home-made MBE system [33] [Fig. 1(b)]. CaRuO3(110) is grown on a NdGaO3 (110) substrate with crystal
periodicity of 7.689 Å and containing two layers of RuO6
octahedra [16,17] [Fig. 1(a)].
We deposit 50 Å of CaF2 insulator as a barrier layer on
CaRuO3 ultrathin films below 20 °C as shown in the Supplemental Material [34]. It is difficult to measure the electricalresistivity of atomic layer films reproducibly without thebarrier due to the high resistivity, which destroys the film surface in the atmosphere. The barriered films have less surface

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roughness because they are not exposed to the atmosphere.
We observe the surface of the films in situ using RHEED.
The growth direction of CaRuO3 (110) on the NdGaO3 (110)substrate is confirmed by electron back-scattering diffraction(EBSD) as shown in Fig. 1(e).
B. Measurements

We employ the CaRuO3 ultrathin film to measure the x-ray
diffraction (XRD) shown in the Supplemental Material [34].
We also observe the surfaces of the films using field emissionscanning electron microscopy (FE-SEM; JSM-7000F, JEOL)
and an atomic force microscope (AFM) (SPA-400). We
measure the electrical properties in helium by using the conventional four-probe and two-probe methods for metal andinsulating samples, respectively. The electrode is solderedwith indium to destroy the CaF2 barrier layer as shown in
the Supplemental Material [34]. Some samples are measured
at temperatures of as low as 0.5 K using a home-made 3 He
refrigerator. We also measure the electrical resistivity and Hall
effect at temperatures as low as 2.2 K with a magnetic field of
up to 6 T by using a physical property measurement system(PPMS, Quantum Design). The measurement setup is shownin the Supplemental Material [34] where a six-probe method
is used to measure electrical resistivity and Hall effects. The
UPS measurements and argon ion milling are performed witha JPS-9010MC (JEOL). The data are collected at room temperature with He Iα (hν = 21.2 eV) photons. The energy
resolution is set at 50 meV.
III. EXPERIMENTAL RESULTS
A. Sample configuration

When fabricating ultrathin films, it is important to control
their thickness with a smaller than nanometer order. Figure 1(c) shows the reflection high-energy electron diffraction(RHEED) patterns of a CaRuO3 film with a thickness of
8 Å. The sharp streak pattern is observed even in nanometerthick films, which proves that the epitaxial films grow witha highly crystalline form and are flat with few impurities[28] (see the Supplemental Material [34]). The lattice matting between a NdGaO3 substrate and CaRuO3 is as small
as 0.8% and 0.5% to the c-axis and another direction in the(110) plane, respectively. Furthermore, the oxygens in the
RuO6 octahedron are in matching positions. Consequently,
the epitaxiality is excellent [31,32]. Growth reproducibility
is also good, suggesting that the self-regulation of the elements of MBE is performed efficiently, and oversupplied Ca
and Ru are reevaporated. Figure 1(d) shows the film surface
observed with atomic force microscopy (AFM). The averagesurface roughness of CaRuO3 ultrathin film is 199 pm, whichis half the size of a RuO6 conductive layer. Film thickness isconfirmed using AFM, which is very accurate as it is withina few percent error compared to MBE molecular beam rateestimates (see the Supplemental Material [34]).
B. Electrical resistivity

We measure the electrical resistivity on CaRuO3 ultrathin
films at each thickness. Film with a conventional thickness of504 Å has the same resistivity as the reported metal and isaccompanied by a magnetic transition and non-Fermi liquidbehavior [18–25] (see the Supplemental Material [34]). Surprisingly, the electrical resistivity of CaRuO3 ultrathin films
changes systematically by orders of magnitude. Figure 2(a)shows the temperature dependence of the electrical resistivity on CaRuO3 ultrathin films with thicknesses between 101
and 85 Å. Film with a thickness of 101 Å is metallic, andthe electrical resistivity increases exponentially as the film
thickness decreases. Film with a thickness of 85 Å exhibits
typical insulating behavior with maximum resistivities of
1 × 103 and 2 × 108 mcm at 300 and 4.2 K, respectively.
The magnitudes of the electrical resistivity decrease again andrevert to metallic behavior in the thinner films [Fig. 2(b)].
The magnitudes of the electrical resistivity on 71 Å thick
CaRuO3 ultrathin film are 3 × 10−1 and 7 × 10−2 mcm at
300 and 4.2 K, respectively. Despite there only being a slightdifference between the sizes of the films with thicknesses of
71 and 85 Å, there is the large change in electrical resistivity of
three orders of magnitude at room temperature and nine ordersof magnitude or more at low temperature. The dependence ofelectrical resistivity on scale has not been reported for thickfilms or bulk samples on CaRuO3 . Figure 2(c) shows electricalresistivity as a function of temperature on CaRuO3 ultrathin
films grown with different thicknesses between 50 and 35 Å.
The 50 Å thick film is metallic, and the electrical resistivity
increases as the film thickness decreases. The 35 Å thick film
exhibits its maximum electrical resistivity with an upturn inelectrical resistivity below 70 K. The electrical resistivity infilms less than 26 Å thick decreases again with typical metallic
behavior [Fig. 2(d)]. The magnitudes of electrical resistivity
increase or decrease systematically as the thin films becomethinner. Since the magnitude of the Hall coefficient also corresponds to the electrical resistivity, the electronic state changes
with film thickness (see the Supplemental Material [34]).
Figure 2(e) shows plots of electrical resistivity at 4.2 and300 K on CaRuO3 with different film thicknesses between
8 to 160 Å and a reference thickness of 504 Å. Figure 2(f)shows the corresponding plots of the sheet conductance tohighlight the conductivity. It is noteworthy that semiconducting and metallic films appear alternately. The maximum
resistivity/conductivity values are numbered in ascending order of film thickness and plotted against the film thickness[Fig. 2(g)]. The linearity fitting makes it clear that the electrical resistivity oscillates periodically depending on film
thickness. The period estimated from the slopes of resistivity
and conductivity are 25.1 ± 0.1 and 24.0 ± 1.2 Å, respectively. The “magic” thickness of 25 Å corresponds to threeunit cells of CaRuO3 (110) as shown in Fig. 1(a). The resistivity increases below the intercept thickness of ∼10 Å in thefitting. The epitaxiality is confirmed from RHEED observations in the atomic layers [Figs. 1(c)] (see the Supplemental
Material [34]). The lattice parameter of CaRuO3 is 0.5%
smaller in the [110] direction and 0.8% smaller in the [001]direction than that of NdGaO3 substrate [35]. The crystal
lattice in CaRuO3 expands due to the significant influence ofthe epitaxial strain from the NdGaO3 (110) substrate latticeover several atomic layers from the interface.
The temperature dependence of the electrical resistivity
on the 85 Å thick film is well fitted by the variable range

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FIG. 2. Thickness dependence of electrical resistivity on CaRuO3 ultrathin films. (a), (b) Electrical resistivity on CaRuO3 thin films withthicknesses between 101 and 71 Å as a function of temperature. (c), (d) Electrical resistivity on CaRuO3 thin films with thicknesses between
50 and 26 Å as a function of temperature. (e), (f) Electrical resistivity and sheet conductance as a function of thickness on CaRuO3 films at 4.2
and 300 K, respectively. (g) Dependence of film thickness on maximum resistivity/conductance at low temperature. (h) Logarithm of electricalconductance as a function of T 1/2 (lower), and T 1/3 (upper) on 85 Å thick CaRuO3 ultrathin film. The inset shows the current-voltage curve at
4.2 K.
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CaRuO3 ultrathin films exhibit crystal anisotropy, and they
are not seen or are greatly suppressed in the CaRuO3 (001)ultrathin films on a NdGaO3 (001) substrate. The crystal
anisotropy of the quantum phase transition is thought tooriginate from the anisotropy of the electronic state. The
anisotropic electronic state of low-dimensional FS is the key
to the metal-insulator transitions.
D. Photoelectron spectroscopy

FIG. 3. Properties of CaRuO3 (001) grown on NdGaO3 (001)substrate. (a) RHEED pattern of CaRuO3 (001) with thickness of
25 Å. It shows a sharp streak pattern, which means a flat surface andhigh crystallinity. (b) EBSD pattern of 500 Å thick CaRuO3 (001)film. CaRuO3 grows in the [001] crystal direction on a NdGaO3 (001)substrate. (c) Electrical resistivity as a function of thickness at 300 K
and 4.2 K.

hopping (VRH) of ρ ∼ exp[(T0 /T )1/(d+1) ] with a large excitation energy of T0 ∼ 26 000 K [Fig. 2(h)]. The exponential
factor d = 1 proves that there is insulation with a strong
Coulomb force. The large cyclotron effective mass observed
thanks to the Shubnikov-de Haas effect [24] also indicates that
CaRuO3 has a heavy fermion state. CaRuO3 is close to thequantum critical point to consider non-Fermi liquid behavior[19–26], which is adjacent to the Mott insulating phase. It canbe interpreted to mean that CaRuO3 is similar to the Mott
insulator Ca2 RuO4 [36].
C. Anisotropy of thickness dependence

We fabricated CaRuO3 ultrathin films on NdGaO3 (001)substrate to investigate the scale-dependent anisotropy. The
epitaxiality of CaRuO3 on NdGaO3 (001) is excellent sincea sharp streak pattern can be observed at a film thickness of
25 Å similar to the growth on the NdGaO3 (110) substrates[Fig. 3(a)]. The growth of (001) surface of CaRuO3 is confirmed by EBSD [Fig. 3(b)]. We grow CaRuO3 (001) ultrathin
films with thickness of 10–125 Å and measure the temperaturedependence of electrical resistivity of each film. The electricalresistivity at 4.2 and 300 K is plotted for each film thickness[Fig. 3(c)]. The electrical resistivity of CaRuO3 is extremely
high at a film thickness of about 10 Å, which is supposed tobe due to the epitaxial strain from the substrate on the (001)growth causing the lattice to become larger as seen in the (110)growth. No alternations of the electrical resistance with a
25 Å period are observed in the range of film thicknesses
above 15 Å. Namely, the metal-insulator transitions on

We perform ultraviolet photoelectron spectroscopy (UPS)on CaRuO3 ultrathin film etched by using argon-ion millingin situ to reproduce the thickness dependence of the properties
in one sample. Figure 4(a) shows the overall spectrum of the
CaRuO3 ultrathin film etched every second from 0 to 15 s.
The initial film thickness is 110 Å. The peak derived fromthe oxygen state seen around a binding energy (BE) of 5.6
eV is high in the nonetched film [37]. Considering the probe
depth of a few angstroms realized with He I phonons, thecalcium ions on the surface of the film form strong bonds withoxygen. It shows that the CaRuO3 surface is oxidized by theatmosphere.
The valence band represents an insulating layer with low
conduction. The oxygen peak becomes sharper after 1 s of
etching. The noticeable increase in the valence band below
3 eV exhibits the CaRuO3 spectrum. After 7 s of etching,
the optical intensity reaches its maximum value. It starts todecrease after 8 s, and no change is observed after 11 s, whichindicates that the CaRuO3 is completely removed.
Figure 4(b) shows a close-up spectrum of another CaRuO3
film with a BE between 0.5 and 3.5 eV to measure in detailthe result for etching performed every half second. Etching tends to increase the intensity with good reproducibility
compared with the previous sample. The optical intensity
tends to increase with the etching time in the energy rangeof BE = 0.5−3.0 eV (see the Supplemental Material [34]).
In general, as the thickness of the film becomes thinner, theconduction becomes lower, and thus the optical intensity decreases. The increase in its UPS intensity essentially indicatesthat the CaRuO3 insulator is broken down and metallized.
A crossover can be observed between 0.9 and 1.6 eV after
1.0–2.0 s of etching. The hump was reported to originate from
Ru-4d electrons as observed by angle resolved photoelectron
spectroscopy [26,38]. It has been reported that phonons, polarons, or magnons cannot contribute to the hump becauseof the large energy [38], which can be confirmed from thelarge T0 .
Next, in Fig. 2 we confirm the reproduction of the film
thickness dependence of the electrical conduction in termsof optical conductivity. Figure 4(c) compares the sheet conductance as a function of thickness at 300 K and the opticalintensity of UPS at 1.1 eV as a function of etching time.
The arrows represent the coincidence between the increase in
optical intensity and the peak of the electrical conduction at
etching time t = 1.0, 4.0, and 6.0 s. Finally, it is reproducibly
proven on one etched film that the periodicity of the thickness
in terms of optical intensity is the same as that for electrical conductivity. The periodicities show good agreement at
BE = 1.1 eV where the hump is prominent, which reveals thatsuppression on the Ru-4d orbital is related to insulation.

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SAKODA, NOBUKANE, SHIMODA, AND TANDAPHYSICAL REVIEW B 104, 195420 (2021)

FIG. 4. Correspondence of periodic transitions in optical intensity to a CaRuO3 ultrathin film etched by argon ion milling. (a) Overall UPS
spectra of 110 Å thick CaRuO3 ultrathin film etched from 0 to 15 s in situ. (b) Details of spectra with BE between 0.5 and 3.5 eV of another110 Å thick CaRuO3 ultrathin film etched every 0.5 s from 0 to 8.5 s. The shaded area highlights the large increase in optical conductivity.
(c) Comparison of electrical conductance as a function of film thickness and optical intensity as a function of etching time. The arrows indicate
the correspondence to the periodicity of the oscillating transitions.
IV. DISCUSSION

What is the mechanism of the metal-insulator transitions
that oscillate with thickness? The important features are that(1) the transitions alternate with the magic thickness periodof 25 Å corresponding to three times the thickness of a
CaRuO3 (110) unit cell, (2) the transitions are accompanied
by a large excitation energy equivalent to a few electron volts,and (3) anisotropy, namely, they can be clearly seen only
in CaRuO3 (110) growth. Until now, it has been believedthat oscillations of properties depending on scale are caused
by quantum size effects [1–3]. CaRuO3 ultrathin films form
typical one-dimensional quantum wells sandwiched by thesubstrates and barriers. However, the activation energy that
accompanies metal-insulator transitions is too large to be interpreted as quantum wells within a bandwidth as small as∼200 meV in CaRuO3 [26]. Therefore, the size effect causedby the quantum wells does not dominate the scaling dependence in this paper. When the strong Coulomb interaction in
the quantum critical phase is taken into consideration, it isnecessary to discuss the Mott insulation for a large excitationenergy. The Fermi wavelength of the cylindrical FS in the[110] direction has been observed between 22 and 33 Å in
ARPES experiments [26].
Although typical Mott insulators appear in half fillingbands, compounds that have no half filling bands also become

Mott insulators as a result of the stripe correlations of spinsand carriers [39]. The concept of commensurability on stripe
Mott insulation is suitable for 2D systems with several unit
cells. It is considered that the Mott insulation on CaRuO3(110) ultrathin films is dependent on the commensurability on
stripe correlations when the thickness is a multiple of threeunit cells [Figs. 5(a) and 5(c)]. Considering the period of
25 Å for the oscillating transitions, it is assumed that there
is a single RuO6 layer of domain wall for every three unit
cells. The other RuO6 layers form the Mott insulator with
antiferromagnetism. Since electrons are left over except forthe multiple of the magic thickness, the Mott insulating stripe
on CaRuO3 is dissolved and reverts to metal [Fig. 5(b)].
The stripe correlations of spins and carriers with three time
periods are triggered by Peierls instability [40–44]. CaRuO3
consists of a square pole FS [26], which is advantageous fornesting properties. Since the wavenumber k[110] of the FS
corresponds to one-third of the Brillouin zone, the energy gainfrom the stabilization of Peierls transition is large enough toform a period of 25 Å in real space. The Peierls instability
is proven by the anisotropy of the metal-insulator transitions.
They are clearly observed on CaRuO3 (110) where the nesting
property is excellent in the growth direction. By contrast, they
can be hardly seen on CaRuO3 (001) films where the pole FS
has an open orbit in the growth direction [001], i.e., it cannot

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PHYSICAL REVIEW B 104, 195420 (2021)

FIG. 5. Commensurability schematic of Mott insulation on CaRuO3 (110) ultrathin films. The film thicknesses are (a) three units, (b) four
units, and (c) six units. The circles indicate the Ru ions. The closed circles indicate the domain walls occupied by electrons or holes. The
open circles indicate the Mott insulating localized electrons. The arrows indicate the antiferromagnetism state. The circles with diagonal lines
indicate the metallic state of nonfilled bands.

take any nesting vectors. This is definitive proof that the size
effect is related to this anisotropic Fermi surface.
Namely, the metal-insulator transitions are caused by
the dimensional restrictions in different directions caused
by each 2D-FS and the ultrathin films. The metal-insulatortransitions can be rephrased as the incommensurabilitycommensurability transitions that occur only under clear
boundary conditions. No scaling dependences on CaRuO3
have been discovered in thick films or bulk samples becauseof the mean free path of electrons.
Finally, we will also mention other possible mechanisms.
There is a possibility that the Kondo effect caused by Ru
impurities may appear [45], and that Anderson localizationis enhanced in the 2D state by ultrathin films [46]. However,
we considered the large changes in electrical resistivity andeliminated the possibility that these were the nature of thescale dependence. The RHEED patterns at each film thickness removed the possibility of structural transition. Pressure
experiments [10] and thin films [11] on Ca2 RuO4 have shownthat the metal-insulator transition is closely related to thelattice. Assuming that the Mott-Hubbard model can be applied
to the novel size effect of CaRuO3 , it is consistent the metalinsulator transition will involve a change in the lattice.

shows that their surface roughness was controlled at 199 pm.
We measured the temperature dependence of the electricalresistivity at each film thickness and found that the magnitude of the electrical resistivity changes systematically. We
observed that electrical resistivity oscillates with a thicknessof 25 Å, and changes by three and nine orders of magnitude
at room temperature and at low temperature, respectively.
We observed the same periodicity with UPS by etching theultrathin film. We establish “scales” as a new parameter for
quantum phase transitions following the angle [47].
ACKNOWLEDGMENTS

We grew CaRuO3 ultrathin films with the MBE method.
We have fabricated thin films that exhibit sharp streak patternsof RHEED at thicknesses above 8 Å. The AFM observation

The authors thank Prof. M. Naito, K. Ichimura, R. Suzuki,
N. Matsunaga, T. Kurosawa, Dr. Y. B. Nanao, and K. Nakatsugawa for valuable discussions and support. Part of this work
was conducted at the Laboratory of XPS Analysis, Joint-use
Facilities, Hokkaido University. The Open Facility of theInstitute for Catalysis was used for the UPS. This study isfinancially supported by the Takahashi Industrial and Economic Research Foundation, Japan Prize Foundation, Murata
Science Foundation, Yashima Environment Technology Foundation, Inamori Foundation, Iketani Science and Technology
Foundation, Samco Science and Technology Foundation,
Foundation for Interaction in Science & Technology, Izumi
Science and Technology Foundation, Ito Science Promotion
Association, and Sumitomo Electric Group SRC Foundation,
and Nippon Sheet Glass Foundation for Material Science andEngineering.

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