Bean-Livingston barrier enhancement on nodal surface of the d-wave superconductor YBa2Cu3O{7-x}

0.24 MB·English

by  G. Leibovitch

Bean-Livingston barrier enhancement on nodal surface of the d-wave superconductor
YBa Cu O
2 3 7−x
G. Leibovitch,∗ R. Beck,† A. Kohen, and G. Deutscher
School of Physics and Astronomy, Raymond and Beverly Sackler
Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv, 69978, Israel
(Dated: January 13, 2009)
Vortexentryinto(110)orientedYBa2Cu3O7 x filmshasbeenstudiedbytunnelingintoAndreev
−
9 - Saint-James bound states, whose energy is shifted by surface currents. At low temperatures, the
0 characteristicfieldforvortexentryhasbeenfoundtoincreaseuptovaluesseveraltimeshigherthan
0 that of the Bean-Livingston entry field for conventional superconductors, in agreement with recent
2 theoretical predictions.

n
PACSnumbers: 74.25.Ha,74.50.+r,74.60.Ge,74.72.Bk,74.76.Bz
a
J

3 J
As shown by C. Bean and J. Livingston [1] vortex en-
1
tryinaTypeIIsuperconductorsubmittedtoamagnetic

] fieldparalleltoitssurfacecanbedelayedbeyondthefield
n
H where the mixed state becomes thermodynamically
o c1
stable in the bulk. Vortex entry may not occur up to a
c
- fieldoftheorderofthethermodynamicalcriticalfieldHc
r
p where the free energies of the normal and full Meissner
u states become equal. The delayed vortex entry comes
s from the attraction between a vortex and its anti-vortex x xxx l lll x
.
t image. The vortex is however also submitted to a repul-
a
m sive force from Meissner surface screening currents (Fig.
1. AtlowappliedfieldstheseMeissnercurrentsareweak,
-
FIG. 1: Schematic representation of a vortex and its anti-
d thevortex-anti-vortexattractionwinsandasurfaceen-
n ergy barrier prevents vortex penetration in the bulk. At vorteximage(dotted)togetherwiththesumofMeissnerdia-
o magnetic screening current and the Fogelstr¨om surface para-
high fields, Meissner currents are strong, the repulsive
c magnetic current. The vortex anti-vortex interaction is at-
[ interaction wins, the surface barrier disappears and vor- tractive, theeffect of thediamagnetic Meissner current is re-
tices can penetrate freely. The attractive and repulsive pulsive and that of the Fogelstr¨om paramagnetic current is
1
interactions balance each other at a field of the order of attractive. Dashed and full arrows indicate the directions of
v
H . In practice, vortex penetration occurs in general at theparamagneticanddiamagneticcurrents. Atlowtempera-
4 c
tures,thesumofbothcurrentsbecomesparamagneticonthe
7 a field lower than Hc, as the sample surface roughness
scale of thecoherence length ξ.
7 can locally enhance the surface field value above that of
1 the applied field because of demagnetization effects.
.
1 Recently, Iniotakis et.al. [2] have predicted than in
0 away from the surface.
9 a dx2−y2 wave superconductor having its surface normal
paralleltoanodaldirection,vortexpenetrationforfields In this work, we present a study of the temperature-
0
: applied along the z direction (the c-axis perpendicular magnetic field dependence of the Bean - Livingston sur-
v to the CuO planes in the cuprates, see Fig. 2) can be face barrier for vortex entry on the nodal surface of
i
X delayed well beyond the field of first vortex entry Hs. slightly overdoped YBa2Cu3O7−x (YBCO) thin films.
r The increaseofthe barrier,being particularlysignificant Our results basically confirm the theoretical predictions.
a
at low temperatures, is due to is due to strong surface Thin films of YBa Cu O (YBCO) were grown by
2 3 7−x
currents carried by Andreev - Saint-James bound states DCoff-axissputteringonsubstratesofSrTiO with(110)
3
[3]. This current is paramagnetic and flows in the op- orientation. A buffer layer of PrBa Cu O , was de-
2 3 7−x
posite direction with regards to that of the diamagnetic posited using RF off-axis sputtering on top of the sub-
screening Meissner current. A schematic illustration of strate [4] in order to reduce the (103) orientated grains.
thecurrentsispresentedinFig. 1. Onemustnoticethat The YBCO growth time was 3 hours corresponding to
the Fogelstro¨m paramagnetic current flows at a distance a thickness of 2400˚A. Normal metal - Insulator - Super-
of the order of the coherence length ξ from the surface conductor(NIS) junctions werepreparedby placingthin
while the Meissner screening current flows at the scale Indium rods on top of the surface of the thin film[5, 6].
of the penetration length λ from the surface. The effect OxidationoftheIndiumtoInOatthe contactareagives
of the paramagnetic current on vortex entry is to reduce the Insulating layer of the NIS junction. Figure 2 shows
the repulsive force driving the vortex into the bulk and the NISjunctionorientationswithregardstothed-wave
2
T=1.4K, H=2.5T -1 ] 00..5526 d e 2cr.5e aTseinsgla field
0.45 increasing field dV [ 0.48
decreasing field dI/ 0.44
field cooled
0.40
-20 -10 0 10 20
1 ]
- V [ 0.42 V [mV]
d
dI/
0.39
-8 -6 -4 -2 0 2 4 6 8
FIG.2: Schematicillustrationoftheexperimentalsetup. The
V [mV]
CuO2 planes with the d-wave order-parameter are scathed.
The thin film surface is [110] oriented. The magnetic field
is applied parallel to both the surface and the c-axis. The FIG.3: dI/dV at2.5Teslaforincreasing,decreasingandfield
round rod represents the planar tunnel junction (Indium in cooledconditions. Defining2δtobethedistancebetweenthe
grey, InOin black). two peaks, we note δ is maximum for increasing field, min-
imum for decreasing field and has an intermediate value for
thefieldcooledmeasurement. Insetshowsthemeasurement’s
full scale (±20mV) for the decreasing field condition. The
order parameter. The samples discussed in this work
were all slightly overdoped with a Tc downset of 89K. YBa2Cu3O7−x coherence peaks are located at ∼16mV.
Andreev - Saint-James zero energy surface bound
states (ASJ bound states) are known to develop at sur-
faces perpendicular to a node direction, such as (110) HS wherethebarrierdisappears(followingthenotations
surfaces in YBa Cu O [7, 8]. In a tunneling experi- by C. Bean and J. Livingston [1]). Tunneling measure-
2 3 7−x
ment, these states show up as a Zero Bias Conductance ment at relative high temperatures have thermal smear-
Peak(ZBCP),whichsplitsdue toaDopplereffectunder ing that makes it impossible to follow the ZBCP split-
superfluid currents flowing parallel to the surface [3] as ting. In order to follow the temperature dependance of
occurs in the geometry show in Fig. 2. We have used the barrier by tunneling measurements and to eliminate
this split 2δ to investigate the field and temperature de- the effect of thermal smearing on the tunneling charac-
pendence of the barrier against vortex entry. teristic,wehavepursuethe followingprocedureindeter-
In films thicker than the London penetration length mining the temperature dependence Hs(T). After cool-
as is the case for the samples investigated here, the field ing in zero field down to 1.4K, the field is raised up to a
evolution is known to be hysteretic, being larger in in- value H∗. The temperature is then raised up to a value
creasing than in decreasing fields [5, 9, 10]. The split Ta (hence annealingtemperature)foratime sufficientto
in increasing fields has been interpreted as due to the reach equilibrium (2 minutes), then cooled down again
Dopplereffect inducedbyMeissnercurrents[3,11]while to 1.4K for a measurement of δup(H∗,Ta). In order to
that in decreasing fields has been shown to be a field return to the virgin conditions (zero field cooled from
rather than a current effect [10]. A third case is that above Tc), the temperature is then raised up to 105K,
of a field cooled condition, in which there should be no the field is lowered to zero, and a new measurement is
Bean-Livingstoneffect. Asetofthreesuchmeasurement carriedoutatadifferentvalueofTa. Onceseveralvalues
is shown in Fig. 3. In order to cancel out the field ef- of Ta have been explored, a new cycle is started with a
fect, we have characterized currents resulting from the different value of H∗. In order to check if the performed
Bean-Livingstonbarrierbythe differencebetweenvalues field-thermal cycle damaged the sample or the junction,
of δ measured in increasing field after cooling the sam- the tunneling characteristic was measured every time a
ple inzerofieldandfieldcooledconditions,(δ −δ ). virgin state was reached and also at the increasing field
up F.C.
This quantity has been measured as a function of field stateatthe previousH∗ value andcomparedto the tun-
and annealing temperature T as described in the next neling characteristics obtained at the beginning of the
a
paragraph. measurements. No change in the tunneling characteris-
tic occurred during the measurements.
In the absence of any Bean-Livingston barrier effect,
(δ − δ ) should reach a maximum value at H = Fig. 4 summarizes our results for (δ (T )−δ ) as
up F.C. up a F.C.
H . In the presence of a barrier against vortex entry, afunctionofH∗ atdifferentannealingtemperatures. At
c1
(δ −δ )shouldreachits maximumvalue atthe field T = 20K and higher, the curves present a broad max-
up F.C. a
3
1 Tesla
1.00 fit with Ts =37.3K – 1.7K
1.8 Ta= 2fit Tweitshla Ts = 21.9K – 2.5K
1.4K 3 Tesla
1.6 20K )FC0.37 fit with Ts = 14.4K –1.0K
V] 1.4 40K K)-
[m F.C. 11..02 50K (1.4)(/Cup0.14
- F
T)a0.8 T)-a
(p 0.6 (up
u ( 0.05
0.4
0.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0 1 2 3 Ta/Tc
0H [Tesla]
FIG. 5: The decay of δ as a function of the annealing tem-
tFδeFIr.GeCs..i)s4:fionTrcrhTeeaahs=eysst1ue.n4rteKisli,st2hi0neKstp,hl4ei0tZtKiBnCganPsmdsep5al0irKtstii.nntgAovttah1lue.4ebK(aδcuktphg(erTohau)yn−sd- pbeoxryedpraetorhtnueeornfevtdaiTaleualc.eadyeTocfThaSey(δvuiosapfl(0ufi1.er1.4ss6tKo±of)r0(−dδ.e0urδ1p.F,(.T0WCa..2))i5.t−h±SδToF0cl..i0Cd=3.)La8an9irnKdees0nT.oa4hrr2mee±afifilt0tizt.e0etdd2o
at fieldshigherthen 3 Tesla. When annealingto highertem- Tc
for 1,2and3 Teslarespectively.
peratures, a broad maximum for the hysteresis appears. For
Ta =50K,thebroadmaximumisalreadyachievedatfieldof
about 1 Tesla. Solid arrows are guideto the eye.
?
3.5 Bean-Livingston
imum at a field HM that goes down as the annealing Nodal surface
temperaturegoesup,asexpected. Atthelowesttemper- 3.0 Ts
atures, no clear maximum can be seen up to the highest 2.5 HM
a]
field where the value of δup(Ta) can be identified. sl
e 2.0
Ideally,thefielddependenceof(δ (T )−δ )should T
show a sharper maximum than thuapt wahichFw.Ce.observe H [ 1.5
0
since a reduction in surface currents and hence of δup is 1.0
expected once vortices start to penetrate. Yet, we ten-
0.5
tatively identify the field at maximum with H . What
S
is clear from the data is that surface currents keep in- 0.0
0.0 0.2 0.4 0.6 0.8 1.0
creasing up to a field that is much higher than H (of
the orderof1·10−2Tesla)atalltemperatures,andC1than T/Tc
HC (of the order of 1 Tesla [1, 12] ) at low tempera- FIG.6: Fieldoffirstvortexentryasafunctionofthereduced
tures, this basically confirms the prediction of Iniotakis temperature T . ThelinescorrespondtotheBean-Livingston
Tc
et.al. [2]. In order to check whether thermal fluctua- fieldoffirstvortexentry,usingHc =1Tesla[12],inthecase
tions are the reason for the continuous change in δ , a of conventional superconductor (dashed line) and in thecase
up
set of measurements was done with much longer time of of nodal surface calculated by Iniotakis et. al. [2] (full line).
Thecirclesarerepresentthefieldwherethehysteresisvalueof
temperatureannealing-upto6hours. No differencebe-
tween the short and long annealing time was found and thesplitting,(δup(Ta,H∗)−δF.C.)isatmaximumthatisHM
takenfromFig. 4. Thelowesttemperature(notedalsowitha
hence - the thermalfluctuation is ruledout frombeing a
questionmark)isonlyalowerboundarysincenomaximumis
reason for this behavior. observed. The stars represent the decay order Ts(H∗) taken
Another way to represent the results is shown Fig. 5, fromFig. 5. Bothmethodsofanalysisshowtheenhancement
where the dependence of of δup(Ta)−δup(1.4K) is dis- of Hs for low temperatures.
played for a fixed field H∗ as a function of Ta. δ(H∗)
Tc
is reduced progressivelyfrom its value in increasing field
down to its field cooled value as a function of the an- H∗ is equal to the vortex entry field.
nealing temperature (5). This reduction can be fitted to There are several possible reasons for the observed
anexponentialdecay,givinga temperature scaleT (H∗) broadmaximum(Fig. 4)andforthecontinuousdecayof
s
thatdecreasesasH∗ isincreased. Insteadofthisprogres- δ (Fig. 5). A first one is the surface roughness of the
up
sivereduction,onewouldhaveexpectedδ(H∗)tosustain sample that can have weak spots for vortex entry where
its low temperature value up to the temperature where the surface is not (110) oriented. A second one is the
4
height of the barrier which may become of order K T rameter can strongly effect the Bean-Livingston barrier
B
athigh fields. One mustalso take into accountthe finite enhancement due to the node removal effect. In such a
thickness of the sample which is only a few penetration case, strong over-doped samples and/or high magnetic
depths. fields are necessary in orderto allow the existence of the
The formation of an id subdominant order parame- subdominant order paramter at temperatures as high as
xy
ter [10, 13], can be expected to reduce the paramagnetic 0.3T [10, 13].
c
currents and hence Hs. However, at fields of less than The Authors would like to thank S. Hacohen and B.
3 Tesla the id component disappears above about 7K
xy Alomg for the use oftheir low noise dI/dVmeasurement
[13]. Therefore, it can not effect the results presented in
system. This work was supported by the Heinrich Herz-
Fig. 4 andFig. 5 at temperaturesabove14K.As for the MinervaCenterforHighTemperatureSuperconductivity
1.4K data (Fig. 4), it only allows to determine a mini-
and by the ISF.
mum value for H which was not calculated by Iniotakis
s
et.al. [2].
To summarize the results, we show Fig.6 values of
Ts(H∗) and of H (Ta). Within error bars, both sets
Tc M Tc
of values fall on the same line, showing that both cap- ∗ Electronic address: [email protected]
ture the same physics. The dashed line in Fig. 6 is † Current address: University of California, Santa Bar-
bara, California 93106
thetemperaturedependenceoftheBean-Livingstonfield
[1] C. Bean and J. Livingston, Phys. Rev. Lett. 12, 14
of first entry in a conventional superconductor, taking
(1968).
H =1 Tesla [12]. The solid line is the temperature de-
c [2] C.Iniotakis,T.Dahm,andN.Schopohl,Phys.Rev.Lett.
pendenceoftheBean-Livingstonfieldoffirstentryinthe 100, 037002 (2008).
case of a nodal surface, taken from Iniotakis et. al. [2], [3] M. Fogelstr¨om, D. Rainer, and J. A. Sauls, Phys. Rev.
again with H = 1 Tesla. The predicted large enhance- Lett. 79, 281 (1997).
c
ment is clearlyseen experimentally at low temperatures. [4] S. Poelders, R. Auer, G. Linker, R. Smithey, and
R. Schneider,Physica C 247, 309 (1995).
The reason for the low temperature enhancement of
[5] R.KrupkeandG.Deutscher,Phys.Rev.Lett. 83,4634
the field of first entry is easily understood. As shown by
(1999).
Fogelstro¨m et.al. [3] the Andreev - Saint-James states [6] Y.DaganandG.Deutscher,Phys.Rev.Lett. 87,177004
carry paramagnetic currents at nodal surfaces. Iniotakis (2001).
et.al. [2]haveshownthatthesecurrentsstronglyincrease [7] C.-R. Hu,Phys. Rev.Lett. 72, 1526 (1994).
at low temperatures, thus reducing the usual repulsive [8] G. Deutscher,Rev.Mod. Phys. 77, 109 (2005).
Lorenz force due to Meissner currents. This reduction [9] R. Beck, Y. Dagan, A. Milner, A. Gerber, and
G. Deutscher,Phys. Rev.B 69, 144506 (2004).
of the repulsive force allows the attractive force of the
[10] G. Leibovitch, R. Beck, Y. Dagan, S. Hacohen, and
image vortex to remain dominant up to higher fields at
G. Deutscher,Phys. Rev.B 77, 094522 (2008).
low temperatures.
[11] M. Covington, M. Aprili, E. Paraoanu, L. H. Greene,
In order to better understand the barrier further the- F. Xu, J. Zhu, and C. A. Mirkin, Phys. Rev. Lett. 79,
oretical and experimental work is needed in lower tem- 277 (1997).
peratures regime where the barrieris strongly enhanced. [12] Taking ξ =15˚A ,λ=1500˚A and Hs= 4πφξ0λ ≈ H√c2.
The doping dependence of the enhancement and espe- [13] G. Elhalel, R. Beck, G. Leibovitch, and G. Deutscher,
cially the appearance of a subdominant nodal order pa- Phys. Rev.Lett. 98, 137002 (2007).