Fermi liquid behavior of the in-plane resistivity in the state of YBa2Cu4O8 Cyril Prousta,1, Baptiste Vignollea, Julien Levalloisa,b, S. Adachic, and Nigel E. Husseyd,e,1

aLaboratoire National des Champs Magnétiques Intenses–European Magnetic Field Laboratory (CNRS–Institut National des Sciences Appliquées–Université Grenoble Alpes–Université Paul Sabatier), Toulouse 31400, France; bDepartment of Quantum Matter Physics, University of Geneva, CH-1211 Geneva 4, Switzerland; cSuperconductivity Research Laboratory, Tokyo 135-0062, Japan; dHigh Field Magnet Laboratory–European Magnetic Field Laboratory, Radboud University, 6525 ED Nijmegen, The Netherlands; and eInstitute of Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands

Edited by Laura H. Greene, National High Magnetic Field Laboratory and Florida State University, Tallahassee, FL, and approved September 20, 2016 (received for review February 17, 2016) Our knowledge of the ground state of underdoped hole-doped pocket in the nodal region of the Brillouin zone (23). Depending cuprates has evolved considerably over the last few years. There is on the initial pseudogapped FS and on the wavevectors of the now compelling evidence that, inside the pseudogap phase, charge charge order, FS reconstruction can also lead to additional, smaller order breaks translational symmetry leading to a reconstructed hole pockets (24, 25). In Y123 (doping level p ∼ 0.11) the QO made of small pockets. Quantum oscillations [Doiron- spectra consist of a main frequency Fa = 540 T and a beat pattern Nature – Leyraud N, et al. (2007) 447(7144):565 568], optical conduc- indicative of nearby frequencies Fa2 = 450 T and Fa3 = 630 T. A Proc Natl Acad Sci USA – tivity [Mirzaei SI, et al. (2013) 110(15):5774 smaller frequency Fh ∼ 100 T has been detected by thermo- 5778], and the validity of Wiedemann–Franz law [Grissonnache G, power and c-axis transport measurements and attributed there et al. (2016) Phys Rev B 93:064513] point to a Fermi liquid regime at to an additional small hole pocket (26). The presence of the low temperature in the underdoped regime. However, the observa- three nearby frequencies Fai can be explained by a model in- tion of a quadratic temperature dependence in the electrical resistiv- volving a bilayer system with an electron pocket in each plane ity at low temperatures, the hallmark of a Fermi liquid regime, is still and magnetic breakdown between the two pockets (27, 28). missing. Here, we report magnetoresistance measurements in the In this scenario, the low-frequency Fh could originate from magnetic-field–induced normal state of underdoped YBa2Cu4O8 that T2 quantum interference or the Stark effect (29). However, this are consistent with a resistivity extending down to 1.5 K. The scenario predicts the occurrence of five nearby frequencies magnitude of the T2 coefficient, however, is much smaller than and thus requires fine-tuning of certain microscopic param- expected for a single pocket of the mass and size observed in quan- eters such as the bilayer tunneling t⊥. Moreover, the doping tum oscillations, implying that the reconstructed Fermi surface must dependence of the Seebeck coefficient is difficult to reconcile consist of at least one additional pocket. with a FS reconstruction scenario leading to only one electron pocket per plane. high T | electrical transport | Fermi liquid | Fermi surface c More generally, the observation of QOs is a classic signature of Landau quasiparticles. In underdoped Y123, the temperature de- he generic phase diagram of Fig. 1 summarizes the temper- – ρ pendence of the amplitude of the oscillations follows Fermi Dirac Tature and doping dependence of the in-plane resistivity ab(T) statistics up to 18 K, as in the Landau– (30). of hole-doped cuprates (1). Starting from the heavily overdoped This conclusion is supported by other observations, such as the side, nonsuperconducting La1.67Sr0.33CuO4, for example, shows a validity of the Wiedemann–Franz law (31) in underdoped Y123 purely quadratic resistivity below ∼50 K (2). Below a critical doping pSC where superconductivity sets in, ρab(T)exhibits 2 Significance supralinear behavior that can be modeled either as ρab ∼ T + T or as Tn (1 < n < 2). When a magnetic field is applied to suppress superconductivity on the overdoped side, the limiting low-T be- High-temperature superconductivity evolves out of a metallic havior is found to be T linear (3–5). Optimally doped cuprates are state that undergoes profound changes as a function of carrier concentration, changes that are often obscured by the high upper characterized by a linear resistivity for all T > Tc, although the slope often extrapolates to a negative intercept, suggesting that, at critical fields. In the more disordered cuprate families, field suppression of superconductivity has uncovered an underlying the lowest temperatures, ρab(T) contains a component with an ground state that exhibits unusual localization behavior. Here, exponent larger than 1 (1). In the underdoped regime, ρab(T) varies approximately linearly with temperature at high T,butas we reveal that, in stoichiometric YBa2Cu4O8, the field-induced the temperature is lowered below the pseudogap temperature T*, ground state is both metallic and Fermi liquid-like. The manu- it deviates from linearity in a very gradual way (6). At lower script also demonstrates the potential for using the absolute temperatures, marked by the light blue area in Fig. 1, there is now magnitude of the electrical resistivity to constrain the Fermi sur- compelling evidence from various experimental probes of in- face topology of correlated metals and, in the case of YBa2Cu4O8, cipient charge order (7–11). High-field NMR (12, 13) and ultra- reveals that the current picture of the reconstructed Fermi surface sonic (14) measurements indicate that a phase transition occurs in underdoped cuprates as a single, isotropic electron-like pocket may be incomplete. below Tc. This is also confirmed by recent high-field X-ray mea- surements that indicate that the charge density wave (CDW) order Author contributions: C.P. and N.E.H. designed research; C.P., B.V., J.L., S.A., and N.E.H. becomes tridimensional with a coherence length that increases performed research; S.A. grew the crystals; C.P., B.V., and N.E.H. analyzed data; and C.P. with increasing magnetic field strength (15, 16). This leads to a and N.E.H. wrote the paper. Fermi surface (FS) reconstruction that can be reconciled with The authors declare no conflict of interest. quantum oscillations (QOs) (17, 18) as well as with the sign This article is a PNAS Direct Submission. change of the Hall (19) and Seebeck (20) coefficients. Whether 1To whom correspondence may be addressed. Email: [email protected] or the charge order is biaxial (21) or uniaxial with orthogonal do- [email protected]. mains (22) is still an open issue, but a FS reconstruction involving This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. two perpendicular wavevectors leads to at least one electron 1073/pnas.1602709113/-/DCSupplemental.

13654–13659 | PNAS | November 29, 2016 | vol. 113 | no. 48 www.pnas.org/cgi/doi/10.1073/pnas.1602709113 Downloaded by guest on September 29, 2021 αH2 ρðHÞ = ρð0Þ + , [1] 1 + βH2

where ρ(0) is the zero-field resistivity and α and β are free param- eters that depend on the conductivity and the Hall coefficient of the electron and hole carriers (35) (see Fig. S1 for a comparison of the two-band and single-band, quadratic forms for the magneto- resistance). To obtain reliable values of ρ (H → 0, T) = ρ(0) and corresponding error bars for each field sweep, the data were fitted

A 100 sample #1

80

60 Fig. 1. Generic phase diagram of hole-doped cuprates. Generic phase dia-

gram of hole-doped cuprates mapped out in terms of the temperature and (cm)

doping evolution of the in-plane resistivity ρab(T). The solid lines are the a phase boundaries between the normal state and the superconducting (SC) or 40 4.2 K antiferromagnetic (AFM) ground state. The dashed lines indicate crossovers 20 K

in ρab(T) behavior. The light blue area corresponds to where incipient charge 40 K order (I-CDW) has been detected by X-ray measurements in Y123 (39, 40). 60 K The CDW order becomes long-range order below Tc when a large magnetic 20 70 K field is applied (12–14). 80 K 100 K

and the quadratic frequency and temperature dependence of the 0 quasiparticle lifetime τ(ω, T) measured by optical spectroscopy 0204060 (32) in underdoped HgBa2CuO4+δ (Hg1201). An important out- standing question is whether the in-plane resistivity of underdoped H(T) cuprates also exhibits the behavior of a canonical Landau–Fermi liquid, namely, a quadratic temperature dependence at low T.In B ρ ∼ 2 underdoped cuprates, several studies have shown ab T ,but sample #2 always at elevated temperatures (indeed, most are above Tc)and 100 only over a limited temperature range that never exceeds a factor of 2.5 (6, 33–36) (see Table S1 for a detailed list of studies). At low temperatures, either ρab(T) starts to become nonmetallic (36), suggesting that the T2 behavior observed at intermediate temper- 80 atures could just be a crossover regime, or a quadratic behavior has previously been hinted at (19), rather than shown explicitly. Here, we present high-field in-plane magnetoresistance measurements in 60

underdoped YBa2Cu4O8 (Y124) that are consistent with the form (cm)

2 a ρa(T) = ρ0(T) + AT from T = Tc down to temperatures as low as 4.2 K 1.5 K, that is, over almost two decades in temperature. In addition, 40 10 K we investigate the magnitude of the resultant A coefficient and 20 K compare it with some of the prevalent FS reconstruction scenarios. 40 K In conclusion, we find that the magnitude of A is difficult to rec- 60 K oncile with the existence of a single electron pocket per plane, with 20 70 K an isotropic mass. 80 K 100 K Results 0 PHYSICS We have measured the a-axis magnetoresistance (i.e., perpen- 0 204060 dicular to the conducting CuO chains) of two underdoped Y124 H(T) (Tc = 80 K) single crystals up to 60 T at various fixed tempera- tures down to 1.5 K. From thermal conductivity measurements at high fields, the upper critical field H of Y124 has been esti- Fig. 2. Field dependence of the in-plane resistivity in Y124 for sample 1 (A) c2 ρ = mated to be ∼45 T (37). Raw data for both samples are shown in and sample 2 (B). Electrical resistivity a of two samples of YBa2Cu4O8 (Tc 80 K) for current I jj a and magnetic field H applied along the c axis at different Fig. 2. Above Tc, that is, in the absence of superconductivity, the temperatures (solid lines). With lowering the temperature, a strong mag- transverse magnetoresistance can be accounted for, over the netoresistance develops, which can be accounted for by a two-band model entire field range measured, by a two-carrier model (35) using (35). Dashed lines correspond to fits using this model (Eq. 1 in the text) to the following formula: extrapolate the normal-state data to H = 0.

Proust et al. PNAS | November 29, 2016 | vol. 113 | no. 48 | 13655 Downloaded by guest on September 29, 2021 to Eq. 1 in varying field ranges using the procedure described in A detail in Figs. S2–S5 and Tables S2 and S3. Precisely the same form is used to fit the high-field data at all temperatures studied below Tc. This procedure has been found to yield reliable ρ(0) values in both cuprate (5) and pnictide (38) superconductors. Extrapolation of the high-field data to the zero-field axis ρ(0), as shown by dashed lines in Fig. 2, allows one then to follow the evolution of ρa(T) down to low temperatures. The extrapolated ρ(0) values are plotted versus temperature in Fig. 3 (symbols) for both crystals, along with the zero-field temperature dependence of the resistivity (solid line). The dashed lines in Fig. 3 correspond to fits of the ρ(0, T)datato 2 the form ρ0(T) = ρ0 + AT . A fit of the data to the form ρ0(T) = n ρ0 + AT yields n = 1.9 ± 0.2 is shown in the Fig. S6.TheInsets of 2 Fig. 3 are corresponding plots of ρa(T) versus T to highlight the approximately quadratic form of ρa(T). From the dashed line fits, we obtain ρ0 = 7.5 ± 1.0 and 10.0 ± 1.0 μΩ·cm and A = 10.0 ± 1and − 8.5 ± 0.5 nΩ·cm·K 2 for samples 1 and 2, respectively. Discussion The first key result of this study is our observation, within experi- mental resolution, of a quadratic temperature dependence of the in-plane resistivity in Y124 down to low temperatures, which in- dicates that the low-lying (near-nodal) electronic states inside the pseudogap phase of underdoped cuprates bear all of the hallmarks of Landau quasiparticles. Intriguingly, the magnitude of the T2 − B term, A = 9.5 ± 1.5 nΩ·cm·K 2, is similar to that measured at high temperature, for example, above 50 K in underdoped Y123 at p = − 0.11 (A ∼ 6.6 nΩ·cm·K 2)(33)aswellasinsingle-layerHg1201 − above 80 K where A varies between ∼10 and 15 nΩ·cm·K 2 for 0.055 ≤ p < 0.11 (34). Note that, in Y124, such comparison cannot be made because the temperature dependence of the resistivity is not quadratic above Tc. In Y123, it is known that an incipient CDW is formed below T*, which onsets at about TCDW ∼ 130–150 K in the doping range at p = 0.11–0.14 (39, 40). At a lower temperature TFSR ∼ 50 K, high-field NMR (12) and ultrasound (14) measure- ments for p = 0.11 have revealed a phase transition, below which long-range static charge order appears and FS reconstruction is believed to take place. Taking into account that the ρ(0) values shown in Fig. 3 are extrapolated from this high-field phase, there would appear to be no significant change in the A coefficient be- tween the low-T regime where long-range CDW sets in and the high-T regime where only incipient CDW order is detected. This is reminiscent of the situation in NbSe2, where there is negligible change of the resistivity at the CDW transition TCDW = 33 K (41). This behavior can be understood if no substantial change of the FS occurs at the CDW transition (for a discussion, see ref. 42). To make an analogy with Y124, we first acknowledge that the effect of the pseudogap is to suppress quasiparticles near the Brillouin zone boundaries. A FS reconstruction due to charge order with domi- Fig. 3. Temperature dependence of the in-plane resistivity in Y124 for sample 1 nant wavevectors (Qx,0)and(0,Qy) will create a small electron- (A)andsample2(B). Temperature dependence of the a-axis resistivity of YBa2- like pocket composed of the residual “nodal” density of states, in Cu4O8 from which the magnetoresistance has been subtracted using a two-band contrast to the large hole-like FS characterizing the overdoped model to extrapolate the normal-state data to H = 0 for the two samples shown state. This FS reconstruction can be seen as a folding of the FS, and in Fig. 2. Solid lines show the resistivity measured in zero magnetic field. Dashed lines are fits to the Landau–Fermi liquid expectation for the temperature de- in terms of transport properties, the same nodal states will be in- 2 pendence of the resistivity at low temperature, ρa(T) = ρ0 + AT (see text). To volved in scattering processes below T* and below TFSR when the estimate error bars, we fitted each field sweep dataset to Eq. 1 between a lower FS is reconstructed. Thus, the similar value of A at high and low bound Hcutoff and the maximum field strength and monitored the value of ρ(0) as temperatures can be reconciled. Note that, in canonical 1D CDW afunctionofHcutoff (see Supporting Information for more details). The Insets are ρ 2 ρ systemssuchasNbSe3 (43) and organics metals (44), there is a corresponding plots of a(T) versus T to highlight the quadratic form of a(T). marked change of slope of the resistivity below the charge ordering temperature due to nesting of part of the original FS. The scenario discussed above for Y124 is also consistent with pseudogap regime, therefore, one expects the T-linear scattering 2 the observation of an anisotropic scattering rate Γ in cuprates. In rate to become much diminished, leaving the T scattering term as ρ overdoped Tl2Ba2CuO6+δ (Tl2201) (45), for example, it has been the dominant contribution to a(T). shown that the scattering rate is composed of two distinct terms, a In correlated metals, both the T2 resistivity and the T-linear T2 term that is almost isotropic within the basal plane and a specific heat are the consequence of the Pauli exclusion principle. T-linear scattering rate that is strongly anisotropic, vanishing along Thus, the strength of the T2 term in ρ(T) is empirically related to the zone diagonals and exhibiting a maximum near the Brillouin the square of the electronic specific heat coefficient γ0 via the 2 zone boundary, where the pseudogap is maximal. Inside the Kadowaki–Woods ratio (KWR) A/γ0 (46). An explicit expression

13656 | www.pnas.org/cgi/doi/10.1073/pnas.1602709113 Proust et al. Downloaded by guest on September 29, 2021 for the KWR has been derived for correlated metals taking into account unit cell volume, dimensionality, and carrier density (47). In a single-band quasi-2D metal, the A coefficient reads as follows: ! ! 8π3ack2 mp2 A = B . , [2] KWR 2Z3 3 e kF

where a and c are the lattice parameters, and m* and kF are the (isotropic) effective mass and Fermi wavevector, respectively. A similar expression has also been obtained recently using the Kubo formalism (48). As shown in Supporting Information, com- parison of AKWR with experimentally determined values for both single-band and multiband correlated oxides shows good agree- ment for AKWR values spanning over three orders of magnitude. Electron–electron collisions involve two quasiparticles that re- side within a width of order kBT near the Fermi energy, providing the factor T2. However, the total electron momentum is conserved in normal electron–electron scattering for the simple metals with a nearly free-electron–like FS. Additional mechanisms, such as Umklapp or interband scattering, are thus needed to understand the dissipation (see refs. 49–51 for a discussion). With regards to the hole-doped cuprates, it is debatable whether the KWR should hold at all within the pseudogap phase. However, given the in- creasing amount of data pointing to a rather conventional state at sufficiently low temperature, we believe that such analysis and comparison are appropriate, and in the following, we consider briefly a number of these possible mechanisms (47–51) in turn.

Umklapp Scattering. Assuming a single electron pocket per CuO2 plane, Umklapp collisions can lead to dissipation for electron– electron scattering because the condition on the reconstructed FS, Fig. 4. FS reconstruction by biaxial charge order. Sketch of the recon- kF > G/4, is fulfilled in the reconstructed Brillouin zone (G is a structed FS adapted from ref. 24 using the CDW wavevectors measured in reciprocal lattice vector). In Y124, the QO frequency linked to the Y123, showing a diamond-shaped nodal electron pocket (red) and two hole- like ellipses (blue and green). A and A are the A coefficients estimated electron pocket (Fe = 660 ± 30 T) converts into kFe = 1.42 ± e h −1 0.03 nm (52, 53), whereas the most recent QO measurements from Eq. 2 for the electron and hole pockets, respectively. Atot is the expected A coefficient for a parallel resistor model taking into account one have indicated that m* = 1.9 ± 0.1 me (54, 55). Eq. 2 thus gives an electron and two hole pockets and the two CuO2 planes. estimate of the A coefficient for the electron pocket, Ae = 86 ± −2 −2 20 nΩ·cm·K ,thatis,AKWR = 43 ± 10 nΩ·cm·K , taking into account the two CuO planes. Significantly, this is almost five −2 −2 2 Ae = 56 ± 9nΩ·cm·K and Ah = 89 ± 42 nΩ·cm·K (note that times larger than the experimental value. Assuming that the KWR the large error here is due to the relative error in the effective ratio holds in underdoped cuprates, it implies that a reconstructed mass). Finally, applying the parallel-resistor formula and taking into FS containing only one electron pocket (with an isotropic m*) 2 account the bilayer nature of Y123, the A coefficient is estimated to cannot account fully for the magnitude of the T resistivity term in −2 be AKWR ∼ 12 ± 6nΩ·cm·K , in reasonable agreement with the − Y124. Similar conclusions are also drawn from comparison of the value measured at high temperature (A ∼ 6.6 nΩ·cm·K 2) (33). Fermi parameters reported for underdoped Y123 (18) and the CDW order has not yet been directly observed by X-ray or by measured A coefficient (33) (albeit at elevated temperatures). NMR in Y124, but the similar QO frequency (presumed to arise from the electron pocket) and the sign change in the Hall co- Multiband Scenario. In a second scenario initially proposed by Baber (49), the momentum transfer between two distinct reser- efficient observed in both families (58) point to a very similar FS voirs can also lead to dissipative scattering. In underdoped Y123, a reconstruction. Assuming the presence of additional (although as- small QO frequency (F ∼ 95 T) was discovered and attributed to yet-undetected) hole pockets in the reconstructed FS of Y124 and h = ± Ω· · −2 2 a hole pocket based on the doping dependence of the Seebeck given that A 9.5 1.5 n cm K , we can estimate using Eq. coefficient (26). A FS comprising at most one electron and two the effective magnitude of the A coefficient associated with an = ± Ω· · −2 hole pockets with the measured areas and masses is consistent individual hole pocket to be Ah 49 10 n cm K .Giventhe with a scenario based on the FS reconstruction induced by the strong sensitivity of AKWR to the absolute values of m*andkF, this CDW order observed in Y123 (24) (Fig. 4). It is also compatible, estimate is considered to be in good agreement with the value of Ah deduced for Y123. This is also in agreement with the two-band

within error bars, with the value of the electronic specific heat PHYSICS measured at high fields in YBCO (56, 57) (see Supporting In- description of transport data in Y124 (35) and the doping de- formation for details). [Before proceeding, it is worth noting that the pendence of the Seebeck (20) and Hall (19) coefficients in YBCO. 2 ρ multiband scenario relies on the assumption that the low-frequency The magnitude of the T term in a(T) can thus be considered as oscillations detected in ref. 26 derive from a small hole pocket. yet further evidence that the reconstructed FS of underdoped Other studies have suggested that the small oscillation Fh owes its Y123 and Y124 contains not only the well-established electron origin to quantum interference or the Stark effect (29) in a magnetic pocket, but also at least one additional hole-like pocket. This is in breakdown scenario between the bilayer of Y123 (23, 27, 28).] agreement with the FS reconstruction scenario proposed within Taking the parameters for the two types of pockets in under- the biaxial CDW model (24, 25), assuming that the initial FS is the −1 doped Y123 (p = 0.11): kFe = 1.28 ± 0.02 nm and m*e = 1.4 ± pseudogapped FS (e.g., without states at the antinode) and not the −1 0.1 me, kFh = 0.54 ± 0.03 nm and m*h = 0.45 ± 0.1 me, we obtain band structure-derived FS.

Proust et al. PNAS | November 29, 2016 | vol. 113 | no. 48 | 13657 Downloaded by guest on September 29, 2021 The multiband scenario has a number of other implications. magnitude of A with such a scenario is similar to the coefficient First, in the Hg1201 family, QOs have been measured at a doping found at low temperatures and from high-field studies. It is level p = 0.09 with a frequency F = 840 ± 30 T and an effective important to recognize, however, that a Fermi arc has only mass m* = 2.45 ± 0.15 me (59). Accordingly, Eq. 2 gives AKWR = hole-like curvature, and thus can in no way account for the two- −2 73 ± 10 nΩ·cm·K .AboveTc, the measured A coefficient is A ∼ carrier form of the magnetoresistance in Y124, nor for the − 10 nΩ·cm·K 2 (34). This large discrepancy between the estimated negative sign of the Hall coefficient at low temperatures and and measured values of A again indicates that the reconstructed FS high fields. of Hg1201 may also contain an additional pocket or pockets that Until now, all estimates and comparisons have been made have not yet been observed in QO experiments (60). Second, in under the assumption that the effective mass does not vary Y123, QOs have been observed over a wide range of doping, yet F around the FS. In an alternative scenario (62), the effective mass is found to increase only by ∼20% between p = 0.09 and p = 0.152 of the diamond-shaped electron pocket is taken to be aniso- (61). These measurements also reveal a strong enhancement of the tropic. The effective mass deduced from QOs is large because it quasiparticle effective mass as optimal doping is approached and is dominated by the corner of the pocket that corresponds to the suggest a quantum critical point at a hole doping of pcrit ∼ 0.17. If hot spot of the CDW. By contrast, transport is dominated by the electron pocket was indeed the only pocket that persists in the those regions of the FS with the highest Fermi velocity, that is, reconstructed phase, this marked enhancement in m* should lead the light quasiparticles in the near-nodal state. This scenario can to a corresponding enhancement of the A coefficientonbothsides explain the factor of five discrepancy between the expected value of pcrit, as has been observed, for example, in the transport prop- of the KWR ratio and the experimental one (assuming a single erties of the isovalently substituted pnictide family BaFe2(As1-xPx)2 electron pocket), but the anisotropy needs to be abnormally (38). In cuprates, however, the situation is far from clear. Certainly, strong and would need to increase with doping to explain the there is no sign of a divergence of the A coefficient near p ∼ 0.18 behavior of the effective mass deduced from QOs (61). Similar from existing high-temperature measurements (34). Moreover, considerations would also apply if the scattering rate Γ, rather measurements of the low-temperature in-plane resistivity of sev- than the effective mass, were strongly anisotropic (63). eral overdoped LSCO samples in high magnetic field have The picture of underdoped cuprates now emerging from X-ray revealed a regime of “anomalous” or “extended” criticality regime spectroscopy is of a lengthening of the correlation length ξ as- around p ∼ 0.19 where the coefficient of the T-linear term is sociated with the charge ordering with increased field strength maximal yet there is no sign of divergence or an enhancement in A (15, 16), in agreement with NMR and thermodynamic mea- (from the overdoped side) (5). Within this multiband scenario, it is surements. At what value of ξ, relative to the mean free path of possible that the marked enhancement in m* of the electron the remnant quasiparticles, does FS reconstruction appear, or is pocket, and thus in Ae, is offset by changes in Ah (assuming that manifest in the magnetotransport properties, is a crucial open the hole pockets are always present). question. At high temperatures, where the mean free path is short, the quasiparticle response will be susceptible even to short- Alternative Scenarios. Finally, we consider an alternative scenario range charge order. At low temperatures, however, the situation is for the pseudogap in which only Fermi arcs exist at low field and less clear. The findings reported in this manuscript point to a ask what is the magnitude of the A coefficient expected in such a strong influence of the incipient charge order on the transport scenario. This is relatively easy to do, at least approximately. For properties over a wide region of the temperature–doping– = Y124, p 0.14. Thus, the full FS is expected to occupy 57% of magnetic-field phase diagram, and calls for a systematic study of the Brillouin zone. If we assume that the quasiparticles on the the evolution of the low-T in-plane resistivity of underdoped full FS have a comparable mass to those found in overdoped −2 cuprates inside the pseudogap regime. cuprates, that is, m* ∼5 me, one obtains AKWR = 2.5 nΩ·cm·K for the full unreconstructed FS. At low T, the “normal-state” ACKNOWLEDGMENTS. We thank K. Behnia, M. Ferrero, A. Georges, and L. specific heat coefficient γ0 in Y124 is estimated using the entropy Taillefer for useful discussions. Research support was provided by the project conservation construction to be approximately one-third of its SUPERFIELD of the French Agence Nationale de la Recherche, the Laboratory of Excellence “Nano, Extreme Measurements and Theory” in Toulouse, the value at high temperature, that is, above T* (52). For a Fermi arc High Field Magnet Laboratory–Radboud University/Fundamental Research on that is one-third the length of the full quadrant, AKWR is cor- Matter, and Laboratoire National des Champs Magnétiques Intenses, members respondingly tripled (again assuming an isotropic m*). Thus, the of the European Magnetic Field Laboratory.

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