Effect of disorder on the pressure-induced superconducting state of CeAu2Si2

0.41 MB·English

by  Z. Ren

Effect of disorder on the pressure-induced superconducting state of CeAu Si
2 2
Z. Ren1,∗ G. Giriat1, G. W. Scheerer1, G. Lapertot2, and D. Jaccard1
1DQMP - University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland and
2SPSMS, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble, F-38054, France
(Dated: March 25, 2015)
CeAu2Si2 isanewlydiscoveredpressure-inducedheavyfermionsuperconductorwhichshowsvery
5 unusualinterplay between superconductivityand magnetism underpressure. Herewe compare the
1 results of high-pressure measurements on single crystalline CeAu2Si2 samples with different levels
0 of disorder. It is found that while the magnetic properties are essentially sample independent, su-
2 perconductivityisrapidlysuppressedwhentheresidualresistivityofthesampleincreases. Weshow
that the depression of bulk Tc can be well understood in terms of pair breaking by nonmagnetic
r
a disorder, which strongly suggests an unconventional pairing state in pressurized CeAu2Si2. Fur-
M thermore, increasing the level of disorder leads to the emergence of another phase transition at T∗
within themagnetic phase, which might bein competition with superconductivity.

4
2 PACSnumbers: 74.62.Fj,74.62.En,74.70.Tx

]
n I. INTRODUCTION Inthispaper,wepresentthepressureresponsesoftwo
o
CeAu Si crystals grown from different fluxes with in-
c 2 2
- plane residual resistivities ρ0 = 1.8 and 12.2 µΩcm, re-
r Ce-based magnetic compounds that become super- spectively. The results show that while the critical pres-
p conducting under pressure have attracted a lot of at-
u sures for the disappearance of magnetism and the delo-
tention because of the intimate connection between su-
s calizationof the Ce 4f electrons are almost independent
. perconductivity (SC) and magnetic or valence instabil-
t on ρ0, the high-ρ0 sample shows a much narrower pres-
a ities [1]. Prominent examples include CeCu Ge [2],
2 2 sure range for SC and a considerably lower maximum
m CePd Si [3], CeIn [4] and CeRhIn [5]. Very recently,
2 2 3 5 T . A detailed analysis indicates that at ∼21.2 GPa, SC
c
- pressure-induced heavy fermion SC with transition tem-
d with an initial onset Tc of ∼2.5 K is destroyed when ρ0
peratures T up to 2.5 K is observed in the antiferro-
n c exceed ∼46 µΩcm, i.e. when the carrier mean free path
magnet CeAu Si [6], which is both isostructural and
o 2 2 isreducedtobesimilartothesuperconductingcoherence
c isoelectronic to the first unconventional superconductor
length. Sincethereisgoodevidencethatρ isdominated
[ CeCu Si [7]. It is quite remarkable in CeAu Si that 0
2 2 2 2 by the contribution of nonmagnetic disorder, our results
SC coexists with long-range magnetic order over a huge
2 point to unconventionalSC in CeAu Si under pressure.
2 2
v pressureintervalof 11 GPa. Moreover,in approximately
In addition, the high-ρ sample displays another phase
2 one-third of this pressure range, the magnetic ordering 0
transitionatatemperature below T , whichis probably
7 temperature T and T are simultaneously enhanced by M
1 M c competing with SC.
pressure[6]. Thesebehaviorsarehardlyexplainedwithin
5
the common scenarios of Cooper pairing mediated by
0
. spin[8]orvalence-fluctuations[9],andthusitisofpartic- II. EXPERIMENTAL
1
ular interest to clarify the nature of SC in this material.
0
5 TheT responsetothelevelofnonmagneticdisorderis Crystal growth of CeAu Si samples by Sn flux and
c 2 2
1
knownto provideuseful informationfor the phase of the Au-Si self-flux are described in detail in Ref. [6]. The
:
v superconducting gap function. For conventional s-wave resulting crystals are labeled hereafter as CeAu Si (Sn)
2 2
i superconductors, no pair breaking is expected by non- and CeAu Si (self), respectively. Within the resolution
X 2 2
magneticdisorderaslongasthesystemremainsmetallic, limits of x-ray and microprobe techniques, no difference
r
a according to the Anderson’s theorem [10]. By contrast, is observedin the crystalstructure and chemicalcompo-
for non s-wave superconductors, in which there is a sign sition of the Sn- and self-flux samples.
reversal in the superconducting gap function, scattering High pressure experiments were performed using a
fromnonmagneticdisorderaveragesoutthegapoverthe Bridgman-type sintered diamond-anvil cell with steatite
Fermi surface and results in a strong suppression of T . as soft-solid pressure medium and lead (Pb) as pressure
c
This effect has been observed in a number of unconven- gauge [17]. The results of high-pressure experiments
tionalsuperconductors,suchas UPt [11], YBaCu O on CeAu Si (Sn) have been reported in Ref. [6]. For
3 3 6+x 2 2
[12], Sr RuO [13], BEDT-TTF salts [14] and CePt Si CeAu Si (self), measurementsarecarriedoutintwodif-
2 4 3 2 2
[15]. Although it is commonly believed that the pairing ferent pressure cells. In the first pressure cell, only resis-
symmetry is non s-wave for Ce-based pressure-induced tivity is measured up to 25.5 GPa. The second pressure
superconductors[16], thereis little systematicstudy ofa cell is designed to measure both resistivity and ac heat
similar effect at high pressure. capacity, but the pressure is limited to 20.5 GPa. In
2

150
CeAu2Si2 (a) 25.5
30 p (GPa) = 0 m) CeAu Si (self) 20.5
2 2
c

)
cm 20 ph (100 p (GPa) =
h
self-flux p 15.9 max
( T
1 max
10 50 T2
9.4
Sn-flux

0
0
1 10 100 0
0.1 1 10 100
T (K) T ( K)
)
m
FIG. 1: (Color online) Logarithmic temperature dependence c40 (b) 80 (c) 80 (d)
of the in-plane resistivity at ambient pressure before (solid
lines)andafter(dashedlines)subtractionofthephononcon- ( 9.4 1 5 .9 40 20 . 5
fltruibxuest.ioTnhfeorvethrteicCaleAdout2tSeid2lcinryesstaarlsegarogwuindefrtoomthteheeydeisff.erent a. u.)2200 4200 200
(
ac
C
both cells, the CeAu Si (self) sample with its ab plane 0 0 0
2 2
0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5
perpendiculartothecompressiveforceisconnectedinse-
T (K) T (K) T (K)
ries with the Pb gauge. The resistivity was measured by
using a standard four-probe method. For ac-calorimetry FIG. 2: (Color online) (a) For typical pressures, logarithmic
temperaturedependenceofin-planeresistivityoftheself-flux
measurements,achromelwire,whichisotherwiseusedas
a voltagelead,servesas the heater,and the sample tem- grownCeAu2Si2(self)crystalsaftersubtractionofthephonon
contribution. ThetwocharacteristicmaximaT1max andT2max
perature oscillations are detected by a Au/AuFe(0.07%)
at 15.9 GPa are marked by arrows. The dashed lines are
thermocouple. More details of the measurement proce- a guide to the eyes, evidencing the −lnT behavior. Panels
dureanddataanalysiscanbefoundinRef. [17]. Agood (b)−(d) show the comparison of the resistivity and ac heat
agreement is found between the results of the two cells, capacity for three different pressures. The solid lines are a
indicatingthattheyreflectthe intrinsicpropertiesofthe guide tothe eyes.
sample.
B. Pressure response of CeAu2Si2(self)
Typical results at selected pressures of the resistiv-
III. RESULTS AND DISCUSSION
ity (ρ) and ac heat capacity (Cac) of CeAu Si (self) are
2 2
showninFig. 2. Apartfromamuchlargerresidualresis-
A. Ambient pressure results
tivity ρ , the overall behavior of the non-phononic resis-
0
tivity[Fig. 2(a)]isverysimilarto thatofCeAu Si (Sn).
2 2
Figure1showsthecomparisonoftheambientpressure At the intermediate pressure of 15.9 GPa, two broad
resistivity data of the CeAu Si crystals grownfrom the maxima exist at Tmax and Tmax, and above each max-
2 2 1 2
different fluxes. It can be observed that the resistivity imathedatafollowa−lnT dependence,whichmanifests
curveofCeAu Si (self) is analmostrigidupshift ofthat the incoherent Kondo scattering of the groundstate and
2 2
of CeAu Si (Sn). After subtraction of the phonon con- excitedcrystal-filed(CF) levels,respectively[19, 20]. As
2 2
tribution to the resistivity (ρ ), which is assumed to pressure is increased to 20.5 GPa, Tmax almost doubles
ph 1
be linearintemperature andpressureindependent, both while Tmax remains nearly unchanged. At the highest
2
samples exhibit a resistivity maximum at ∼140 K and pressure of 25.5 GPa, the Kondo effect dominates over
a sharp drop in resistivity due to the magnetic ordering the CF splitting so that the two maxima are already
below T ≈ 10 K. Furthermore, ρ ≈ 0.067T (µΩcm) merged into a single peak at ∼180 K. Concomitantly,
N ph
estimated for CeAu Si (self) is in agreement with that boththemagnitudeoftheresistivityandthe−lnT slope
2 2
of CeAu Si (Sn) [6] within the geometricalfactor uncer- increase rapidly with pressure, signifying a strong en-
2 2
tainty(∼10%). Hencetheresistivitiesofthetwocrystals hancement of the Kondo interaction under pressure.
differ only bytheir ρ values, whichcorrespondto differ- InFig. 2(b)−(d), we comparethe results ofρ andCac
0
ent degrees of disorder. below 5 K at three typical pressures. At 9.4 GPa, the
3
undergoes two successive phase transitions, similarly to
10 CeCu Ge at ∼3 GPa [22]. At 20.5 GPa, the highest
2 2
8 CeAu2Si2(self) only (a) pressure at which Cac is measured, only one magnetic
and C ac transition is detectable in both ρ and Cac(T) at 3.3 K,
K) 6 and, below 1 K the incomplete resistive transition with-
T ( out any corresponding anomaly in Cac(T) indicates SC
4 TM of filamentary nature.
T onset The resulting pressure-temperature phase diagram is
2 T
c shown in Fig. 3(a). The magnetic ordering tempera-
n K) 0 ture TM initially decreases with increasing pressure, as
m/8 (b) expected, due to the enhancement of the Kondo interac-
c6
tion. However, T already starts to increase with pres-
4 M
A (2 sure above 8 GPa. At 15.9 GPa, another transition ap-
∗ ∗
0 pears at T < TM. With further increasing pressure, T
5 (c) riseswhileTMshowsamaximum,andthetwotransitions
4
n merge at 18.9 GPa. At higher pressures, TM exhibits a
3
dome-shapeddependenceandfinallydisappearsabruptly
2
above22.5GPa. Ontheotherhand,SCisobservedfrom
1
m) 60 (d) 19.9 GPa up to the highest investigated pressure. It is
c 40 pointed out that zero resistivity is achieved only at 21.2
(020 GPa,thepressureatwhichtheonsetTc reachesits max-
imum of ∼1.1K. Both T andT areenhanced within a
c M
0 01norm 2131 0400 KKKK C(OeliVn)e 468000 (cm)0 npaoFrwrieogrwulrapewre3ρs((sbTu)r-)(e=dr)aρn0sgh+eowAbsTetnwthteeoentfih1tet9ir.n9egsaisnptdaivri2at0my.6detaGetraPsapo.loftttehde
-1 Tcr = 25(8) K 6 K 20 - as a function of pressure. Thanks to a sufficiently broad
-0.05 0.00 0.05 3.1 K temperature window between Tc and TM, we are able to
h1/23 0
extractreliable parametersfor the whole pressurerange.
0 10 20 30
pcp The A coefficient exhibits two maxima at 13.9 and 22.5
p (GPa)
GPa, respectively. The latter together with a minimum
FIG. 3: (Color online) (a) Experimental p-T phase diagram
nexponent(n≈1.5)coincideswiththedisappearanceof
ofCeAu2Si2(self). TconsetandTMrepresentthesuperconduct-
the magnetic order,indicating a magnetic quantum crit-
ingtransitiononsetandthemagneticorderingtemperatures,
ical point at p = 22.5 ± 0.5 GPa. However, the former
respectively. The open (closed) symbols denote the data ex- c
tractedfromtheresistivitymeasurementsonly(bothresistiv- with n ≈ 2 occurs at a pressure close to that of the in-
∗
ity and heat capacity measurements). (b), (c) and (d) show terpolation of T to 0 K, which points to the possibility
the pressure dependencies of the coefficient A, temperature of a putative quantum phase transitionoccurring within
exponentn,andresidualresistivityρ0,respectively,obtained the magnetic phase. Actually, ρ shows a broad peak at
n 0
fromthefittingofthepowerlawρ(T)=ρ0 +AT tothelow ∼20 GPa, suggesting that the maximum scattering rate
temperature resistivity data. (e) Plot of ρ∗ = ρ – ρ0 versus
happens in between these two QCPs. Nevertheless, the
p at selected temperatures up to 30 K. The closed circles in-
∗ largeA value at13.9GPa may containa significantcon-
dicate for each isotherm the 50% drop of ρ compared to its
value at 22.5 GPa and define the crossover (COV) line. The tribution from the electron-magnonscattering, and thus
inset shows the collapse of all normalized data ρnorm when provides little information of the effective mass.
plottedasafunctionofthegeneralizeddistanceh/θ fromthe Figure 3(e) shows the plot of isothermal resistivity
critical end point located at p∗ ≈ 23.9 GPa and Tcr = −25 ρ∗(p) = ρ(p) − ρ (p) versus p at selected temperatures
0
K.Theverticaldashedlinesareaguidetotheeyes. Thetwo ∗
∗ up to 30 K. Above 22.5 GPa, ρ (p) decreases steeply
critical pressures pc and p are indicated by labeled arrows.
with pressure, revealing the continuous delocalization of
the Ce 4f electrons. For the data analyses, we follow
the procedure described in Ref. [23], which is based on
change of slope in resistivity at ∼2.7 K coincides with the assumption of an underlying critical end point lo-
the midpoint of the sharp jump in Cac(T), indicating a cated at (p , T ) in the p-T plane. It turns out that
cr cr
∗
magnetic ordering [21]. Notably, at 15.9 GPa two jumps all the normalized resistivity curves ρ (p) = (ρ (p)
norm
inCac(T)are observed. The one at∼ 4.4K corresponds − ρ∗(p ))/ρ∗(p ) below 30 K fall on a single curve
50% 50%
to a slightslope change ofthe resistivity,while the other when plotted against h/θ, where for each temperature,
at ∼ 1.5 K is accompanied by a steep resistivity drop p denotesthe pressurecorrespondingtothe midpoint
50%
∗
thatisindependent ofthe appliedcurrentandis notdue of the ρ (p)-drop compared to its value at 22.5 GPa, h
to SC. Thus it appears that at this pressure the sample = (p − p )/p and θ = (T − T )/|T | with the
50% 50% cr cr
4

(a) CeAu2Si2(self) n ) 1.5 (a)
K
1T (K)1000 T1max T2max TM C OlVine A (cm/ 01..50 sSenlf--f fluluxx
onset
Magnetic Tc
1 0.0
Order SC
4 (b)
(b) CeAu2Si2(Sn)
3 self-flux
1K)00 max T2max COlVine n 2 Sn-f lux
T (10 T1 TM
onset 1
Tc
Magnetic
1 Order SC 60 (c)
m) s elf-flux
0 10 20 30 c S n-flux ( 4.7)
p (G Pa) 40
(
FIG. 4: (Color online) p − T phase diagrams of (a) 0
CeAu2Si2(self) and (b) CeAu2Si2(Sn) including the temper- 20
aturesT1max and T2max. Note thatthevertical axisis in loga-
rithmic scale. The crossover(COV) line is determined by the 20 22 24 26 28
scaling analysis of the resistivity.
p (GPa)
FIG.5: (Coloronline)Comparison ofthepressuredependen-
cies of the fitting parameters, (a) the A coefficient, (b) the
only free parameter T = −25(8) K. The negative T
cr cr
n exponent, (c) the residual resistivity ρ0 for CeAu2Si2(self)
indicates a crossoverrather than a first-order transition.
and CeAu2Si2(Sn). The open and closed symbols denotethe
Moreover, the extrapolation of the temperature depen-
dataforCeAu2Si2(Sn)andCeAu2Si2(self),respectively. Note
∗
denceofp50% to0Kyieldsthecriticalendpressurep (≈ that theρ0 data for CeAu2Si2(Sn)are multiplied by a factor
pcr) = 23.9 ± 0.7 GPa. of 4.7. The vertical dashed line is a guide tothe eyes.
C. Comparison with the results of CeAu2Si2(Sn) superconductingphasesisrestrictedto∼3GPa. Itisalso
noteworthy that the pressure evolution of the magnetic
orderismorecomplexforCeAu Si (self). While theori-
Figure 4 shows the p-T phase diagrams of 2 2
∗
gin of the transition at T remains unclear, it is possible
CeAu Si (self) and CeAu Si (Sn) including the lines
2 2 2 2
defined by the temperatures Tmax and Tmax of the that the resulting groundstate is competing with SC, as
1 2
will be discussed further below.
resistivity maxima in the paramagnetic phase, as well
as the crossover (COV) lines obtained by the 50% drop Figure 5 compares the power-law fitting parameters
of ρ∗. Clearly, these lines are almost identical for both of the resistivity data above Tc for CeAu2Si2(self) and
crystals. Since the temperatures T1max and T2max (for CeAu2Si2(Sn). It can be noted that the pressure depen-
p > 15.9 GPa) scale approximately with the Kondo dencies of the three parameters are very similar in both
temperature and CF splitting energy respectively [20], cases. The maximumA coefficientand minimum n(< 2)
it is obvious that the pressure evolution of the charac- exponent at pc are typical for a QCP. Above pc, while
teristic high-temperature energy scales are essentially the n values increase only slightly, the A values drop
sample independent. This reflects that both the Kondo abruptly by more than one order of magnitude, indicat-
interaction and CF levels depend mainly on the local ing a transition from a strongly to a weakly correlated
environment of the Ce ions. regime. Moreover, the ρ0 data of CeAu2Si2(Sn), when
Bycontrast,attemperaturesbelow5K,thetwophase multiplied by a factor of 4.7, match well with those of
diagramsshow significantdifferences. Althoughthe crit- CeAu2Si2(self). This scaling factor is not far from its
ical pressures p and p∗ are nearly identical for both ambient pressure value (∼6.7), suggesting that the dif-
c
samples, in CeAu2Si2(self) a much higher pressure (19.9 ference in the levels of disorder between CeAu2Si2(self)
GPa) is needed to induce SC and the maximum onset and CeAu2Si2(Sn) does not change much with pressure.
T is reduced by a factor of 2.3. As a consequence, the We next turn our attention to the scaling behavior
c
∗
pressurerangeforthe overlapbetweenthe magnetic and of the resistivity near p . Figure 6(a) shows the tem-
5

5 (a) CeAu Si p 21.2 GPa
(a) 60 2 2
4 CeAu2Si2(self) self-flux
CeAu2Si2(Sn) m)
1/ 3 CeCu2Si2 (Ref. 23) c 40 Sn-flux
( after p cycling
2
20
1
0
0 0 1 2 3
-30 -20 -10 0 10 20 30
T ( K)
T (K) 3
(b) CeAu2Si2(self) (b) ) pC e A21u.22S Gi2P a
norm01 TT pCccrre ((SsA en2ul)3f2 )S.= 6=i 2 G(1S2P4n5(a)6(,8 ) )K K bulk (K)c2 bulk T (Kc12 pCCp ee C 4C1.u62u 22GGS GPPi2eaa 2
T
1 0
0 50 100 150 200
-1 Cp e =C u42.5S iG2 (PRae, f. 23) 0 ( cm)
Tcr = 8(5) K 0
0 50 100 150
-0.10 -0.05 0.00 0.05 0.10 0.15
( cm)
h/ 0
FIG. 6: (Color online) (a) Temperature dependencies of the FIG. 7: (Color online) (a) Temperature dependencies of the
inverse slope 1/χ (see text for details) for CeAu2Si2(self), resistivity of CeAu2Si2 at ∼21.2 GPa for different level of
CeAu2Si2(Sn), and CeCu2Si2 from Ref. [23]. Tcr values are disorder. Thedashedlinesdenotethepower-lawfitemployed
extracted from linear fits to the data (solid lines). (b) ρnorm toextract theresidual resistivity ρ0. (b)Plot of Tcbulk versus
dataplottedasafunctionofh/θ forthethreecases, showing ρ0 for CeAu2Si2 at ∼21.2 GPa. The solid line is a fit from
a good agreement. the AG theory to the data. The inset shows Tcbulk plotted
as a function of ρ0 for CeAu2Si2 at ∼21.2 GPa, CeCu2Si2 at
∼4.2 GPa and CeCu2Ge2 at ∼16 GPa. Note that we have
collected all available data from Refs. [9, 18, 22–25, 33].
perature dependence of 1/χ, where χ = |dρ /dp|
norm p50%
is the slope of the resistivity drop at the midpoint,
for CeAu Si (self) and CeAu Si (Sn) [6], as well as
2 2 2 2
To gain insight into the pressure-induced SC in
CeCu Si [23] for comparison. In the three cases, 1/χ
2 2
CeAu Si , we show in Fig. 7(a) the resistivity below
diminishes on lowering temperature, indicating that the 2 2
3 K of the Sn- and self-flux grown crystals around 21.2
slopebecomesincreasinglysteepasthesystemsapproach
GPa,a pressurecloseto that ofthe optimum T . As can
their critical end point located at (p , T ). Assuming c
cr cr
be seen, CeAu Si (Sn) has a low ρ and shows a sharp
1/χ∝(T −T ), T canbe obtainedbya linearextrap- 2 2 0
cr cr
superconductingtransitionbelow2.55K witha widthof
olation of the data to the x-axis. Remarkably, despite
0.18 K. By contrast, CeAu Si (self) has a much higher
the large differences in T ranging from −25 K to −8 2 2
cr
ρ , and its superconducting onset temperature is shifted
K, the ρ data below 30 K follow almost the same 0
norm
to 1.15 K while the transitionwidth increases to 0.55 K.
curve when plotted as a function of h/θ especially for
This trend is further corroborated by investigating the
h/θ > 0 (p > p ), as shown in Fig. 6(b). This means
50%
effect of pressure cycling on CeAu Si (Sn), which tends
that, for a generalizeddistance h/θ from the criticalend 2 2
to induce further disorder(dislocation) and therefore in-
point, ρ behavesinthe same wayfor bothCeAu Si
norm 2 2
crease ρ . Indeed, when pressure is increased again up
and CeCu Si . Further study is needed to establish the 0
2 2
to ∼21.2GPa (after a partialdepressurizationfrom 27.6
levelof generalityof sucha behaviorin relatedCe-based
downto10GPa),theρ valuedoubleswhiletheonsetT
compounds. For our two CeAu Si crystals, it appears 0 c
2 2
decreases to ∼2.2 K. Concomitantly, the resistive tran-
that higher (less negative) T corresponds to higher T .
cr c
sition becomes much broader most likely due to the de-
However,despitetheirsimilarT valuesneartheirrespec-
c
∗ crease of pressure homogeneity, which is inevitable after
tive p , the absolute T value of CeAu Si (Sn) is nearly
cr 2 2
the pressure cycling.
twice that of CeCu Si . Nevertheless, the T value of
2 2 cr
CeAu Si could be considerably underestimated due to In Fig. 7(b), we plot the dependence of Tbulk on ρ
2 2 c 0
the unavoidabledegradationofhydrostaticconditions at at ∼21.2 GPa. Here Tbulk is defined as the temperature
c
very high pressure. where zero resistivity is achieved, given that the com-
6
pletenessofresistivetransitioncoincideswiththejumpin >50µΩcm,thedepressionofTbulk ofCeCu Si within-
c 2 2
the ac heat capacity [6]. As can be seen, Tbulk decreases creasing ρ becomes much weaker,and SC survives even
c 0
rapidly with increasing ρ . For f-electron systems, ρ whenρ isoftheorderoftheIoffe-Regellimit[34]. How-
0 0 0
can be expressedas ρ = ρBorn + ρunit, where ρBorn and ever, the large ρ could be due to the effect of Kondo
0 0 0 0 0
ρunit are due to the nonmagnetic disorder of non-f ele- holes [35, 36], and thus is no longer a good indication of
0
mentsandthedefectsofCeions,respectively[24]. Under the level of disorder.
pressure, ρunit remains essentially unaffected while ρBorn
0 0 ThesensitivityofSCinCeAu Si tononmagneticdis-
is subject to a large enhancement due to critical fluc- 2 2
order also allows of an explanation for the transition at
tuations [26]. The values of ρ for both CeAu Si (self)
0 2 2 ∗
T observedinCeAu Si (self). Itistheoreticallydemon-
and CeAu Si (Sn) are much larger at ∼21.2 GPa than 2 2
2 2
strated that when coupled to quantum critical fluctua-
at ambient pressure,indicating that ρBorn dominates ρ .
0 0 tions, disorder can induce regions of local order or even
Therefore, our results are consistent with pair breaking
long range order in the host phase [37]. Indeed, a recent
by nonmagnetic disorder.
experimental study shows that nonmagnetic Cd impu-
According to the Abrikosov-Gor’kov(AG) theory [27]
rities in CeCoIn nucleate magnetic regions even when
generalized for nonmagnetic disorder in a non-s-wave 5
global magnetic order is suppressed and bulk SC is re-
superconductor [28–30], the suppression of T follows
c storedby pressure,which is ascribedto the localcompe-
ln(Tc0) = Ψ(1 + αTc0) − Ψ(1), where Ψ is the digamma
funcTtcion,α=2~/(2TπckBτTc0),2τ isthescatteringtime,and ttihteioenmbeertgweenecnemofatghneettirsamnsaitnidonSCat[T38∗].mAasysbheowrenlaatbedovteo,
T is T in the disorder-free limit (α → 0). The model
c0 c aputativeQCP,andalmostcoincideswiththeestablish-
predictsthatT vanishesatacriticalα,whichisroughly
c ment of bulk SC in CeAu Si (Sn). It is possible that
equivalenttothe factthatthe carriermeanfreepathl is 2 2
nearthedisordersitesinCeAu Si (Sn), SCislocallyde-
comparable to the superconducting (Pippard) coherence 2 2
stroyedandregionsofcompetingorderareformed. With
length ξ . It turns out that the experimental data obey
0 increasing disorder, these regions are expected to grow
well the functional form of the AG theory, with Tbulk ≈
c0 in size and start to overlap. As a result, above a certain
2.7 K and a critical ρcr ∼ 46 µΩcm. The corresponding
0 level of disorder, SC is destroyed completely and long
criticalmeanfree pathlcr canbe estimatedusing the re-
range order develops, as in CeAu Si (self).
lationl =(1.27×104)/ρ (N/V)2/3,whereρ isinΩcm, 2 2
0 0
N isthenumberofconductionelectronsperunitcell,and
V is the unit cell volume in cm3 [31]. Assuming N = 6
(there are twoformula units per unit cell) and with V ≈
1.6 × 10−22 cm3 [6], we obtain lcr ≈ 27 ˚A, which is half
of the Ginzburg-Landau(GL) coherence length ξ (0) =
GL IV. CONCLUSION
55˚A(≈ ξ )deducedfromthe measurementofthe upper
0
critical field at 22.3 GPa with T ∼ 2.5 K [6]. It should
c
be pointed out that lcr could be underestimated due to In summary, we have studied the effect of disorder
the following reasons: (i) The N value is overestimated; on the pressure-induced heavy fermion superconductor
(ii) Only the parts of the sample with a low enough ρ0 CeAu2Si2 through the comparison of high-pressure re-
become superconducting such that ρcr is overestimated; sults from single crystalline samples with two different
0
(iii) The calculated lcr reflects mainly the contribution ρ values. It is found that, with the increase of ρ , both
0 0
from the scattering of the light quasiparticles, while lcr the pressure range for SC and the maximum T are re-
c
fortheheavyquasiparticlesthatformCooperpairscould duced,althoughthecriticalbehaviorsnearthemagnetic-
belonger[32]. Thusitisreasonabletospeculatethatthe nonmagnetic boundary and the delocalization of Ce 4f
actual lcr is close to ξ0. electrons under pressure are essentially unaffected. The
The aboveanalysisshows thatthe suppressionofbulk bulk T dependence onρ nearthe optimumpressurefor
c 0
T can be understood, not only qualitatively but also SC is very similar to that of CeCu Si , and is consistent
c 2 2
quantitatively, within the pair breaking model. This with the pair breaking effect by nonmagnetic disorder.
strongly points to unconventional pairing in the super- These results not only provide evidence for unconven-
conducting state of CeAu Si under pressure. As a mat- tional SC in CeAu Si under pressure, but also suggest
2 2 2 2
ter of fact, in CeCu Si at a similar volume V (p ∼ 4.2 thatthetwoCeX Si (X =CuorAu)compoundsshare
2 2 2 2
GPa)[6],theρ dependenceofthemaximumTbulkshows a common pairing mechanism. Finally, for the sample
0 c
very similar behavior to that of CeAu Si for ρ < 50 with a higher ρ value, a new phase transition appears
2 2 0 0
∗
µΩcm [inset of Fig. 7(b)] [9, 18, 22–25, 33], suggesting at T below T , which is probably related to an order
M
a common mechanism of SC in these compounds. More- that competes with SC. In this respect, the clarification
∗
over,atthisV magneticorderisstillpresentinCeAu Si of the nature of the transition at T , which may help
2 2
but is absent in CeCu Si , which supports the idea that to elucidate the pairing mechanism,is worthpursuing in
2 2
magneticorderandSCarenotdirectlyrelated[6]. Forρ future studies.
0
7
ACKNOWLEDGEMENT (London) 450, 1177 (2007).
[17] A. T. Holmes, D. Jaccard, G. Behr, Y. Inada, and Y.
Onuki,J. Phys.:Condens. Matter 16, S1121 (2004).
We acknowledge technical assistance from M. Lopes,
[18] A. T. Holmes, Ph.D. thesis, Universite´de Gene`ve, 2004
and financial support from the Swiss National Science
[http://archive-ouverte.unige.ch/unige:284].
Foundation through Grant No. 200020-137519.
[19] B. Cornutand B.Coqblin,Phys.Rev.B5,4541 (1972).
[20] Y. Nishida, A. Tsuruta, and K. Miyake, J. Phys. Soc.
Jpn. 75, 064706 (2006).
[21] N. Tateiwa, Y. Haga, T. D. Matsuda, S. Ikeda, T. Ya-
suda,T.Takeuchi,R.Settai,andY.Onuki,J.Phys.Soc.
∗ Electronic address: [email protected] Jpn. 74, 1903 (2005).
[1] G. Knebel, D. Aoki, and J. Flouquet, Comptes Rendus [22] D.Jaccard,H.Wilhelm,K.Alami-Yadri,andE.Vargoz,
Physique12, 542 (2011). Physica 259-261B, 1 (1999).
[2] D.Jaccard,K.Behnia,andJ.Sierro,Phys.Lett.A163, [23] G.Seyfarth,A.-S.Ruetschi,K.Sengupta,A.Georges,D.
475 (1992). Jaccard, S.Watanabe,andK.Miyake,Phys.Rev.B85,
[3] F. M. Grosche, S. R. Julian, N. D. Mathur, and G. G. 205105 (2012).
Lonzarich, Physica 223-224B, 50 (1996). [24] A. T. Holmes, D. Jaccard, and K.Miyake, J. Phys.Soc.
[4] N.D.Mathur,F.M.Grosche,S.R.Julian,I.R.Walker, Jpn. 76, 051002 (2007).
D. M. Freye, R. K. W. Haselwimmer, and G. G. Lon- [25] B.Bellarbi, A.Benoit,D.Jaccard,J.M.Mignot,andH.
zarich, Nature(London) 394, 39 (1998). F. Braun, Phys.Rev.B 30, 1182 (1984).
[5] H.Hegger,C.Petrovic,E.G.Moshopoulou,M.F.Hund- [26] K. Miyake and O. Narikiyo, J. Phys. Soc. Jpn. 71, 867
ley,J.L.Sarrao,Z.Fisk,andJ.D.Thompson,Phys.Rev. (2002).
Lett.84, 4986 (2000). [27] A.A.AbrikosovandL.P.Gor’kov,Sov.Phys.JETP12,
[6] Z. Ren, L. V. Pourovskii, G. Giriat, G. Lapertot, A. 1243 (1961).
Georges,andD.Jaccard,Phys.Rev.X4,031055(2014). [28] P. I. Larkin, Sov.Phys. JETP Lett. 2, 130 (1965).
[7] F.Steglich,J.Aarts,C.D.Bredl,W.Lieke,D.Meschede, [29] A.J.Millis, S.Sachdev,andC.M.Varma,Phys.Rev.B
W. Franz, and H. Schafer, Phys. Rev. Lett. 43, 1892 37, 4975 (1988).
(1979). [30] R.J. Radtke,K.Levin,H.-B.Schu¨ttler, andM. R.Nor-
[8] O. Stockert, J. Arndt, E. Faulhaber, C. Geibel, H. S. man, Phys. Rev.B 48, 653(R) (1993).
Jeevan, S. Kirchner, M. Loewenhaupt, K. Schmalzl, W. [31] M. B. Maple, J. W. Chen, S. E. Lambert, Z. Fisk, J.
Schmidt,Q.Si,andF.Steglich,Nat.Phys.7,119(2011). L. Smith, H. R. Ott, J. S. Brooks, and M. J. Naughton,
[9] A.T. Holmes, D.Jaccard, andK.Miyake, Phys.Rev.B Phys. Rev.Lett. 54, 477 (1985).
69, 024508 (2004). [32] H. Q. Yuan, F. M. Grosche, M. Deppe, C. Geibel, G.
[10] P.W. Anderson, J. Phys. Chem. Solid 11, 26 (1959). Sparn, and F. Seglich, NewJ. Phys.6, 132 (2004).
[11] Y. Dalichaouch, M. C. de Andrade, D. A. Gajewski, R. [33] E. Vargoz, Ph.D. thesis, Universite´de Gene`ve,1998.
Chau, P. Visani, and M. B. Maple, Phys. Rev.Lett. 75, [34] A. T. Holmes, D. Jaccard, H. S. Jeevan, C. Geibel, and
3938 (1995). M. Ishikawa, J. Phys.:Condens. Matter 17, 5423 (2005).
[12] S.K.Tolpygo,J.-Y.Lin,M.Gurvitch,S.Y.Hou,andJ. [35] J.M.Lawrence,J.D.Thompson,andY.Y.Chen,Phys.
M. Phillips, Phys. Rev.B 53, 12454 (1996). Rev. Lett.54, 2537 (1985).
[13] A. P. Mackenzie, R. K. W. Haselwimmer, A. W. Tyler, [36] D.Jaccard,E.Vargoz,K.Alami-Yadri,andH.Wilhelm,
G. G. Lonzarich, Y. Mori, S. Nishizaki, and Y. Maeno, Rev. High Pressure Sci. Technol. 7, 412 (1998).
Phys.Rev.Lett. 80, 161 (1998). [37] A. J. Millis, D. K. Morr, and J. Schmalian, Phys. Rev.
[14] B. J. Powell and R. H. McKenzie, Phys. Rev. B 69, Lett. 87, 167202 (2001).
024519 (2004). [38] S. Seo, X.Lu,J.-X. Zhu,R.R.Urbano, N.Curro, E. D.
[15] M.Nicklas,F.Steglich,J.Knolle,I.Eremin,R.Lackner, Bauer,V.A.Sidorov,L.D.Pham,T.Park,Z.Fisk,and
and E. Bauer, Phys.Rev.B 81, 180511(R) (2010). J. D.Thompson, Nat. Phys.10, 120 (2014).
[16] P. Monthoux, D. Pines, and G. G. Lonzarich, Nature