Point-contact spectroscopy of the heavy-fermion superconductor CePt$_{3}$Si

4.5 MB·English

by  R. Onuki

Point-contact spectroscopy of the heavy-fermion
superconductor CePt Si
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R Onuki1, A Sumiyama1, Y Oda1, T Yasuda2, R Settai2
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and Y O¯nuki2
n
a 1 DepartmentofMaterialScience,FacultyofScience,UniversityofHyogo,
J Ako¯-gun678-1297, Japan
2 GraduateSchool ofScience, OsakaUniversity,Toyonaka 560-0043,Japan
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1 E-mail: [email protected]

]
l Abstract. Differentialresistancespectra(dV/dI−V characteristics)havebeen
e measured for point-contacts between the heavy-fermion superconductor (HFS)
r- CePt3Si and a normal metal. Some contacts show a peak at V = 0 that is
t characteristicofHFScoexistingwithamagneticordersuchasUPd2Al3,UNi2Al3
.s andURu2Si2. Theevolutionofthepeakoccurswellabovetheantiferromagnetic
t transition temperature TN ∼ 2.2 K, so that the direct relationship with the
a
magnetic transition is questionable. The half-width of the peak seems to reflect
m
thecrystalfieldsplittingorthespin-wavegapasobservedfortheabove-mentioned
- HFSs,possiblysuggestingthatsomecommonscatteringprocessinducesthezero-
d biaspeaks inthesematerials.
n
o
c
[ PACSnumbers: 74.50.+r,74.70.Tx,72.15.Qm

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2 Submitted to: J. Phys.: Condens. Matter
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Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 2
3
The heavy fermion superconductor (HFS) CePt Si has attracted much attention
3
in recent years[1, 2], since its noncentrosymmetric crystal structure and strong
correlation between electrons may lead to the mixing of spin-singlet and spin-triplet
superconductivity. The spin triplet superconductivity is supported experimentally by
the large upper critical field[1] and the NMR Knight shift[3], while the Hebel-Slichter
peak in the nuclear spin-lattice relaxation rate suggests conventional spin-singlet
superconductivity[4]. In addition to this duality, the temperature dependence of
various physical properties such as thermal conductivity[5] and magnetic penetration
depth[6] suggests the line node in the energy gap. A theoretical work that combines
and explains all these results has been proposed[7].
Besides unconventional superconductivity, CePt Si is the first Ce-based heavy
3
fermion superconductor that coexists with an antiferromagnetic order at ambient
pressure. Thespinstructurehasbeenrevealedbyneutrondiffractionmeasurements[8].
Its complex pressure-temperature phase diagram has been investigated by specific
heat[9] and magnetic susceptibility measurements[10], although the correlation
between magnetism and superconductivity is still not clear. Since this issue directly
relates to which symmetry of superconductivity is favored in this material, it will be
usefultoinvestigatehowtheelectronicstateismodifiedthroughtheantiferromagnetic
and superconducting transition.
Point-contact spectroscopy, which measures the bias voltage dependence of the
differential resistance of the point-contacts, has given fruitful information for both
normal and superconducting states of heavy fermion materials[11]. In the normal
state, mostmaterialsshowa minimumofdV/dI atzerobias andit hasbeenascribed
to the increase in local temperature due to Joule heating. The exceptions that show
a zero-biasmaximumareURu Si , UPd Al andUNi Al [11,12]. Itshouldbe noted
2 2 2 3 2 3
that these materials show superconductivity that coexists with antiferromagnetism
(UPd Al [13], UNi Al [14]) or so-called ”hidden order”(URu Si [15]). It will be
2 3 2 3 2 2
interesting to test whether such a spectral property is common to the heavy-fermion
superconductors that coexist with a magnetic order.
Inthispaper,weinvestigatethepoint-contactspectroscopyofCePt Siandreport
3
that it alsoshowsa similar structure atzerobias. Possiblefactorsthat determine the
energy width of the structures are discussed also.
A single crystal of CePt Si was grown by the Bridgeman method. Details of
3
the process for producing the crystal are provided in previous papers[16, 17]. In the
presentstudy, a rectangularpiece with edges of about 3 mm was used; point contacts
were made on the (100) and (001) faces. Hereafter, the contacts are denoted as
I ka and I kc, assuming that the preferred current direction is perpendicular to the
surface. Prior to measurements these faces were polished using diamond polish down
to a size of 1 µm to obtain a mirror-likesurface. A Pt needle was gently pressed onto
the sample with a commercial piezo-electric actuator (attocube ANPx100) to form
a point contact between a superconductor and a normal metal. The position of the
contacts were changed using another actuator (attocube ANPz100). These actuators
move stepwise by about 100 nm at low temperatures, which enables precise control
of the contact resistance and position. The point-contact apparatus was set to the
mixing chamber of a dilution refrigerator and cooled down to 80 mK.
ThedifferentialresistancedV/dI ofthepointcontactswasmeasuredbythefour-
wire method using a system that consists of a current source (Keithley 6221) and a
nanovoltmeter (Keithley 2182). The combination of them provides a special pattern
of current sweep and dV/dI is numerically derived; a constant differential current dI
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 3
3
CePt Si (I||a)
1 3
0.3
K
ρρ/270 0.5 ρρ/270K 00..12
0
0 1 2 3 4
T ( K )
0
0 100 200
T ( K )
Figure 1. Temperature dependence of normalized resistance ρ/ρ270K of the
CePt3Sicrystalusedinthiswork. Insetshowsthesuperconducting(Tc∼0.6K)
andantiferromagnetic(TN∼2.2K)transitions.
is addedto or subtractedfroma staircasesweep,andboth thedifferentialvoltagedV
andthe biasvoltageV arecalculatedfromthe voltagemeasuredateachcurrentstep.
The sign of the bias voltage V is referred to the polarity of the needle.
Figure 1 shows the superconducting transition of the CePt Si crystal used for
3
the present investigation. As the temperature is decreased, the resistance of the bulk
CePt Si shows a gradual decrease, followed by a drop below 80 K, and then becomes
3
zero at T ∼ 0.6 K. As seen in the inset, a slight change in slope appears at T ∼ 2.2
c N
K.
We show infigure 2 dV/dI spectra takenbelow T for different contactson (100)
c
and (001) faces. The differential resistance dV/dI for each contact is normalized
by R = dV/dI at V = 0. For both current directions, two types of spectra have
0
been observed. One type shows a zero-bias peak with a voltage width of ∼1 mV
(figure 2(a)). The other is characterized by a minimum at zero bias with a width
varying widely (figure 2(b)). The lack of a clear difference between the a- and
c-axis directions does not necessarily exclude the anisotropy in CePt Si, since the
3
directionality tends to be lost in point-contact spectroscopy due to the roughness of
the surface.
As the temperature is increased, we have observed that both types of structures
gradually diminish, but still exist well above T , so that they are not attributed to
c
superconductivity. As a typical example, the temperature dependence of the spectra
for Contact A in figure 2 (a) is shown in figure 3. The temperature dependence was
measured during the warming process from the lowest temperature, and we often
encountered an abrupt change in R above 3 K, possibly because the boiling of
0
3He/4Hemixturebeginsandcausesthechangeinthecontactconditionbyvibrations.
In figure 3, the spectra after the abrupt change in R are also shown by shifting
0
vertically by an appropriate extent. Although the curve shape also changes a little,
the peak at zero bias seems to diminish successively and vanish above 4.2 K. The
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 4
3
I || c R (Ω) T(K)
1.04 I || c 0
1.1 8.08 0.37
R (Ω) T(K)
0
1.33 0.38
1.02 Contact D 3.92 0.15
1.26 0.53 Contact C 1.03 0.20
1.00
1.0
Contact B
dI dI
V/ 4.03 0.35 V/
d d 2.75 0.22
−1 −1 I || a
0 0
R R
I || a
1.1
1.02 0.903 0.46 1.39 0.38
1.06 0.54
1.00
Contact A 1.24 0.44
1.0 5.14 0.20
−0.002 0 0.002 −0.002 0 0.002
V ( V ) V ( V )
(a) (b)
Figure 2. Normalized dV/dI versus V characteristics of CePt3Si/Pt contacts
belowTc,whereR0 isthedifferentialresistanceatV =0. (a)and(b)areforthe
contactsthatshowazero-biaspeakandazero-biasdip,respectively. Thespectra
areshiftedverticallyby(a)0.01and(b)0.02forclarity.
observation of the zero-bias peak above T ∼ 2.2 K raises the question as to whether
N
the peak structure is ascribed to the antiferromagnetism.
In order to clarify the origin of the peak, we should examine what kind of
information the measured differential resistance contains. In the case that CePt Si
3
and Pt contactthrough a circular plane of radius a, the contact resistance R at zero
0
bias is approximately expressed as the sum of Sharvin resistance R and Maxwell
SHA
resistance R , as given by
MAX
2R ρ
K
R∼ + , (1)
(ak )2 4a
F
where k is the Fermi wave number, R = h/e2 = 25.8 kΩ, and ρ is the electrical
F K
resistivityofCePt Sinearthecontact[18,19]. TheR duetoPtresistivityhasbeen
3 MAX
neglected, because it is supposed to be small and independent of temperature at low
temperatures. ThetwopartsbecomecomparableataresistanceofR ∼ρ2k2/16R .
eq F K
If ρ ∼ 1 µΩ·cm[16] is used and a typical metallic k ∼10 nm−1 is assumed, R is
F eq
about 0.02 Ω; if R > R as seen in the present contacts, R is dominant and
0 eq SHA
the data contain intrinsic spectroscopic information. In the actual point contacts,
however, ρ near the surface is possibly larger than that of the bulk, and an oxide
layer that inhibits a clean metallic contact may be formed on the CePt Si surface.
3
Consequently the dominant part of resistivity should be judged not only from the R
0
value but also from the behaviour of dV/dI.
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 5
3
1.3
1.245
Contact A Ω )
( 1.24
0
T ( K ) R
0.44 1.235
1.28 0 1 2 3
0.55 T ( K )
0.75
1.0
1.4
Ω ) 1.26 1.8
(
dI 2.2 +0.005
V/
d 2.7
3.0
1.24
4.5
6.2
−0.1
1.22 8.0 −0.098
9.1 −0.095
10 −0.03
−0.03
−0.01 −0.005 0 0.005 0.01
V ( V )
Figure3. TemperaturedependenceofdV/dIversusV characteristicsforContact
A. The spectra below 3.0 K are shifted vertically by 0.005 Ω for clarity, while
the shift is indicated by the figure for those above 3.0 K. Inset: temperature
dependence ofR0.
As seen in the inset of figure 3, R increases as the temperature is lowered.
0
This cannot be explained by the temperature dependence of ρ(T) in the Maxwell
resistance,sincetheresistanceofbulkCePt Sidecreasesbyloweringthetemperature,
3
as shown in figure 1. The increase in R should be ascribed to R and contain
0 SHA
some spectroscopic information. Such peak structures have been observed for only a
few heavy-fermion systems: point-contact spectroscopy of URu Si [11] and scanning
2 2
tunnelingspectroscopyofURu Si ,UPd Al andUNi Al [12]. Itshouldbenotedthat
2 2 2 3 2 3
all these materials including CePt Si are heavy-fermionsuperconductors that coexist
3
with an antiferromagnetic order, although for URu Si the order is now regarded as
2 2
some other type, which is so-called hidden order.
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 6
3
Contact A 0.44 K
1.0
I || a 0.04
0.01 Ω) x3
Ω ) m ( V )
symV/dI) ( 1.4 2K∆ syδ(dV/dI) 0.02 0.5 ∆ ( m
d
(
3.0 K
: Contact A (I || a)
0 : Contact B (I || c)
0 0
−0.004 −0.002 0 0.002 0.004 0 1 2 3
V ( V ) T ( K )
(a) (b)
Figure 4. (a) Symmetric part of dV/dI spectra for Contact A, where
(dV/dI)sym at V=2 mV is subtracted. (b) Temperature dependence of peak
heightδ(dV/dI)sym and∆derivedfromthesymmetricpartofdV/dI spectrafor
Contact A(I ka)andContact B(I kc)infigure2(a).
For most of heavy-fermion systems, a minimum in dV/dI at zero bias is usually
observed as seen in figure 2 (b) and is explained by a heating or thermal model;
if the inelastic mean free path ℓ is much smaller than the contact size a, R
in MAX
is dominant and the increase in local temperature T occurs. In this model, the
PC
relationT2 =T2 +V2/4Lissatisfied,whereT andLarethebathtemperature
PC bath bath
and the Lorenz number, respectively[11]. This leads to an approximate expression
T = 3.2(K/mV)×V(mV), when T ≫ T . Since the largest bias voltage 2mV
PC PC bath
in figure 2 corresponds to T = 6.4 K, the temperature dependence of ρ in figure 1
PC
suggests that the spectra should be V-shaped in the thermal model.
Although some of the spectra are nearly V-shaped in figure 2 (b), the broad
maximum at about ± 1 mV observed for Contacts C and D cannot be explained
by the thermal model. Moreover, such a double maximum structure, which
resembles the spectra observed in many superconductors[20], cannot be ascribed to
superconductivity, since it does not disappear well above T as described below. The
c
similarity of the voltage width between the zero-bias peak in figure 2 (a) and the
double maximum structure in figure 2 (b) may suggest that the spectra for Contacts
C and D also reflect R ; the difference in the interface barrier determines whether
SHA
a peak or a dip appears at zero bias, as observed for superconductors in the BTK
theory[21].
As seen in figures 2 and 3, some of the contacts have shown an asymmetry
of dV/dI curves versus V: dV/dI(+|V|) < dV/dI(−|V|). If this asymmetry has a
spectroscopicorigin,itwillreflectenergy-dependentelectronicDOS(densityofstates)
around the Fermi level. However, the fact that the asymmetry is remarkable for the
contacts following the thermal model in figure 2 (b) and at higher bias voltages in
figure3suggeststhatthethermoelectricvoltagecausedbytheincreaseintemperature
at the point contacts is a more likely origin[11], although the details of the Seebeck
coefficient of CePt Si is still not clear.
3
Hereafter,wefocusonthezero-biaspeakthatiscommontoHFSwithamagnetic
order. The evolution of the peak structure is examined by extracting the symmetric
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 7
3
Table1. Propertiesofheavy-fermionsuperconductorscoexistingwithamagnetic
order. FortheU-basedmaterials,thedatain[12]aretabulated.
TN(K) ∆(meV) ∆cr(meV)
URu2Si2 17.5 9.5 9.9
UPd2Al3 14 13 13
UNi2Al3 4.6 10
CePt3Si 2.2 >0.3 1[8]
part from the spectra using the equation
sym
dV 1 dV dV
= (V)+ (−V) . (2)
(cid:18)dI (cid:19) 2(cid:20)dI dI (cid:21)
Typical examples of the symmetric part are shown in figure 4(a) for the spectra in
figure 3. The peak height δ(dV/dI)sym is defined as δ(dV/dI)sym =(dV/dI)sym −
V=0mV
(dV/dI)sym . The half-width 2∆ of the peak is defined at half-height. The
V=2mV
temperature dependence of both properties are given in figure 4(b) for Contact A
(I k a) and Contact B (I k c) in figure 2 (a). For both contacts, ∆ decreases with a
decrease in temperature. This is in contrast to the behaviour observed for URu Si ;
2 2
∆ appearsat T , slightly increasesby loweringthe temperature,whichis regardedas
N
the growth of the energy gap at the Fermi surface[11].
Table 1 summarizes the characteristics of heavy-fermion superconductors that
show a zero-bias peak. For the U-based materials, two possible interpretations of
the peak structure has been proposed. One is a gap opening on the Fermi surface
due to spin-density-wave formation in the antiferromagnetic state[11, 12]. The other
interpretation is based on the fact that ∆ is comparable to the crystal field splitting
∆ betweenthetwolevelsthatareconnectedbyanon-zeromatrixelement;∆reflects
cr
a spin-wave gap determined by ∆ .[12]
cr
Although the temperature dependence of the peak for CePt Si is different from
3
URu Si as described above, ∆ in figure 4 (b) is an order of magnitude smaller than
2 2
∆ for the other U-based materials, suggesting the possible scaling law between ∆
and T . In addition, ∆ is comparable to ∆. It should be noted that the spin-
N cr
wave gaps derived from heat capacity and resistivity data also have similar values:
2.7 K (0.23 mV) and 1.8 K (0.16 mV), respectively[2]. Although ∆ is of the same
order of magnitude as various physical properties related to antiferromagnetism in
CePt Si, the lack of a drastic change of the spectra at T raises a question about its
3 N
antiferromagnetic origin. A comprehensive interpretation of the zero-bias peak is left
to future study.
As for the spectroscopic evidence of superconductivity, we could not observe
it in contrast to the clear unconventional spectra in the normal state, as shown
in figure 3. The absence of a superconducting anomaly has also been reported for
URu Si , especially in high-resistance contacts[22, 23], and ascribed to the normal-
2 2
conducting layer near the surface of URu Si . One possible origin of such a layer
2 2
is the deformation in the contact region and it probably occurs in CePt Si as well.
3
Even if such a deformed regionbecomes superconducting, it will only show a reduced
anomaly, which is often characterized by the finite quasiparticle lifetime in the BTK
theory[11]. Moreover,the unconventionalspectra in the normalstate ofCePt Si that
3
grow at lower temperatures and on a lower voltage scale than in URu Si (T < 17.5
2 2
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 8
3
Contact C
I || c
1.06
T ( K )
1.0
)
Ω 1.05 0.9
0.8
(
I 0.7
d
V/ 0.6
d 0.5
0.4
00..33
1.04 0.2
1.035
)
Ω 0.2 K

(

I
d
/
1.03 V
d 1.03
−0.5 0 0.5
V ( mV )
−0.002 0 0.002
V ( V )
Figure5. TemperaturedependenceofdV/dIversusV characteristicsforContact
C. The spectra are shifted vertically by 0.001 Ω for clarity. Inset shows the
superconducting gapat0.2K.
K, V <10 mV) tend to hide the superconducting anomaly on the scale of the energy
gap (<1 mV), so that the superconducting anomaly has hardly been observed.
The only exception is ContactC in figure 2 (b). Figure 5 shows the temperature
dependence of the spectra for Contact C. The double maximum structures at about
±1 mV change little within this temperature range. In addition, a small local
maximum appears at zero bias below T ∼0.6 K. Such a structure is expected
c
when a superconductor and a normal metal are separated by an interface barrier;
the voltage |V | ∼ 0.15 mV where the double minimum appears indicates the
S
superconducting energy gap[21]. This value, however, only gives the lower limit of
the gap,sincethedoublemaximumstructureoutsideissosteepthatittends tomake
the minimum appear at lower values. Still, |eV |∼0.15 meV is largerthan the weak-
S
coupling limit 1.75k T = 0.09 meV with T ∼ 0.6 K, indicating the strong coupling
B c c
superconductivity in CePt Si.
3
In conclusion, point-contact spectroscopy of CePt Si has shown a dip or a peak
3
of the differential resistance at zero bias. The dip structure varies from contact to
contact, while the peak has a half-width of the order of the crystal field splitting or
Point-contact spectroscopy of the heavy-fermion superconductor CePt Si 9
3
the spin-wave gap. Such a peak structure is commonly observed for heavy-fermion
superconductors that coexist with a magnetic order, although for CePt Si the peak
3
disappears not at T but well above T .
N N
Acknowledgments
This study was partly supported by a Grant-in-Aid from the Ministry of Education,
Culture, Sports, Science and Technology (MEXT), Japan. One of us (Y. O¯.) was
financially supported by the Grant-in-Aid for COE Research (10CE2004) of the
MEXT, Japan.
References
[1] Bauer E, Hilscher G, Michor H, Paul Ch, Scheidt E W, Gribanov A, Seropegin Yu, Noel H,
SigristMandRoglP2004Phys. Rev. Lett.92027003
[2] Bauer E, Kaldarar H, Prokofiev A, Royanian E, Amato A, Sereni J, Bra¨mer-EscamillaW and
BonaldeI2007J. Phys. Soc. Jpn. 76051009
[3] UedaK,HamamotoK,KoharaT,MotoyamaGandOdaY2005 Physica B 359-361374
[4] YogiM,KitaokaY,HashimotoS,YasudaT,SettaiR,MatsudaTD,HagaY,O¯nukiY,RoglP
andBauerE2004Phys. Rev. Lett.93027003
[5] IzawaK,KasaharaY,MatsudaY,BehniaK,YasudaT,SettaiRandO¯nukiY2005Phys.Rev.
Lett.94197002
[6] BonaldeI,Bra¨mer-EscamillaWandBauerE2005 Phys. Rev. Lett.94207002
[7] HayashiN,Wakabayashi K,FrigeriPAandSigristM2006 Phys. Rev B 73092508
[8] MetokiN,KanekoK,MatsudaTD,GalatanuA,Takeuchi T,HashimotoS,UedaT,Settai R,
O¯nukiYandBernhoeftN2004J. Phys.: Condens. Matter 16L207
[9] TateiwaN,HagaY,MatsudaTD,IkedaS,YasudaT,TakeuchiT,SettaiRandO¯nukiY2005
J. Phys. Soc. Jpn. 741903
[10] AokiY,SumiyamaA,MotoyamaG,OdaY,Settai YandO¯nukiY2007J. Phys. Soc. Jpn.76
114708
[11] NaidyukYuGandYansonIK1998J. Phys.: Condens. Matter 108905
[12] AartsJ,VolodinAP,MenovskyAA,Nieuwenhuys GJandMydoshJA1994Europhys. Lett.
26203
[13] GeibelC,SchankC,ThiesS,KitazawaH,BredlCD,Bo¨hmA,RauM,GrauelA,CasparyR,
HelfrichR,AhlheimU,Weber GandSteglichF1991 Z. Phys. B 841
[14] Geibel C, Thies S, Kaczorowski D, Mehner A, Grauel A, Seidel B, Ahlheim U, Helfrich R,
PetersenK,BredlCDandSteglichF1991Z. Phys. B 83305
[15] PalstraTTM,MenovskyAA,vandenBergJ,DirkmaatAJ,KesPH,NieuwenhuysGJand
MydoshJA1985Phys. Rev. Lett.552727
[16] YasudaT,ShishidoH,UedaT,HashimotoS,SettaiR,TakeuchiT,MatsudaTD,HagaYand
O¯nukiY2004J. Phys. Soc. Jpn.731657
[17] TakeuchiT,HashimotoS,YasudaT,ShishidoH,UedaT,YamadaM,ObirakiY,ShiimotoM,
Kohara H, Yamamoto T, Sugiyama K, Kindo K, Matsuda T D, Haga Y, Aoki Y, Sato H,
SettaiRandO¯nukiY2004J. Phys.: Condens. Matter 16L333
[18] WexlerG1966Proc. Phys. Soc.89927
[19] GloosK2000Phys. Rev. Lett.855257
[20] SheetGoutam,Mukhopadhyay SandRaychaudhuri P2004 Phys. Rev. B 69134507
[21] BlonderGE,TinkhamMandKlapwijkTM1982 Phys. Rev. B 254515
[22] NowackA,NaidyukYuG,ChubovPN,YansonIKandMenovskyA1992Z.Phys. B 88295
[23] HasselbachK,KirtleyJRandLejayP1992 Phys. Rev. B 465826