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OPEN

received: 25 July 2016
accepted: 16 December 2016
Published: 23 January 2017

Chern structure in the Boseinsulating phase of Sr2RuO4nanofilms
Hiroyoshi Nobukane1,2, Toyoki Matsuyama2,3 & Satoshi Tanda2,4
The quantum anomaly that breaks the symmetry, for example the parity and the chirality, in thequantization leads to a physical quantity with a topological Chern invariant. We report the observationof a Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms by employing electric transport.
We observed the superconductor-to-insulator transition by reducing the thickness of Sr2RuO4 single
crystals. The appearance of a gap structure in the insulating phase implies local superconductivity.
Fractional quantized conductance was observed without an external magnetic field. We found ananomalous induced voltage with temperature and thickness dependence, and the induced voltage
exhibited switching behavior when we applied a magnetic field. We suggest that there was fractional
magnetic-field-induced electric polarization in the interlayer. These anomalous results are related totopological invariance. The fractional axion angle Θ = π/6 was determined by observing the topologicalmagneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms.
The mathematical structure characterized by Chern numbers1 has yielded very important findings in bothcondensed-matter and high-energy physics2. The quantum Hall effect in graphene provides the quantized Hall
conductance of σ H = (p/q) e 2/h with p and q coprimes3. The quantization of the Hall current and anyonic particles with exotic mutual statistics can be explained by the Chern-Simons (CS) term in (2 +​  1)-dimensional topological field theory, which is known as the parity anomaly4–6. In 3 +​ 1 dimensions, the neutral pion decay7,8 andthe creation of excitation momentum by quantized vortices in the superfluid 3He9 are described by the chiralanomaly. However, as yet there has been no experimental evidence of quantum anomalies and Chern structuresin superconductors. Recently, the magneto-electric effect in topological superconductors and insulators has been
predicted theoretically from the Chern-Pontryagin term (topological Θ​-term with Θ​  =​  ±​π) in 3 +​  1 dimensions10,11. The Chern structure in superconductivity is interesting in itself and may also have implications regarding the esoteric physics of quantum chromodynamics (axion electrodynamics)12,13 in condensed-matter
experiments. In addition to the purely scientific interest that it arouses, the Chern structure may provide the basis
for new applications to magneto-electric coupling devices and for the development of the topological quantum
computation of non-Abelian statistics14.
Layered perovskite Sr2RuO4 is a leading candidate for a spin-triplet and chiral p-wave superconductor inquasi-two-dimensional electron systems15, and is also known as a Chern superconductor with a non-zero Chern
invariant. The spontaneously broken time-reversal and parity symmetry realize novel topological quantum phenomena such as zero-magnetic-field quantum Hall effects16–18, gapless Majorana excitations in an edge or thecore of vortices19 and the non-Abelian statistics of half-quantum vortices20. However, the chiral-multi-domains
in millimeter-scale Sr2RuO4 obscure these novel phenomena. We have reported that the current-voltage (I–V)
curves in the microscale chiral single domain of Sr2RuO4 with submicron thickness violate parity due to theexcitation of the Majorana-Wyle fermions along the one-dimensional chiral edge current21,22. To clarify the Chern
structure through quantum transport in units of e2/h in two-(or quasi-two-) dimensional chiral superconducting
layers, we have investigated electric transport properties by using chiral single domain size Sr2RuO4 with nanoscale thickness23. Specifically, in this paper, we report the fractionalized Chern structure (number) in the quantum

1
Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan. 2Center of Education and Research for
Topological Science and Technology, Hokkaido University, Sapporo, 060-8628, Japan. 3Department of Physics, Nara
University of Education, Nara 630-8528, Japan. 4Department of Applied Physics, Hokkaido University, Sapporo
060-8628, Japan. Correspondence and requests for materials should be addressed to H.N. (email: nobukane@sci.
hokudai.ac.jp) or T.M. (email: matsuyat@nara-edu.ac.jp) or S.T. (email: tanda@eng.hokudai.ac.jp)

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critical region from the results of the anomalous properties, which are revealed by reducing the Sr2RuO4 thickness
to the nanometer range.
One unsolved problem in Sr2RuO4 systems is the two superconducting phases with Tc ~ 1.5 and 3 K. Althoughpure Sr2RuO4 single crystals exhibit a Tc of about 1.5 K, enhancement to about 3 K has been reported in
Sr2RuO4-Ru eutectic systems24. However, recent investigations have found that, even in pure Sr2RuO4 without Ru
inclusions, an enhanced Tc of around 3 K is observed when measuring uniaxial pressure effects along the c axis25,
strain effects26 and the properties near the lattice dislocations27. As regards this discrepancy, electric transportmeasurements in nanoscale thin films of Sr2RuO4 single crystals allow access to both topological quantum states
and the pairing mechanism itself in chiral p-wave superconductors.
In this paper, we report the emergence of a Chern structure in the Bose-insulating phase of Sr2RuO4 single
crystal nanofilms based on the anomalous transport properties observed for the in-plane and interlayer directions. By reducing the Sr2RuO4 thickness to the nanometer range, we found that a fractional quantum Hall resistance of h/4e2 −​  h/2e2 occurred as a consequence of the spontaneous Hall current without an external magnetic
field. The gap structure below 3 K shows localized superconducting islands connected by tunnel junctions. The
anomalous induced voltage and the switching behavior were observed as a function of temperature and thickness
under zero bias current for an applied magnetic field parallel to the c axis. The applied magnetic field induced
electric polarization in the interlayer of Sr2RuO4 nanofilms. In Sr2RuO4 with a nanoscale thickness, we suggested
that the fractional topological magneto-electric effect occurs in three (quasi-two) dimensions, which is characterized by the fractional axion angle (coefficient) Θ​  =​  π/6 of the E · B term in the chiral anomaly.

Results

Figure 1(a) shows the temperature dependence of the longitudinal resistivity ρxx for various thicknesses of exfoliated Sr2RuO4 films. R/layer is resistance per square per RuO2. In general, bulk (thick) superconductors exhibit
zero longitudinal resistivity below Tc. We have observed zero resistivity below Tc =​ 1.59 K for microscale Sr2RuO4
with a thickness of 340 nm, which is consistent with the Tc of bulk Sr2RuO4 crystals15,24. Samples with a thicknessof 147 and 470 nm exhibited a slight drop in resistivity around 1.5 ~ 3 K, and showed non-zero resistivity below Tc.
The result shows that the flow of vortices can be caused by quantum fluctuations of the superconducting phase28,29.
Interestingly, the insulating behavior was observed in samples A and B with nanoscale thickness. It has beenreported that the effect of a negative pressure acts on thin films as the thickness of the exfoliated films decreases
to the nanometer range30. The pressure plays a key role in modifying the electric properties of the family of ruthenium oxides31. Thus we presume that the transition from superconductor to insulator appeared in Sr2RuO4 nanofilms as a result of reducing sample thickness to the nanometer range.
The two-dimensional superconductor-insulator transition allows a quantum resistance near the quantum critical point due to superconducting phase fluctuations32–34. Figure 1(b) shows the temperature dependence of theHall resistance Rxy and longitudinal resistance Rxx in sample A with a thickness of 17 nm. With decreasing temperature, the Hall resistance increased with a log T dependence, and reached about 12.1 kΩ below 0.8 K.
Interestingly, in the absence of an external magnetic field, we measured a Hall resistance of 12.1 kΩ, which is close
to the quantum resistance of h/2e2. A Hall resistance of Rxy =​ 6.8 kΩ ~ h/4e2 was also observed in sample B (seeSupplementary Fig. S1). The quantum Hall resistance was reproduced in other Hall electrodes and samples in theorder of 1 ~ 20 kΩ. We note that the Rxx values of samples A and B were 5.3 kΩ ~ h/5e2 and 6.1 kΩ ~ h/4e2, respec2
2
tively, at lower temperature. These values are very close to the universal resistances of Rxx+ Rxy= (h/(2e)2 )2 in a
two-dimensional superconductor-insulator transition35,36. The universal resistance requires the existence of both
localized Cooper pairs and moving vortices on the insulating side of the quantum phase transition, which is
known as a Bose insulator. Thus we think that the Hall and longitudinal quantum resistance in Sr2RuO4 nanofilms
is related to the dynamics of Cooper pairs and vortices in the Bose-insulating phase of two dimensions. The Rxyand Rxx values in the thick samples with thicknesses of a few hundred nanometers exhibited much smaller valuesof 0.1 ~ 1Ω than the quantum resistance in the thin film samples. We need to determine exact thickness dependence of quantized values of two dimensional samples and thick samples in future works.
We investigated the superconducting properties in the insulating phase of Sr2RuO4 nanofilms at low temperature. Figure 1(c) shows the I–Vxy characteristics of the Hall bar geometry, and dI/dVxy as a function of
the Hall voltage Vxy in a zero magnetic field at several temperatures, which is vertically shifted for clarity (seeSupplementary Fig. S2 for dI/dVxx −​  Vxx). Surprisingly, below 3 K, clear gap structures were observed in boththe Hall and the longitudinal conductance spectra. The temperature dependence of the superconducting gap
extracted from the coherence peak width in the tunneling spectra is shown in the inset of Fig. 1(c). The result
is comparable to the superconducting gap size found in previous reports on tunneling spectroscopy in Sr2RuO4
systems37–41. The appearance of the gap structure above Tc =​ 1.5 K reminds us of the pseudo-gap state in cuprate
superconductors and the 3 K phase in Sr2RuO4 systems24–27. The result shows that the local superconducting
islands connected by small Josephson junctions can emerge even in the insulating phase of Sr2RuO4 nanofilms
below 3 K due to the quantum fluctuation of the superconducting phase θ as shown in Fig. 1(e). Thus, Vxy as wellas Vxx is dependent on the current. The field dependence of the tunneling spectra for sample A at 0.46 K is shownin Fig. 1(d). The observation of the gap behavior at 4 T provides evidence for local superconductivity surviving up
to high fields. Here a 400-nm-thick Sr2RuO4 single crystal (sample C) shows neither the suppression of Tc nor anenhancement to 3 K (see Supplementary Fig. S3).
Quantum fluctuations near a quantum critical region bring out the topological properties of systems. To
examine the topological magneto-electric coupling in the Bose-insulating phase of Sr2RuO4 nanofilms, we measured the voltage V with Hall-bar geometry and the longitudinal voltage V′​at zero bias current. Figure 2(a) shows
the magnetic field dependence of the voltage V when a magnetic field is applied parallel to the c axis from azero magnetic field up to ±​7 T for sample A. Interestingly, we found an anomalous induced voltage of about|Δ​V| =​ 62 V in a zero magnetic field at 0.43 K. In the longitudinal geometry, there was an induced voltage V′​ of
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Figure 1. Superconductor-insulator transition driven by varying thickness and local superconductivity in
Sr2RuO4 nanofilms. (a) Temperature dependence of the resistivity ρxx for different thicknesses of Sr2RuO4
single crystals. R/layer is resistance per square per RuO2 layer. The dotted horizontal line represents(h/4e2) =​ 6.45 kΩ. (b) Scanning electron micrographs of the top and side views of sample A. Temperaturedependence of Rxy and Rxx. The dotted horizontal lines are a guide for the eye. (c) Vxy −​  I characteristics forsample A at temperatures in a zero magnetic field. dI/dVxy as a function of Vxy. The inset shows the temperaturedependence of the superconducting gap Δ​. (d) Tunneling spectra dI/dVxy for sample A in various magnetic
fields. (e) Schematic of local superconducting islands weakly coupled by tunneling junctions, where θ is thesuperconducting phase. This may be similar to small Josephson junction arrays.

|Δ​V′​| =​  40 μV. The spontaneous voltage was reproduced in different terminals. In the Bose-insulating (local
superconducting) state below 3 K, the anomalous voltage appeared as shown in the inset of Fig. 2(b), which isconsistent with the V −​  B characteristics in Fig. 2(a). Figure 2(b) shows the thickness dependence of the induced
voltage at lower temperature. As the sample thickness t was reduced, the induced voltage increased, which is fitted
well by the relation V =​  1/t. Since spontaneous voltage is related to sample thickness, we can eliminate the contribution of the thermoelectric voltage and a junction at the Au/Sr2RuO4 interface or at a microcrack. Furthermore,
the switching behavior of an induced voltage was observed in the region between ±​1.0 and ±​5.8 T. The solid redline in Fig. 2(a) is the average result for the B −​  V characteristics. Figure 3(a) shows the magnetic field dependence of the induced voltage and the switching voltage at various temperatures. With increasing temperature, theanomalous induced voltage and the switching voltage were gradually suppressed, and vanished above 3 K. In sample C with a thickness of 400 nm, we also observed an induced voltage of 1 μV and switching behavior under anapplied magnetic field as shown in Fig. 2(d). The anomalies became smaller than the results observed for sample
A. Table 1 summarizes the properties obtained by varying the thickness.

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Figure 2. Topological magnetic-field-induced electric polarization. (a) Dependence of induced voltage
on magnetic field at 0.43 and 4.3 K with zero bias current. Arrows represent the magnetic sweep direction
from zero magnetic field to ±​7 T. The solid red curve represents the average result for the measured data. (b)Thickness dependence of induced voltage at lower temperature. The dotted line represents the fitting result,which is described well by V =​  1/t. The inset shows the temperature dependence of the induced voltage. (c) The
anomalous switching voltage VSW extracted from the B −​  V curves in (a). (d) Magnetic field dependence of V
and VSW for sample C.

Discussions

To analyze the switching phenomena in more detail, we subtract the average B −​  V curves from the measured
B −​  V characteristics. The results for sample A are shown in Figs 2(c) and 3(b). Here the voltage VSW represents
the switching voltage component of the induced voltage. As the magnetic field increases, the anomalous switching voltage VSW increases above ~±​1 T. The VSW for the applied magnetic field reaches its maximum value near±​3.5 T, and then decreases. Intriguingly, the switching voltage was clearly observed below 1.5 K. We think that theobservation of this anomalous switching voltage is related to the intrinsic properties of the chiral p-wave superconductor Sr2RuO4, because the feature appears below a Tc of about 1.5 K in bulk Sr2RuO4.
We discuss the enhancement of the critical magnetic field in relation to the existence of localized superconducting islands of Sr2RuO4. In sample C as shown in Fig. 2(d), the magnetic field of 0.04 T caused the anomalous
V and VSW to vanish, which is consistent with μ0Hc2 in bulk Sr2RuO4. On the other hand, in Figs 2(a) and 3(a), theanomalous voltage is induced even in a magnetic field beyond μ0Hc2 reported for pure bulk Sr2RuO4. To reveal
whether or not this anomalous behavior is an intrinsic characteristic of Sr2RuO4, we need to consider the physicalproperties of the 3 K phase. The 3 K superconductivity in Sr2RuO4-Ru systems induces the enhancement of theupper critical field to µ0 H c 2//c (0) ≈ 1.5 T and µ0 H c 2//ab(0) ≈ 4 T15. In general, the critical magnetic field in mesoscopic superconductors becomes larger than that in bulk superconductors. We estimated µ0 H c 3//c (0) ≈ 2.6 T andµ0 H c 3//ab(0) ≈ 6.8 T using Hc3 =​  1.7 Hc242. This may be comparable to the result for the B −​  V characteristics in
our nanofilms because we observed the gap structure in a high field of 4 T as shown in Fig. 1(d).
Now let us consider the switching behavior of the resistivity (voltage) in superconducting systems.
The Hall resistivity at very low temperature exhibited erratic switching in the vicinity of the quantum
superconductor-to-insulator transition in La2−xSrxCuO4, which is considered an indication of the charge-cluster
glass state43. In the superconducting state of Sr2RuO4, the dynamics of the chiral domains generates switching
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Figure 3. Temperature dependence of E · B value. (a) Magnetic field dependence of the anomalous voltage atvarious temperatures with zero bias current from zero magnetic field to 7 T. The E · B value in a low magnetic
field (the blue region A) is equivalent to that in the red region A◊ caused by voltage switching at temperatures
below 2 K. (b) Temperature dependence of VSW. (c) Temperature dependence of the E · B integral value. The data
were fitted by an exponential curve.
Sample A

Sample C

Thickness (nm)

17

400

Tc (K)

3

1.5

Rxy (kΩ)12

1 ×​  10−3

Induced V (μV)

62

1

B at maximum VSW (T)

3.5

0.02

Δ​E · Δ​B (h/e2)

6

0.5 ×​  10−3

Table 1. Summary of the properties of Sr2RuO4.

behaviors as a function of magnetic field or time44. Our anomalous switching may resemble these results because
the domains in the Bose-insulating phase of Sr2RuO4 fluctuate in space and time. At present, some possible explanations for the results are conceivable. Below, we discuss in detail a topological interpretation in terms of ourresults as an interesting possibility.
To understand the origin of the anomalous behaviors, we address (I) the fractional quantum Hall conductancein the conducting layer without a magnetic field, (II) the fractional magnetic-induced electric polarization in theinterlayer, and (III) the integral value of E · B in the topological term. First, let us discuss the fractional quantum
Hall conductance in a zero magnetic field in Sr2RuO4 nanofilms. From Rxy =​ 12.1 kΩ and Rxx =​ 5.3 kΩ for sample
A, the sheet Hall conductance σxyns =1 = (1/22.6) e 2/h ∼ (1/24) e 2/h per RuO2 layer was determined by using theScientific Reports | 7:41291 | DOI: 10.1038/srep41291

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n s =1
relation Rxy= ρxy⁎ d , ρxy⁎ = (σ xy )−1 = (ρ xy (ρxx2 + ρxy2 ))−1, d =​ 6 Å (=​c/2). By considering the number of sheetsn s −1
ns, we represent the Hall conductance as σxyns = σxyns =1ns = (ns /24) e 2/h = (Rxy) . Why do Sr2RuO4 nanofilms
exhibit Hall conductance quantized in the unit of conductance quantum G0 ≡ e 2/h? The concept of chiral p-wave
superconductivity can be developed by the induced CS-term of the effective Lagrangian in topological field theory16,17. The CS-term induces the existence of a spontaneous Hall current in a zero magnetic field perpendicular
to the bias current direction. However, the quantum Hall effect in Sr2RuO4 has yet to be observed experimentallyfor the following reasons. The Hall resistance in a thick sample becomes smaller than that in a thin film sample,
and the observation of the ensemble averaging of the Hall current in multi-chiral domains is complicated. With
respect to these issues, an important solution is for the sample to consist of nanoscale thin films of ~10 layers2,18
and for the chiral single domain size to be ~1 μm21. Our samples satisfy these conditions. Thus, by using Sr2RuO4nanofilms, we can observe the fractional quantum Hall conductance near the quantum critical region.
Using the result shown by the fitted slope of |Δ​V|/Δ​B in Fig. 2(a), we discuss the contribution of the electric
polarization under a magnetic field in the Sr2RuO4 interlayer. We assume that our layered sample is a superconducting bilayer system in order to discuss the possibility of magneto-electric polarization. The capacitance
C =​  εIA/d =​ 10 fF of the interlayer is estimated, where εI/ε0 ~ 10 is the interlayer dielectric constant, d (=​6 Å) is theinterlayer distance in Sr2RuO2, and A is the area 0.14 μm2 between the electrodes. We determined the effective
electric charge Q∗ ~ 8 e from the induced voltage of |Δ​V| =​  63 μV. Moreover, we obtained the effective magnetic
flux Φ⁎ ∼ 206 Φ0 from the relation ∆V /∆B = Q ⁎d /εI Φ⁎, where Φ0 = h/2e is the magnetic flux quantum. We
found the fractional magneto-electric polarization P /B = (1/12) e 2/h ( − (1/12) e 2/h) from the slope in the positive(negative) magnetic field. Surprisingly, the fractional coefficient of the magnetic-field-induced electric polarization is equivalent to that of the Hall conductance in the bilayer film.
Below, we consider the topological magneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms
to understand the relationship between fractional Hall conductance and electric polarization. The chiral anomaly 7,8 in the (3 +​ 1 )-dimensional topological field theory can introduce an additional Θ​ - term
Θ e2SΘ = 2π h ∫ d 3xdt E ⋅ B10,11. This topological term denotes the existence of the magneto-electric effects. Namely,2
an applied electric field generates a magnetic polarization M = Θ e E, and an applied magnetic field generates an
2

2π h

2

electric polarization P = Θ e B. The quantum Hall current J H = Θ e E flows as the contribution of the topolog2π h
2π hical surface state in the (3 +​ 1)-dimensional magneto-electric effect. For strongly correlated electron systems, thefractional parameter Θ​  =​  p/q with p, q odd integers is predicted by analogy with fractional quantum Hall
effects45,46. This model of fractionalization in the chiral anomaly appears to be beneficial in terms of understanding our anomalous results.
Furthermore, we discuss the possibility of the fractionalization of the topological Θ​-parameter. Using theexperimental results, we discuss the integral value ∫ d 3xdt E ⋅ B in the topological Θ​-term. We found that thevalue of E (=​Δ​V/d) · B represented by the blue square region A in Fig. 3(a) is equivalent to that of E · B represented by the red rhombic region A◊ in Fig. 3(a,b). An important point is that the obtained value of E · B is 6(h/e2)
at 0.43 K. Similarly, at temperatures below 2.0 K, we estimated the value of E · B in both the square region in a low
magnetic field and the rhombic region provided by the voltage switching. We confirmed that the E · B values are
the same in the blue and red regions at each temperature. The correspondence of the E · B value is also reproducedin sample C in Fig. 2(d). This means that the induced voltage in a low magnetic field is closely related to the occurrence of the switching voltage under a magnetic field, and these are connected to the topological invariant.
Figure 3(c) shows the temperature dependence of the E · B value. The data points are fitted by an exponential
curve. We believe that the E · B value exists in the 6(h /e 2) − 12(h /e 2) region. According to the fitting curve, at
T =​ 0, (III) the E · B value is about 12 h/e2, which is comparable to (I) the zero-magnetic-field quantum Hall conductance σxyns =2 = (1/12) e 2/h and (II) the magnetic-field-induced electro-polarization P /B = (1/12) e 2/h. By substituting ∫ d 3xdt E ⋅ B = 12h /e 2 into the topological term SΘ, we obtained the fractional angle Θ = π N , where N
26
2
is an integer multiple. For the fractional angle Θ​  =​  π/6, the quantum Hall conductance σ xy = Θ e = 1 e , and
2
π
h
6
2
h
2
2
electric polarization P = Θ e B = 1 e B are discussed theoretically10,46. This is consistent with our experimental
2π h
6 2h
observations. Thus, we suggested the presence of the fractional topological magneto-electric effect in Sr2RuO4
layers using the results of both the fractional Hall conductance and the fractional magneto-electric polarizationin the fractional axion angle. Namely, these observations correspond to the fractional Chern structure caused by
the quantum anomaly in Sr2RuO4.
In conclusion, we have detected the emergence of the Chern structure in Bose-insulating Sr2RuO4 nanofilms byobserving the fractional Hall conductance on the surface and the fractional electric polarization in the interlayer. Ina zero magnetic field, a quantized fractional Hall resistance was observed in the local superconducting state below
3 K. Under zero bias current, we found the anomalous induced voltage and the switching behavior of the induced
voltage for an applied magnetic field parallel to the c axis. The applied magnetic field generated electric polarizationin the interlayer of Sr2RuO4. The results suggest the presence of the fractional topological magneto-electric effect in
Sr2RuO4 nanofilms. The fractional axion angle Θ​  =​  π/6 in the topological Θ​-term was also determined.

Methods

To obtain nanoscale Sr2RuO4 thin films, we synthesized Sr2RuO4 single crystals with a solid phase reaction, andselected single crystals with no embedded Ru metal and with homogeneity by observing optical microscope
images, chemical composition and crystal orientation47. Sr2RuO4 single crystal nanofilms were exfoliated on a
SiO2(300 nm)/Si substrate. We then fabricated gold electrodes using standard electron beam lithography methods. Scanning electron micrographs of the Sr2RuO4 nanofilms (samples A and B) are shown in Fig. 1(b) and
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Fig. S1(a). The sample thickness was determined from scanning electron micrographs obtained with a sample
holder tilted at 70-degrees. The electric transport properties of several samples with thicknesses of 17–470 nm
were measured by the four-terminal method using a homemade 3He refrigerator. All leads were equipped with
RC filters (R =​ 1 kΩ and C =​ 22 nF). The longitudinal and Hall voltages and the differential conductance were
measured with a nanovoltmeter (2182, Keithley) and a lock-in-amplifier (5210, Princeton Applied Research),
respectively. The up and down magnetic field sweep rate was 0.102 mT/sec.

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Acknowledgements

We thank Y. Asano, K. Inagaki, T. Honma, K. Ichimura, S. Takayanagi, K. Yamaya, N. Matsunaga, and K. Nomura
for experimental help and useful discussions. This work was supported by JSPS KAKENHI (No. 25800183 andNo. 26287069) and Takayanagi Memorial Foundation.

Author Contributions

H.N. performed the experiments and drafted the manuscript. T.M. and S.T. contributed to the interpretation of
the results. All authors read and approved the final manuscript.

Additional Information

Supplementary information accompanies this paper at http://www.nature.com/srep
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Nobukane, H. et al. Chern structure in the Bose-insulating phase of Sr2​RuO4​ nanofilms.
Sci. Rep. 7, 41291; doi: 10.1038/srep41291 (2017).
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