Coherent caxis transport in the underdoped cuprate superconductor YBa_ {2} Cu_ {3} O_ {y}
ABSTRACT The electrical resistivity ρc of the underdoped cuprate superconductor YBa2Cu3Oy was measured perpendicular to the CuO2 planes on ultrahigh quality single crystals in magnetic fields large enough to suppress superconductivity. The incoherent insulatinglike behavior of ρc at high temperature, characteristic of all underdoped cuprates, is found to cross over to a coherent regime of metallic behavior at low temperature. This crossover coincides with the emergence of the small electron pocket detected in the Fermi surface of YBa2Cu3Oy via quantum oscillations, the Hall and Seebeck coefficients, and with the detection of a unidirectional modulation of the charge density as seen by highfield nuclear magnetic resonance measurements. The low coherence temperature is quantitatively consistent with the small hopping integral t⊥ inferred from the splitting of the quantum oscillation frequencies. We conclude that the Fermisurface reconstruction in YBa2Cu3Oy at dopings from p=0.08 to at least p=0.15, attributed to stripe order, produces a metallic state with threedimensional coherence deep in the underdoped regime.

Article: Evolution of superconducting correlations within magneticfielddecoupled La2−xBaxCuO4 (x=0.095)
Z. Stegen, Su Jung Han, Jie Wu, A. K. Pramanik, M. Hücker, Genda Gu, Qiang Li, J. H. Park, G. S. Boebinger, J. M. Tranquada[Show abstract] [Hide abstract]
ABSTRACT: We explore the evolution of superconductivity in La2−xBaxCuO4 with x=0.095 in magnetic fields of up to 35 T applied perpendicular to the CuO2 planes. Previous work on this material has shown that perpendicular fields enhance both charge and spinstripe order within the planes. We present measurements of the resistivity parallel and perpendicular to the planes, as well as the Hall effect. Measurements of magnetic susceptibility for fields of up to 15 T applied both parallel and perpendicular to the planes provide complementary measures of the superconductivity. We show that fields sufficient to destroy pair tunneling between the planes do not disrupt the superconducting correlations within the planes. In fact, we observe an onset of largeamplitude but phasedisordered superconductivity within the planes at approximately 30 K that is remarkably insensitive to field. With further cooling, we observe a phasetransitionlike drop in the inplane resistivity to an apparent state of superconductivity despite the lack of phase coherence between the layers. These observations raise interesting questions concerning the identification of the upper critical field, where pairing is destroyed, in underdoped cuprates.Physical review. B, Condensed matter 02/2013; 87(6). · 3.66 Impact Factor  SourceAvailable from: Artur P Durajski[Show abstract] [Hide abstract]
ABSTRACT: The model for the cuprates based on the modified electronphonon pairing mechanism has been tested. For this purpose, the superconductors with high value of the critical temperature have been taken into consideration. In particular: ${\rm YBa_{2}Cu_{3}O_{7y}}$, ${\rm HgBa_{2}CuO_{4+y}}$, ${\rm HgBa_{2}Cu_{1x}Zn_{x}O_{4+y}}$, and ${\rm HgBa_{2}Ca_{2}Cu_{3}O_{8+y}}$. It has been shown that the dependence of the ratio $R_{1}\equiv 2\Delta_{tot}^{(0)}/k_{B}T_{C}$ on the doping ($p$) can be properly predicted in the framework of the presented theory; the symbol $\Delta_{tot}^{(0)}$ denotes the energy gap amplitude at the temperature of zero Kelvin, and $T_{C}$ is the critical temperature. The numerical results have been supplemented by the formula which describes the function $R_{1}(p)$.Acta Physica Polonica Series a 10/2014; 126:A92–A96. · 0.53 Impact Factor  SourceAvailable from: C. BerthierT. Wu, H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, C. T. Lin, D. Haug, T. Loew, V. Hinkov, B. Keimer, M.H. Julien[Show abstract] [Hide abstract]
ABSTRACT: Using 63Cu NMR, we establish that the enhancement of spin order by a magnetic field H in YBa2Cu3O6.45 arises from a competition with superconductivity because the effect occurs for H perpendicular, but not parallel, to the CuO2 planes, and it persists up to field values comparable to Hc2. We also find that the spin freezing has a glassy nature and that the frozen state onsets at a temperature which is independent of the magnitude of H. These results, together with the presence of a competing chargeordering instability at nearby doping levels, are strikingly parallel to those previously obtained in La214. This suggests a universal interpretation of magnetic field effects in underdoped cuprates where the enhancement of spin order by the field may not be the primary phenomenon but rather a byproduct of the competition between superconductivity and charge order. We also observe that lowenergy spin fluctuations are manifested up to relatively high temperatures where they partially mask the signature of the pseudogap in 1/T1 data of planar Cu sites.Physical Review B 07/2013; 88(1). · 3.66 Impact Factor
Page 1
arXiv:1107.5422v1 [condmat.suprcon] 27 Jul 2011
Coherent caxis transport in the underdoped cuprate superconductor YBa2Cu3Oy
B. Vignolle,1B. J. Ramshaw,2James Day,2David LeBoeuf,1St´ ephane Lepault,1
Ruixing Liang,2,3W.N. Hardy,2,3D.A. Bonn,2,3Louis Taillefer,3,4and Cyril Proust1,3, ∗
1Laboratoire National des Champs Magn´ etiques Intenses,
UPR 3228, (CNRSINSAUJFUPS), Toulouse 31400, France
2Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z4, Canada
3Canadian Institute for Advanced Research, Toronto M5G 1Z8, Canada
4D´ epartement de physique & RQMP, Universit´ e de Sherbrooke, Sherbrooke, Qu´ ebec J1K 2R1, Canada
(Dated: July 28, 2011)
The electrical resistivity ρcof the underdoped cuprate superconductor YBa2Cu3Oy was measured
perpendicular to the CuO2planes on ultrahigh quality single crystals in magnetic fields large enough
to suppress superconductivity. The incoherent insulatinglike behavior of ρc at high temperature,
characteristic of all underdoped cuprates, is found to cross over to a coherent regime of metallic
behavior at low temperature. This crossover coincides with the emergence of the small electron
pocket detected in the Fermi surface of YBa2Cu3Oy via quantum oscillations, the Hall and Seebeck
coefficients and with the detection of a unidirectional modulation of the charge density as seen by
highfield NMR measurements. The low coherence temperature is quantitatively consistent with
the small hopping integral t⊥ inferred from the splitting of the quantum oscillation frequencies.
We conclude that the Fermisurface reconstruction in YBa2Cu3Oy at dopings from p = 0.08 to at
least p = 0.15, attributed to stripe order, produces a metallic state with 3D coherence deep in the
underdoped regime.
PACS numbers: 74.25.Bt, 74.25.Ha, 74.72.Bk
Understanding the behavior of the interplane c
axis transport in the underdoped,
temperature (highTc), cuprate superconductors is of
crucial importance to elucidate the normal state proper
ties of these materials [1, 2]. While the inplane resistivity
is metallic down to Tcin many underdoped cuprates, the
interplane resistivity along the caxis is insulatinglike
[3]. The peculiar properties of caxis charge transport
are demonstrated by caxis optical conductivity measure
ments by the absence of a Drude peak at low frequencies
in the underdoped normal state above Tc [4]. This be
havior of the caxis charge transport has been ascribed
to the opening of the pseudogap and the lack of a well
defined quasiparticle peak in those regions of momentum
space that control interplane transport [5], but theoret
ical models differ as to whether the ground state is insu
lating [6] or metallic (see ref 7 and ref. therein). In order
to understand caxis transport in cuprates, an important
new experimental fact must be taken into account: the
Fermi surface (FS) of underdoped cuprates undergoes a
profound transformation at low temperature, as revealed
by the observation of quantum oscillations [8]. Combined
with the negative Hall [9] and Seebeck coefficients [10] at
low temperature, these measurements demonstrate that
the FS of underdoped YBa2Cu3Oyis made of small elec
tron pockets in contrast to the large, holelike FS of the
overdoped cuprates [11]. de Haasvan Alphen [12] and
tunnel diode oscillation [13] (TDO) measurements in un
derdoped YBa2Cu3Oyrevealed the presence of multiple
frequencies, which have been interpreted as bilayer split
ting and warping of the FS effect in one case [12, 14][38]
and as compensated electron and hole pockets in another
hightransition
[13]. Quantum oscillations cannot give direct information
on the sign and the location of the FS but interpreting the
splitting of the frequency as warping of the FS leads to a
hopping integral, t⊥, of order of 15 K [12] (1.3 meV). This
value is one order of magnitude smaller than the value
of the interbilayer hopping predicted by band structure
calculations [15], which overestimates the transfer inte
gral between layers (t⊥≈ 30 meV) and therefore predict
a metalliclike caxis resistivity, even at high tempera
ture. The small t⊥ deduced from quantum oscillations
implies that quasiparticle motion in the interplane di
rection should be coherent at temperatures lower than
t⊥/kB, contrary to the current belief. Here we directly
address the possibility of coherent motion between CuO2
planes by measuring the caxis resistivity at low temper
ature in magnetic fields large enough to suppress super
conductivity.
We found that the caxis resistivity becomes metallic
like at low temperature, and interpret this as a conse
quence of caxis coherence. The low coherence temper
ature implies a small caxis dispersion and therefore a
small t⊥, in quantitative agreement with the splitting
of the multiple quantum oscillation frequencies [12, 14].
The onset of this crossover coincides with the emergence
of an electron pocket, as inferred from the change of sign
of the Hall [9, 16] and Seebeck [10, 17] coefficients at
low temperature, and concomitant with the onset of a
unidirectional modulation of the charge density observed
in recent NMR measurements [18]. This high mobility
pocket produces metalliclike transport both in the plane
[16] and along the caxis. Since caxis transport is mostly
dominated by the antinodal states [19], the coherent be
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FIG. 1:
YBa2Cu3Oy (p=0.109) for a current I and a magnetic field B
along the c axis (I ? B ? c) at different temperatures below
Tc. Inset: Same data between 10 K and 50 K with a fit of
each isotherm (dashed lines) using a twoband model above
the superconducting transition.
(color on line) Electrical resistivity ρc
of
haviour and the large amplitude of the quantum oscilla
tions in the caxis resistivity suggest that they arise from
antinodal states. The coherence temperature decreases
as the doping level decreases and vanishes at a hole dop
ing p ≈ 0.08, corresponding to the doping level where
the electron pocket disappears [16]. In the absence of
the electron pocket, transport along caxis remains inco
herent.
Fig. 1 presents the longitudinal caxis resistiv
ityupto60Tforan
YBa2Cu3Oy (Tc=61.3 K, p=0.109). Data for two other
compositions (p= 0.097 and 0.12) are shown in the sup
plementary material [20]. Below 60 K, a strong positive
magnetoresistance (MR) grows with decreasing temper
ature, in good agreement with earlier highfield measure
ments [21] of ρcon YBa2Cu3Oycrystals with Tc= 60 K.
At very low temperature, strong quantum oscillations
can clearly be seen, arising from the quantization of cy
clotron orbits perpendicular to the magnetic field. The
frequencies and temperature dependence of these oscil
lations are consistent with previous reports [8, 12–14].
Two features common to all three samples are the rise
of the infield caxis resistivity down to about 4 K, and
the clear saturation at lower temperature. This behavior
is best captured in Fig. 2 where the resistivities mea
sured at zero field (solid line) and at B = 50 T (green
open squares) are compared with the insulatinglike high
temperature behavior, where the caxis resistivity fol
lows a 1/T dependence (dashed line in Fig. 2). The inset
of Fig. 2 makes it evident that the saturation of ρc(T),
at low temperature and for a given field above 50 T, is
underdopedsampleof
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FIG. 2: (color on line) Temperature dependence of the caxis
resistivity of YBa2Cu3Oy (p=0.109) measured at zero mag
netic field (black solid line) and at B = 50 T (blue circles).
Dashed line is a 1/T fit to the high temperature data up to
300 K. The saturation of the infield resistivity at low temper
ature contrasts with the insulatinglike behavior seen at high
temperature. The green open squares correspond to the resis
tivity from which the magnetoresistance has been subtracted
using a twoband model to extrapolate the normalstate data
of Fig. 1 to B = 0 (see [20]). The inset shows data of Fig. 1
plotted as a function of 1/T for different values of the mag
netic field. Dashed lines are a guide to the eye.
not due to some compensation between superconducting
drop (as seen for the data below 40 T) and insulating
like normalstate resistivity since the saturation persists
at fields higher than 50 T. From Nernst, inplane and
outofplane transport measurements [20], the threshold
field above which there is negligible fluxflow contribu
tion to the resistivity was identified; at all three dopings,
50 T is above this threshold field down to the lowest tem
peratures. The magnetoresistance measured at 50 T is
purely a normalstate property at all three dopings. Con
sequently, in fields of 50 T and above, where the caxis
resistivity saturates as T→0, the nonsuperconducting
ground state of YBa2Cu3Oy is coherent in all three di
rections at p = 0.10 − 0.12.
The observation of caxis coherent transport implies
that charge carriers are not confined to the CuO2planes
[2] and that coherent Bloch bands along the caxis
form at low temperature.
about the existence of a threedimensional Fermi sur
face in overdoped cuprate superconductors [22], our find
ings suggest that interplane transport in underdoped
YBa2Cu3Oy can also, in principle, be described at low
temperature within the same conventional theory of met
als. In this case, the caxis conductivity is given by σc=
4e2ct2
π?4
where c is the caxis lattice parameter, τcis
the relaxation time, and m∗is the effective mass. For a
tetragonal cuprate material, the interlayer hopping inte
While there is no doubt
⊥m∗τc
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FIG. 3: (color on line) The slope of the caxis magnetore
sistance evaluated at B = 50 T (red circles; left axis) and
inplane Hall coefficient RH (blue squares; right axis) of
YBa2Cu3Oy (p=0.108) as a function of temperature.
data measured at B = 54 T is taken from ref. 16 and nor
malized by its value at T = 100 K. T0 is the temperature
at which RH(T) changes sign from positive at high temper
ature to negative at low temperature [9, 16]. Tonset is the
temperature below which ρc(T) deviates downward from its
1/T dependence at high temperature (vertical dashed line).
RH
gral t⊥depends strongly on the inplane momentum k of
carriers, namely [23] : t⊥(k) =
It is maximum at the antinode i.e. at the (π, 0) (and
equivalent) points in the Brillouin zone. The coherent
caxis transport we observe at low temperature can be
interpreted in two different ways. Assuming that elec
tronic states exist only at the node and considering the
large value of t0
⊥deduced from band structure calcula
tions, the fact that t⊥(k) is minimum at the nodes may
explain why the caxis coherence appears only at very
low temperature. Conversely, if one assumes that t0
is strongly renormalized (by electronelectron interaction
for instance) in comparison to the band structure cal
culations value, the caxis coherence is a consequence of
electronic states at the antinode. ARPES measurements
in overdoped Bi2Sr2CaCu2O8+δ[24] and in underdoped
YBa2Cu3Oy[25, 26] have shown that t⊥(connected with
the bilayer effect) is strongly suppressed in comparison
with the band structure calculations value. This argues
for the second scenario, where those states at (π, 0) are
in fact the small closed pocket responsible for the oscil
lations.
In this scenario, the presence of electronic states at
the antinode is difficult to reconcile with the observa
tion of Fermi arcs in ARPES measurements above Tc
in underdoped cuprates [27]. However, the observation
of quantum oscillations has revealed that the FS of un
derdoped YBa2Cu3Oyundergoes a profound transforma
tion at low temperature. This interpretation has been
recently strengthened by nuclear magnetic resonance
(NMR) measurements [18] showing that the translational
t0
⊥
4[cos(kxa) − cos(kyb)]2.
⊥
symmetry of the CuO2planes in YBa2Cu3Oy is broken
by the emergence of a unidirectional modulation of the
charge density at a temperature Tcharge= 50 ± 10 K for
p=0.108 and above a threshold field B ≈ 20 T. Tcharge
deduced from NMR measurement coincides roughly with
the temperature T0, the temperature at which RH(T)
changes sign.Combined with the evidence that this
pocket is electronlike [9, 10, 16, 17], its location at
(π, 0), where most densitywave scenarios predict the
emergence of such a pocket (see for example refs 28–
30), greatly strengthens the case for FS reconstruction
in YBa2Cu3Oy.
Although recent specific heat [31] and Seebeck coeffi
cient [17] measured at high fields point to a Fermi surface
made of only one pocket [32], the emergence of a strong
MR at low temperature is naturally explained by the FS
reconstruction into electron and hole sheets, due to the
ambipolar character of the Fermi surface. In Fig. 3 we
compare the slope of the magnetoresistance ρc(B) and
the inplane Hall coefficient RHas a function of temper
ature measured at the same hole doping. The onset of
the MR in ρccoincides with the FS reconstruction thus
revealing the two roles played by the electron pocket: it
enhances the orbital MR due to inplane motion of carri
ers and it allows that the MR to be reflected in interplane
transport.
It now becomes necessary to deduce the MRfree tem
perature dependence of ρc(T) by extrapolating the in
field resistivity ρc(B) to B = 0, defined as ρc(0). Since
a strong MR develops at low temperature, any smooth
extrapolation to B = 0 will give the same trend for
the temperature dependence of ρc(0), namely an ini
tial rise with decreasing temperature turning into a drop
at low temperature. To illustrate this, we extrapolate
the infield resistivity ρc(B) to B = 0 using the same
twoband model (electron and hole carriers) that self
consistently accounted for the temperature and field de
pendence of the longitudinal and transverse (Hall) resis
tivities of YBa2Cu4O8[33]. Fitting every isotherm down
to 10 K in Fig. 1 (dashed lines) yields the extrapolated
zerofield resistivity ρc(0) shown in green open squares
in Fig. 2. The initial rise in ρc(0) with decreasing tem
perature turns into a drop at low temperature, passing
through a maximum at Tcoh= 27±3 K. This is in reason
able agreement with the energy scale t⊥≈ 15 K obtained
from the splitting of frequencies in quantum oscillations
for YBa2Cu3Oy at p = 0.10  0.11 [12, 14]. The same
analysis for the two other compositions are shown in the
supplementary material [20] and yields Tcoh= 20 ± 5 K
for p= 0.097 and Tcoh= 35 ± 5 K for p= 0.12.
Several models based on incoherent tunneling between
layers, assisted by interplanar disorder, have been in
voked to explain the anomalous caxis transport in
cuprates (see ref 7 and ref. therein). However, several
experimental facts demonstrate that the coherent caxis
transport at low temperature is a direct consequence of
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FIG. 4: (color on line) Temperaturedoping phase diagram of
YBa2Cu3Oy , with the superconducting phase in zero mag
netic field delineated by the transition temperature Tc. Black
circles mark the temperature T∗below which the inplane re
sistivity deviates from its linear temperature dependence at
high temperature (from data in ref. 37), a standard definition
for the onset of the pseudogap phase. The onset of coher
ence in the caxis resistivity at Tonset (red squares) is plot
ted along Tcoh (green circles), the temperature where ρc(T)
peaks (see Fig. 2 and ref. 20). The coherence crossover splits
the phase diagram into two regions: an incoherent 2D regime
above and a coherent 3D regime below. T0 is the temperature
at which the normalstate inplane Hall coefficient RH(T) of
YBa2Cu3Oy changes sign from positive at high temperature
to negative at low temperature (blue diamonds; from ref. 16)
the Fermi surface reconstruction occurring at a temper
ature scale Tcharge ≈ T0. From caxis transport mea
surements, we define Tonset as the temperature below
which ρc starts deviating from its 1/T dependence at
high temperature and Tcohas the characteristic temper
ature for the crossover to the coherent regime at which
ρc(0) peaks (see Fig. 2). In Fig. 4, we compare these tem
peratures as a function of doping on the phase diagram
of YBa2Cu3Oy. Not only do the two phenomena start
at the same temperature for a given doping, they also
trend similarly as a function of doping, both decreasing
to lower T with decreasing p. In addition, these charac
teristic temperatures extrapolate to zero at lower doping
p ≈ 0.08, where RH(T) no longer shows any downturn
(see data for sample with Tc= 44.5 K in ref. 16). This
qualitative change has been attributed to the disappear
ance of the electron pocket, either caused by a Lifshitz
transition [16] or by a phase transition [34]. Earlier mea
surements of caxis transport on a sample with Tc= 49 K
[21] are consistent with such a transition: the MR in
ρc(T) is entirely gone and ρcis now incoherent, increas
ing down to the lowest temperatures.
A natural explanation of our results is to invoke an
electron pocket at the antinodal position when the Fermi
surface reconstruction occurs. Between the pseudogap
temperature T∗and the temperature characteristic of the
FS reconstruction T0, the lack of welldefined quasiparti
cle peak seen by ARPES in the antinodal regions leads
to a semiconductinglike behavior in ρc. The emergence
of a unidirectional modulation of the charge density seen
by highfield NMR in YBCO [18] and the similarity in the
thermoelectric transport properties of YBa2Cu3Oy and
La1.8−xEu0.2SrxCuO4[17]  a cuprate where stripe order
is wellestablished from Xray diffraction [35]  argue for
a chargestripe order causing the reconstruction of the
FS at low temperature for p > 0.08. The resulting FS
contains at least a highmobility electron pocket, which
produces a metalliclike transport in the plane and along
the caxis at low temperature. The electron pocket dis
appears below p ≈ 0.08, probably because of a transition
from a chargestripe order (p > 0.08) to a phase with
spin order (p < 0.08) [36]. In the absence of this electron
pocket, both inplane and outofplane transport proper
ties are incoherent at low temperature.
Wethank A.Carrington,S.Chakravarty,A.
Chubukov, M. H. Julien, S. Kivelson, A. Millis, M. Nor
man, R. Ramazashvili, T. Senthil, G. Rikken and M. Vo
jta for useful discussions. Research support was provided
by the French ANR DELICE, Euromagnet II, the Cana
dian Institute for Advanced Research and the Natural
Science and Engineering Research Council.
∗Electronic address: cyril.proust@lncmi.cnrs.fr
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Supplementary material for ”Coherent caxis transport in the underdoped cuprate
superconductor YBa2Cu3Oy”
SAMPLE PREPARATION AND
EXPERIMENTAL SETUP
Thesamplesstudiedweresinglecrystals of
YBa2Cu3Oy , grown in nonreactive BaZrO3 crucibles
from highpurity starting materials and subsequently
detwinned. The doping p of each crystal was inferred
from its superconducting transition temperature Tc
[1].Electrical contacts to the sample were made by
evaporating gold, with large current pads and small
voltage pads mounted across the top and bottom so as
to short out any inplane current (Corbino geometry).
Several samples of different thicknesses were measured,
each giving similar values of the absolute caxis resis
tivity.The resistivity was measured at the LNCMI
in Toulouse, in pulsed magnetic fields up to 60 T. A
current excitation of 5 mA at ≈ 60 kHz was used. The
voltage (and a reference signal) was digitized using a
highspeed digitizer and postanalysed to perform the
phase comparison.
CAXIS MAGNETORESISTANCE AT
DIFFERENT DOPING LEVEL
Fig. 1a and Fig. 1b present the longitudinal caxis re
sistivity up to 60 T for two other underdoped samples
of YBa2Cu3Oy at a hole doping p=0.097 (Tc=57.0 K)
and p=0.120 (Tc=66.4 K), respectively.
the p=0.109 sample, a strong positive magnetoresistance
grows with decreasing temperature below 60 K and the
infield caxis resistivity increases down to about 4 K,
followed by a saturation at lower temperature.
Similarly to
FLUX FLOW CONTRIBUTION TO THE
RESISTIVITY
Upon cooling, the resistivity drops because of super
conductivity. This drop starts at lower temperature for
higher fields. We define the threshold field beyond which
the normal state is reached as the field for which ρc(T)
shows no drop. To confirm that this saturation of ρc(T)
at low temperature is not due to some compensation be
tween superconducting drop and insulatinglike normal
state resistivity, we show that the saturation persists at
fields above the threshold field (see Fig. 2). In all three
samples, 50 T is above the threshold field down to the
lowest temperatures. Therefore the magnetoresistance
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FIG. 1: Electrical resistivity ρc of YBa2Cu3Oy : (a) p=0.097
and (b) p=0.120 for a current I and a magnetic field B along
the c axis (I ? B ? c) at different temperatures below Tc.
measured at 50 T is purely a normalstate property, at
all three dopings.
The Nernst effect is a sensitive probe of flux flow, be
cause moving vortices make a large positive contribution
to the Nernst coefficient. In Fig. 3, we compare the field
dependence of the inplane Hall coefficient [2] and caxis
resistivity with that of the Nernst coefficient measured
in YBa2Cu3Oy at p = 0.12 and T = 10 K [3].
Nernst coefficient develops a strong positive peak above
the melting line due to vortex motion in the vortex liquid
phase and is followed by a gradual descent to negative
values (the quasiparticle contribution) until it becomes
almost flat as the field approaches 30 T. This saturation
is best captured by the field derivative of the Nernst coef
ficient shown by a red line in Fig. 3a. Above the threshold
field of about 30 T, the Hall coefficient becomes flat (as
indicated by the blue dashed line in Fig. 3b) and the two
band model used to fit the normal state caxis resistivity
merges with the data (see Fig. 3c).
confirms that fluxflow contribution to the normalstate
transport is negligible for fields greater than 30 T at this
doping level (and temperature). Therefore, the magne
toresistance above 30 T is entirely due to quasiparticles,
The
This comparison
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FIG. 2: Electrical resistivity ρc of YBa2Cu3Oy : (a) p =
0.097, (b) p = 0.109 and (c) p = 0.120 plotted as a function of
temperature for different values of the magnetic field. Dashed
lines are a guide to the eye. The increase of the infield caxis
resistivity down to about 4 K is in part due to the strong
magnetoresistance which develops at temperature below 60 K.
demonstrating that the ρc(0) values deduced from the
fits are a property of the normal state.
In the supplementary information of ref. 2, the field
scale above which the effects of vortex motion and su
perconducting fluctuations have become negligible in Rxx
and Rxy, have been determined such that these transport
coefficients reflect predominantly the properties of the
normal state. T0(B) is the temperature at which RH(T)
changes sign. The key observation is that T0is indepen
dent of field at the highest fields (up to 60 T) in three ma
terials (p=0.100.14). This shows that the temperature
induced sign change in RH at high fields is not caused
by flux flow and is thus clearly a property of the normal
state. The case is particularly clear in the p = 0.120
sample, where the sign change occurs above Tc(0) and
is totally independent of field over the entire field range
from 0 to 45 T. In addition flux flow yields a contribu
tion to the Hall resistance which is strongly nonlinear in
B, so that the Hall coefficient should depend strongly on
magnetic field. This is not the case for the three samples
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FIG. 3: Field dependence of (a) the Nernst coefficient [3], (b)
the Hall coefficient [2] and (c) the caxis resisitivity (Fig. 1c)
of YBCO at p = 0.12 and T = 10 K. Above a threshold field
of about 30 T (indicated by the right vertical dashed red line),
the Nernst coefficient ν (panel a; green curve) saturates to its
negative quasiparticle value, as demonstrated by its deriva
tive (panel a; red curve) which goes to zero as B ≈ 30 T.
This saturation shows that the positive contribution to the
Nernst coefficient from superconducting fluctuations has be
come negligible above 30 T. Above this field, the Hall coef
ficient is almost flat (dashed blue line in panel b) and the
twoband model fit to the caxis resistivity (dashed magenta
line in panel c) merges with the data. We conclude that at
10 K and above 30 T the fluxflow contribution to the trans
port properties is negligible, and the large magnetoresistance
at high field is purely a property of the normal state.
at the highest fields, where RHis flat. This is further ev
idence that we are probing the normal state properties of
these compounds in the field/temperature range. Earlier
highfield measurements of ρcin YBa2Cu3Oy[4] show a
striking difference between the large magnetoresistance
observed in samples with Tc= 60 K and the absence of
the magnetoresistance in sample with Tc = 49 K. This
can only be due to normal state transport properties and
can be explained by the vanishing of the very mobile elec
tron pocket for the low doping sample [5]. There is no
alternative explanation in term of flux flow.
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FIG. 4: The raw resistivity curves of Fig. 1 are fitted using
the twoband model (see text). The dashed lines are a fit of
each isotherm to Eq. 1 above the superconducting transition
for (a) p = 0.097, (b) p = 0.120. The parameter ρ0 gives the
zerofield extrapolation ρc(0), plotted in Fig. 5.
TWOBAND MODEL
Assuming that the Fermi surface of underdoped
YBa2Cu3Oycontains both electrons and holes, the trans
verse magnetoresistance can be fitted with a twoband
model:
ρ(B) =(σh+ σe) + σhσh(σhR2
(σh+ σe)2+ σ2
h+ σeR2
e(RH+ Re)2B2
e)B2
hσ2
= ρ0+
αB2
1 + βB2
(1)
σh(σe) is the conductivity of holes (electrons) and Rh
(Re) is the Hall coefficient for hole (electron) carriers.
Using the three free parameters ρ0, α and β, we were
able to subtract the orbital magnetoresistance from the
field sweeps and get the temperature dependence of the
zerofield resistivity ρc(0) = ρ0(T). In order to estimate
error bars, we fitted each field sweep data set to eq. 1
between a lower bound Bcut−offand the maximum field
strength and monitored the value of ρc(0) as a function
of Bcut−off. The resulting fits to ρc(B) at different tem
peratures for the samples p = 0.097 and p = 0.120 are
shown in Fig. 4.
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FIG. 5: Temperature dependence of the caxis resistivity of
YBa2Cu3Oy from which the magnetoresistance has been sub
tracted using a twoband model (see text).
TEMPERATURE DEPENDENCE OF THE
ZEROFIELD EXTRAPOLATED RESISTIVITY
Fig. 5 shows the temperature dependence of the c
axis resistivity of YBa2Cu3Oy from which the magne
toresistance has been subtracted using a twoband model
(Eq. 1) to extrapolate the normalstate data to B = 0,
for the three samples, as labelled. Solid lines show the
resistivity measured in zero magnetic field. Dashed lines
are a guide to the eye. The onset of this crossover occurs
at a temperature Tonset, below which the zerofield caxis
resistivity ρc(0) deviates downward from its 1/T depen
dence at high temperature. A characteristic temperature
for the crossover between incoherent caxis transport at
high temperature and coherent transport at low tempera
ture is the temperature at which ρc(0) peaks, with values
Tcoh= 20, 27 and 35 K for p = 0.097, 0.109 and 0.120
respectively. This is in reasonable agreement with the
energy scale t⊥ ≈ 15 K obtained from the splitting of
frequencies in quantum oscillations for YBa2Cu3Oy at
p = 0.10  0.11 [6].
∗Electronic address: cyril.proust@lncmi.cnrs.fr
[1] R. Liang et al., Phys. Rev. B 73, 180505(R) (2006).
[2] D. LeBoeuf et al., Nature 450, 533 (2007).
[3] J. Chang et al., Phys. Rev. Lett. 104, 057005 (2010).
[4] F. F. Balakirev et al., Physica C 341348, 1877 (2000).
[5] D. LeBoeuf et al., Phys. Rev. B 83, 054506 (2011).
[6] A. Audouard et al., Phys. Rev. Lett. 103, 157003 (2009).
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