PHYSICAL REVIEW B 83, 144502 (2011)

Majorana-Weyl fermions in the chiral superconductor Sr2 RuO4
Hiroyoshi Nobukane,1,* Akiyuki Tokuno,1,† Toyoki Matsuyama,2 and Satoshi Tanda1
1

Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan2
Department of Physics, Nara University of Education, Nara 630-8528, Japan(Received 15 February 2010; revised manuscript received 10 August 2010; published 4 April 2011)
We found Majorana-Weyl fermions in a chiral superconductor Sr2 RuO4 . The current-voltage curves reveal
anomalous behavior: The induced voltage is an even function of the bias current. The zero-bias conductance peak
was observed through the tunnel junction at the edge. The magnetic-field dependence suggests the excitation of
the Majorana-Weyl fermions along the closed chiral edge current of the single domain under a bias current. We
also discuss the relationship between a change in the chirality and the spontaneous magnetization of the single
domain Sr2 RuO4 .
DOI: 10.1103/PhysRevB.83.144502

PACS number(s): 74.78.Na, 11.30.Er, 73.23.−b, 74.70.Pq

I. INTRODUCTION

Parity violation provides important insights about physicalphenomena of particle physics and condensed-matter physics,
and at least two different parity violation mechanisms areknown. The first is due to a quantum anomaly in the Diracfermions of (2+1)-dimensional quantum electrodynamics.1,2Intriguingly, the quantum Hall conductivity in graphene,
whose electrical properties are described by Dirac fermions,reveals the parity violation3,4 and provides an excellent
analog with (2+1)-dimensional quantum electrodynamics.
Theoretical prediction suggests that the other mechanism iscaused by (2+1)-dimensional Majorana fermions, where aparticle is identified as its own antiparticle. However theparity-violating Majorana fermions have not yet been found.
Research on this topic is particularly interesting in relation
to both condensed-matter physics and high-energy physics.
Moreover, applications to topological quantum computation5–7
are expected.
Sr2 RuO4 8 is a promising candidate for a spin-triplet chiralp-wave superconductor (i.e., electrons are paired with spin
S = 1 and orbital angular momentum L = 1). Since theground states are twofold degenerate with different chiralities,millimeter-scale Sr2 RuO4 is considered to include chiraldomain structures. Recently, the chiral single domain sizehas been experimentally estimated to be 1 ∼ 50 μm.9–11
The millimeter-scale Sr2 RuO4 data should be considered asa result of ensemble averaging over possible chiral domain
configurations. Hence transport measurements of samples witha single domain size are very important when studying gaplessexcitations,12,13 the structures and dynamics of unconventionalvortices,14,15 and quantum Hall effects.16 In our previous
report,17 we suggested that the hydrodynamics of the helicalvortex cause the parity violation of current-voltage (I -V )curves. However, this interpretation of the anomalous data
has not been confirmed. In this work, we performed transportmeasurements at the edges of the chiral single domain Sr2 RuO4
because its topological nature appears at the edge.
In this paper, we report anomalous I -V characteristics
and magnetic field dependence in a chiral single domain ofSr2 RuO4 . The induced voltage V is an even function of the bias
current I in the superconducting state. Namely, this violates
the parity. The parity-violating I -V curves are dependent on
the direction of the applied magnetic field parallel to the c axis.
1098-0121/2011/83(14)/144502(6)The results revealed spontaneous magnetization of about 450
Oe and a change in the chirality of the single domain Sr2 RuO4 .
Indeed the induced voltage V shows the result of the edge
conduction. The result of the zero-bias conductance peak in
the tunnel junction at an edge of a microscale Sr2 RuO4 single
crystal shows the existence of the gapless chiral Majorana
state. We suggest that the parity-violating I -V curves withmagnetic field dependence result from the low-energy excitation of the right- and the left-handed quasielectrons-holes(Majorana-Weyl fermions) along the closed chiral edge currentof the single domain under a bias current.
II. EXPERIMENT

To obtain microscale Sr2 RuO4 single crystals, we synthesized Sr2 RuO4 crystals with a solid phase reaction, and thenselected microscale Sr2 RuO4 single crystals based on chemicalcomposition and crystallinity results.18 We fabricated gold
electrodes connected to the sample edges by overlay electron
beam lithography. Figure 1(a) shows a micrograph of themeasured sample. The size is 13.0 μm × 6.67 μm × 0.34 μm.
The electrode spacing is 4.0 μm. To attach gold electrodes
to the sample, we employed a welding technique18,19 using
electron-beam irradiation as illustrated in Fig. 1(b). Electrictransport properties were measured by the four-terminal
method using a dilution refrigerator (Kelvinox, Oxford). All
the measurement leads were shielded. The lead lines were
equipped with low pass RC filters (R = 1 k, C = 22 nF). In
the DC measurements, a bias current was supplied by a precise
current source (6220, Keithley) and the voltage was measured
with a nanovoltmeter (182, Keithley).
III. RESULTS

Figure 1(c) shows the superconducting transition temperature Tc = 1.59 K with a transition temperature widthT ≈ 30 mK. We measured the temperature dependence ofthe resistivity for bias current I = ±1 μA using a current
reversal method. The resistivity is estimated from the size of
4.0 μm (length) × 5.0 μm (width) × 0.3 μm (thickness), andis obtained by averaging the observed data. From the results,
the temperature dependence of the resistivity in the microscale
Sr2 RuO4 was consistent with the properties of bulk crystals.20

144502-1©2011 American Physical Society

NOBUKANE, TOKUNO, MATSUYAMA, AND TANDAPHYSICAL REVIEW B 83, 144502 (2011)

H // c, T = 96 mK

0.50 Oe

(b)

(a)
V+(B)
R<0Electron beamirradiation

VI+(A)
R>0400 Oe

V (μV)

Sr2RuO4I-2 μm(d)0500 Oe

0.40.51200 Oe

V (μV)

ρab (μΩ cm)

0.2

V (μV)−1800 Oe(c)

96mK0.2

Tc= 1.59 K

2400 Oe

4.2 K

0.1ΔT ≈ 30 mK
00012T (K)

3(C)
R>00−0.5
4−50−0.5−50

I (μA)

5(D)R<05−5I (μA)

FIG. 1. (Color online) (a) A micrograph of a microscale Sr2 RuO4
single crystal connected to gold electrodes. (b) Schematic of electron
beam irradiation welding. (c) Temperature dependence of resistivityof microscale Sr2 RuO4 in zero magnetic field. (d) Voltage V plotted
as a function of bias current I at 96 mK and 4.2 K in zero magnetic
field. The induced voltage shows anomalous behavior, which is aneven function of the bias current. Notably, the I -V curve at 96 mK
implies the parity violation.

We successfully observed the superconducting properties ofthe microscale Sr2 RuO4 single crystal.
We found the parity-violating I -V characteristics of the microscale Sr2 RuO4 in zero magnetic field below Tc . Figure 1(d)shows I -V characteristics at 96 mK and 4.2 K. In general,the voltage V in I -V curves is always an odd function ofbias current I , which is a result of parity conservation. TheI -V curve at 4.2 K is an odd function of I . Surprisingly, theI -V curve at 96 mK shows that V has an anomalous component
that is an even function of I . This implies the parity violationof the I -V characteristics. With decreasing temperature, theanomalous voltage increases in zero magnetic field. The parityviolation of I -V curves is observed even in replaced current
and voltage leads. The resistance R for ± 1μA is zero at
96 mK, which is consistent with the result in Fig. 1(c).
The anomalous result seen in the I -V curves is an intrinsic
effect of Sr2 RuO4 superconductors. The resistivity of about
0.2 μ·cm was observed at 4.2 K by measuring various
electrode arrangements for the six-terminal electrodes inFig. 1(a). All I -V curves at 4.2 K exhibited ohmic conduction.
Thus the resistivity was unaffected by geometrical factors. Theresult was confirmed in the AC measurements as reported inRef. 17. In particular, several samples exhibited the anomalous
behavior. We also observed a superconducting gap through thetunnel junction at the edge of the microscale Sr2 RuO4 , which
was grown in the same batch as the measured sample shownin Fig. 1(a). Our results indicate that the observed anomalous
I -V characteristics represent a fundamental superconducting
property of microscopic Sr2 RuO4 single crystals.

05I (μA)
FIG. 2. (Color online) I -V characteristics for several choices ofmagnetic fields applied parallel to the c axis at 96 mK. Applying
the magnetic field from zero magnetic field to 1200 Oe, the induced
voltage changes from a positive voltage of V (+I ) = V (−I ) to anegative voltage of −V (+I ) = −V (−I ). The plotted data are fitted
to the region between I = +(−)0.5 μA and I = +(−)5.0 μA (solidlines). The inset shows I -V characteristics at 2400 and −1800 Oe.
We eliminated the offset voltage of about 0.2 μV, which does notchange with the magnetic field.

Figure 2 shows I -V characteristics for several magnetic
fields applied parallel to the c axis at 96 mK. We found that allof the I -V curves are symmetric with respect to the zero bias
current: V (+I ) = V (−I ) or −V (+I ) = −V (−I ). Applying
the magnetic field from zero magnetic field to 1200 Oe, theresistance R on a bias current I > 0 changes from a positive
value (R > 0) to a negative value (R < 0). On the other hand,for a bias current I < 0, a negative R changes to a positive
R. The inset shows I -V curves under higher magnetic fields.
The I -V curve for magnetic field H = 500 Oe shows zero
resistance for a low-bias current. The zero resistance seen inthat case may indicate superconductivity.
To analyze the result in Fig. 2, we plotted the magnetic-fielddependence of conductance for a bias current I > 0 or I < 0as shown in Fig. 3. Here the conductance was extracted fromthe slope of the linear I -V characteristics in Fig. 2. The
conductance of conventional superconductors with a magnetic
field has symmetric curves with respect to zero magnetic field
and has an infinite conductance at zero magnetic field. Figure 3,
however, shows that the sample has a finite conductance at thezero magnetic field, and the point at which the conductancediverges shifts to a finite H ≈ 450 Oe. Furthermore, the signof the conductance is reversed around the critical magnetic
field 450 Oe. In contrast, the conductance is robust against
a magnetic field applied in the opposite direction (H < 0).
In a magnetic field away from 450 Oe, the conductance

144502-2

MAJORANA-WEYL FERMIONS IN THE CHIRAL . . .

PHYSICAL REVIEW B 83, 144502 (2011)at the edge of the microscale Sr2 RuO4 . The tunneling spectra
were measured by a standard lock-in technique. The junction
resistance exhibited 19.3 k in zero magnetic field at 60 mK.
This is comparable with a quantum resistance of ∼ h/e2 ,where e is the charge of an electrons and h is Planck’sconstant. We observed differential conductance peaks in thevicinity of zero-bias voltage. To analyze the peaks, we subtract
background part of the spectra from the curves in Fig. 4(a). The
results of the extracted spectra (dI1 /dV1 curves) are shownin Fig. 4(b). We found that the position of the conductancepeak for the applied magnetic field was shifted from a minus
bias voltage to a plus voltage as shown by the blue arrows
in Fig. 4(b). Under an external magnetic field of 500 Oe, thezero-bias conductance peak was observed. These results weresimilar to the behavior of the anomalous I -V curves withmagnetic field dependence in Fig. 2.

100I>0H // c, T = 96 mKI<0~ +10 Ω−1~ −10 Ω−1−1G (Ω )H ~ 450 Oe0→z−100+l−20000
H (Oe)

2000

IV. DISCUSSION

FIG. 3. (Color online) Magnetic field dependence of conductance
G on bias current. The shift of the infinite conductance point toH ∼ 450 Oe and its change of its sign are shown. The conductanceof ±10 −1 is represented by horizontal dotted lines. The insets show
the ±l chiral domains in the ab plane. Here we assume that a +l chiralsingle domain with broken time-reversal symmetry is spontaneously
formed in the +z direction in zero magnetic field.

asymptotically reaches ±10 −1 as shown by the horizontal
dotted lines in Fig. 3.
Figure 4(a) shows the differential conductance dI /dV as
a function of the bias voltage for magnetic fields applied
parallel to the c axis at 60 mK through the tunnel junction
(a)

(b)

T = 60 mK0 Oe

H = 0 Oe
100 OedI1/dV1 (arb. units)

dI/dV (arb. units)

100 Oe200 Oe400 Oe200 Oe400 Oe500 Oe500 Oe600 Oe600 Oe−0.1

00.1bias voltage(mV)

−0.1

00.1

bias voltage (mV)

FIG. 4. (Color online) (a) Differential conductance dI /dV versus
bias voltage for magnetic fields applied parallel to the c axis at
60 mK. The dotted line represents the result of the fitting curves.
The conductance peaks in the vicinity of zero bias voltage wereobserved. (b) Magnetic field dependence of the extracted spectrawith conductance peaks. The peak positions are represented by thearrows.

To understand the physical origin of the parity-violating
I -V characteristics, we first discuss the dependence of thechirality of the single domain of Sr2 RuO4 on an external
magnetic field. The chiral domain can explain the shift in thesingular point of the conductance and the change of its signin Fig. 3. Now let us suppose that a chiral vector of a single
 spontaneously points in the +z direction (c axis)
domain, +l,in zero magnetic field as shown in the left panel of the inset
in Fig. 3. The vector l represents the pair angular momentum
parallel to the c axis. Assuming that a magnetic field Hex
 would suppress
applied in the −z direction (opposite to +l)
the chirality of the domain, the chiral vector of the domain
 in awould eventually point in the opposite direction (i.e., −l)positive effective magnetic field Heff > 0, where the effective
magnetic field is defined as Heff = (Hex − 450 Oe). In contrast,
if the assumption is correct, the magnetic field applied in the+z direction is expected to affect the change of the chiral and the sign of the conductance does notdomain with +l,change in Heff < 0. In fact, according to Fig. 3, the assumption
appears to be valid. Our sample size ∼ 10 μm is comparable
to the single domain size 1 ∼ 50 μm estimated from theexperiments,9–11 so the sample should exhibit a single domain
structure. Thus the microscale Sr2 RuO4 itself is a chiralsingle domain with spontaneous magnetization and the appliedmagnetic field causes the chirality of the domain to change.
How can we interpret the anomalous I -V curves in terms of
the peculiar transport phenomena in the chiral single domain?
We focus on the existence of Majorana-Weyl fermions in theedge of Sr2 RuO4 . The edge modes of spin-polarized chiralsuperconductors are fermionic Bogoliubov quasiparticles,
which are mixture of electrons and holes. The absolute
distinction is blurred in order to modify their interaction withthe surrounding sea of Cooper pairs.21 Thus, they should not
be treated as ordinary fermions, but as Majorana fermions.22,23
With a spontaneous magnetic field of 450 Oe as shown inFig. 3, Sr2 RuO4 may realize spin-polarized Cooper pairs.
Both chiral edge supercurrent and quasielectrons-holes current
flow in the edge. The Majorana-Weyl fermions pass througha gapless state and generate the induced voltage. In Fig. 4,the conductance peaks with magnetic field dependence in thevicinity of zero-bias voltage show the existence of the gapless

144502-3

NOBUKANE, TOKUNO, MATSUYAMA, AND TANDAPHYSICAL REVIEW B 83, 144502 (2011)(b)Right-handed quasiholes
I <0(a)Right-handed quasielectrons
I >0

Right-handed
quasielectrons

Right-handed
quasiholes
→→+l

V++l

V+z

V−y

Vz

V−yVxxEEpp(c)Left-handed quasiholes
I <0(d)Left-handed quasielectrons
I >0Left-handed
quasiholes

Left-handed
quasielectrons

zV+V−→−lyVzV+x

V−E→−lyVxEpp

FIG. 5. (Color online) A circulating model of Majorana-Weyl fermions along the closed edge of the sample and energy spectrum in chiraledge states. Under a bias current I > 0 (I < 0), right- and left-handed quasielectrons (quasiholes) are created by the excitation from the Fermi
surface (point). The closed edge of the single domain is regarded as a one-dimensional annular line. Here we assume a clockwise direction forthe +l domain as the positive momentum p. The solid and open circles represent quasielectrons and quasiholes, respectively. The arrangementof panels (a)–(d) corresponds to regions (A)–(D) in Fig. 2.

chiral Majorana state at the edge. The transport phenomena
at least in a low-energy state appear to be governed by theedge excitation of the Majorana-Weyl fermions. Based on theresult of the peak shift in Fig. 4(b), we think that the appliedmagnetic field affects the topological conduction path in thechiral edge excitation. It is possible to explain the I -V curvesin terms of the characteristics of Majorana-Weyl fermions.
The parity-violating I -V curves can be understood as
being the result of the selective excitation of Majorana-Weylfermions along a closed edge of the single domain in the bias
current direction (i.e., I > 0 or I < 0). As shown in Fig. 5,
we assume that each region of the I -V curve can be related tothe paths of quasielectrons or quasiholes carrying the current:
Panels (a)–(d) in Fig. 5 respectively correspond to regions(A)–(D) shown in Fig. 2. Here we assume that the chiraledge supercurrent of the +l domain flows clockwise in the+z direction along the boundary even in the absence of thebias current. With a bias current I > 0, when right-handed
quasielectrons are created by low-energy excitation fromthe Fermi surface (point), they circulate along the closed
line [Fig. 5(a)]. By contrast, for a bias current I < 0, theright-handed quasiholes created by the excitation circulate
in the opposite direction [Fig. 5(b)]. As a consequence, ananomalous induced voltage of V (+I ) = V (−I ) was observed.
Furthermore, similarly to the above explanation, when the−l domain, which has a chiral edge supercurrent that flows
counterclockwise, produces left-handed quasielectrons andquasiholes, a voltage of −V (+I ) = −V (−I ) is induced asshown in Fig. 5(c) and 5(d). The excitation of quasiholes tothe negative energy is considered as the same excitation ofquasielectrons to the positive energy in Majorana fermions.23
Since, in an effective magnetic field Heff ≈ 0, the number ofspin-polarized Cooper pairs decreases, no voltage is induced.
The excitation is determined by the bias current and the144502-4

MAJORANA-WEYL FERMIONS IN THE CHIRAL . . .

PHYSICAL REVIEW B 83, 144502 (2011)

direction of the applied magnetic field. In this manner, theparity-violating I -V curves can be understood as relating tothe excitation of the Majorana-Weyl fermions. This is evidence
for the existence of parity-violating Majorana-Weyl fermionsin the chiral single domain of Sr2 RuO4 .
Let us discuss the resistivity in both the normal (T Tc ) and the superconducting states (T  Tc ). As shown inFig. 1(c), the normal resistivity ρN (= RN wt) is 0.10 μ cmLat temperature just above Tc with a sample width w ≈ 5 μm,a electrode spacing L ≈ 4 μm and a thickness t ≈ 0.3 μm.
If we assume the width of the state of the edge excitations tobe λab , we can estimate the edge resistivity at 96 mK to beρedge = 0.11 μ cm (= R  λLab t ) using the constant resistanceR  = 0.1  in Fig. 3, and a magnetic penetration length
λab ≈ 152 nm. The edge resistivity ρedge is equivalent to thenormal resistivity ρN at temperature just above Tc . Namely,
the conduction path in the superconducting state becomes theedge. Thus our result reflects the quasielectrons-quasiholes ofthe edge current. From these results such as the parity-violating
I -V curve and the edge conduction, we can conclude thatthe anomaly of the induced voltage is the signature of theobservation of the Majorana-Weyl fermions carrying the chiralcurrent along the closed edge of the single domain Sr2 RuO4
under a bias current.
We mainly describe the contribution of Majorana-Weylfermions based on the edge transport properties. At present, it
seems to be more reasonable than considering an inhomogeneous current path because the simple conduction path appears
topologically at the edge in the gapless chiral state. In general,
however, the experimental data for Sr2 RuO4 include not only
the contribution of Majorana-Weyl fermions, but also thatof other exotic effects such as unconventional vortices. We
believe that further studies will reveal these contributions indetail from measurements of the electric properties in various
electrode arrangements that involve Hall-bar geometry.
Finally we discuss the physical implications of our results.
As is well known, the Majorana-Weyl fermions may describe

the nature of neutrinos in high-energy physics. Thus, theMajorana-Weyl fermions of chiral single domain Sr2 RuO4
might be regarded as neutrinos in condensed-matter systems.
This means a possibility of studying cosmology in thelaboratory. Our results suggest a novel effective action like theChern-Simons term in (2 + 1)-dimensional quantum electrodynamics, where it is hard to find the most relevant action of thetheory without a phenomenon. In addition to attracting purely
scientific interest, the anomalous transport phenomena havethe potential applications as regards realizing the topologicalquantum computation of non-Abelian statistics.

*

10

Present address: Department of Physics, Hokkaido University,
Sapporo 060-0810, Japan.
†
Present address: DPMC-MaNEP, University of Geneva, 24 quaiErnest-Ansermet, 1211 Geneva 4, Switzerland.
1G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984).
2
T. Matsuyama, Prog. Theor. Phys. 77, 711 (1987).
3
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I.
Katsnelson, I. V. Griorieva, S. V. Dubonos, and A. A. Firsov, Nature(London) 438, 197 (2005).
4
Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London)
438, 201 (2005).
5
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma,
Rev. Mod. Phys. 80, 1083 (2008).
6
M. Dolve, M. Heiblum, V. Umansky, A. Stern, and D. Mahalu,Nature (London) 452, 829 (2008).
7I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Preiffer,and K. W. West, Science 320, 899 (2008).
8A. P. Mackenzie and Y. Maeno, Rev. Mod. Phys. 75, 657 (2003).
9J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and A. Kapitulnik,Phys. Rev. Lett. 97, 167002 (2006).

V. SUMMARY

In summary, we have observed Majorana-Weyl fermionsin the edge of a chiral single domain of Sr2 RuO4 throughelectric transport. In four terminal measurements, theI -V curves exhibited parity violation with magnetic fielddependence. We observed the zero-bias conductance peak inthe tunnel junction at the edge. The Sr2 RuO4 itself provides
spontaneous magnetization. An applied magnetic field changes
the chirality of the single domain. We show that the MajoranaWeyl fermions are excited along the chiral edge current undera bias current and are detected in the edge of Sr2 RuO4 .

ACKNOWLEDGMENTS

We thank K. Inagaki, Y. Asano, K. Ichimura, K. Yamaya,
S. Takayanagi, K. Konno, T. Tsuneta, S. Tsuchiya, J. Ishioka,I. Kawasaki, K. Tenya, H. Amitsuka, and T. Honma forexperimental help and fruitful discussions. We also are grateful
to A. J. Niemi, E. Babaev, M. Chernodub, J. Goryo, andN. Hatakenaka. This work was supported by a Grant-in-Aidfor the 21st Century COE program on “Topological Scienceand Technology” from the MEXT. H.N. was supported by
KAKENHI (No. 21840004).

F. Kidwingira, J. D. Strand, D. J. V. Harlingen, and Y. Maeno,Science 314, 1267 (2006).
11H. Kambara, S. Kashiwaya, H. Yaguchi, Y. Asano, Y. Tanaka, andY. Maeno, Phys. Rev. Lett. 101, 267003 (2008).
12G. E. Volovik, Pis’ma Zh. Eksp. Teor. Fiz. 61, 935 (1995) [JETP
Lett. 61, 958 (1995)].
13G. E. Volovik, Pis’ma Zh. Eksp. Teor. Fiz. 66, 492 (1997) , [JETP
Lett. 66, 522 (1997)].
14E. Babaev, Phys. Rev. Lett. 88, 177002 (2002).
15
S. B. Chung, H. Bluhm, and E.-A. Kim, Phys. Rev. Lett. 99, 197002(2007).
16J. Goryo and K. Ishikawa, Phys. Lett. A 260, 294(1999).
17
H. Nobukane, K. Inagaki, K. Ichimura, K. Yamaya,S. Takayanagi, I. Kawasaki, K. Tenya, H. Amitsuka, K. Konno,Y. Asano, and S. Tanda, Solid State Commun. 149, 1212
(2009).
18
H. Nobukane, K. Inagaki, S. Tsuchiya, Y. Asano, K. Ichimura,
K. Yamaya, S. Takayanagi, I. Kawasaki, K. Tenya, H. Amitsuka,and S. Tanda, Jpn. J. Appl. Phys. 49, 020209 (2010).

144502-5

NOBUKANE, TOKUNO, MATSUYAMA, AND TANDA
19

PHYSICAL REVIEW B 83, 144502 (2011)

K. Inagaki, T. Toshima, S. Tanda, and K. Yamaya, Appl. Phys. Lett.
86, 073101 (2005).
20A. P. Mackenzie, R. K. W. Haselwimmer, A. W. Tyler, G. G.
Lonzarich, Y. Mori, S. Nishizaki, and Y. Maeno, Phys. Rev. Lett.
80, 161 (1998).

21F. Wilczek, Nature Phys. 5, 614 (2009).
N. Read and D. Green, Phys. Rev. B 61, 10267(2000).
23
X.-L. Qi, T. L. Hughes, S. Raghu, and S.-C. Zhang, Phys. Rev. Lett.
102, 187001 (2009).
22144502-6