Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor

Daou, Ramzy; Doiron-Leyraud, N.; LeBoeuf, David; Li, S. Y.; Laliberté, F.; Cyr-Choinière, O.; Jo, Y. J.; Balicas, Luis; Yan, Jiaqiang; Zhou, Jianshi; Goodenough, John B; Taillefer, Louis

doi:10.1038/nphys1109

Cited by 232 publications

(325 citation statements)

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“…Strong evidence for the QCP at x = x m , and its associated T > 0 crossovers comes from recent experiments on Nd-LSCO [3,4]. They detected the crossover between "Strange Metal" and "Fluctuating paired Fermi pockets" regions of Fig.…”

Section: H C2mentioning

confidence: 94%

“…Nevertheless the Luttinger theorem continues to be obeyed, after accounting for the large unit cell created by the SDW order. The ultimate theory of this quantum critical point is not fully understood, despite much theoretical attention [2].Strong evidence for the QCP at x = x m , and its associated T > 0 crossovers comes from recent experiments on Nd-LSCO [3,4]. They detected the crossover between "Strange Metal" and "Fluctuating paired Fermi pockets" regions of Fig.…”

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confidence: 99%

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Quantum criticality and the phase diagram of the cuprates

Sachdev

2010

Physica C: Superconductivity and its Applications

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I discuss a proposed phase diagram of the cuprate superconductors as a function of temperature, carrier concentration, and a strong magnetic field perpendicular to the layers. I show how the phase diagram gives a unified interpretation of a number of recent experiments. Superconductivity, Tokyo, Sep 7-12, 2009 Keynote talk, 9th International Conference on Materials and Mechanisms of H c2Figure 1: Proposed phase diagram of the cuprates showing the interplay between superconductivity (SC), spin density wave (SDW) order, and Fermi surface configuration as a function of carrier density (x), temperature (T ), and magnetic field (H) perpendicular to the layers. Full lines are thermal or quantum phase transitions, dashed lines are crossovers, and dotted lines are guides to the eye. The phase transitions associated with valence bond solid (VBS) (or "charge") and nematic order are not shown. The superconducting regions are colored pink. We have assumed the absence of interlayer coupling, and so the SDW order is long-ranged only at T = 0: it is present in the regions labeled "SDW" and on the thick orange line for x < x s . In the blue normal regions, the 'pseudogap' is between T c and T * , the 'Strange Metal' has an in-plane resistivity which is measured to be linear in T , and the "Large Fermi surface" has a conventional T 2 resistivity.This brief note contains a summary of the key aspects of the proposed phase diagram of the cuprate superconductors shown in Fig. 1, and the central role played by ideas of quantum criticality. A more detailed discussion can be found in another recent review by the author [1], which also contains more complete citations to the literature. Here, I will focus on the central physical ideas and highlight support from recent experiments.The phase transitions and crossovers in Fig. 1 appear quite intricate. However, they can be understood simply by focusing first on the quantum critical point (QCP) at doping density, x = x m , temperature T = 0, magnetic field H = 0. As indicated in Fig. 1, this quantum critical point is pre-empted by the onset of superconductivity.The QCP at x = x m is a transition between two metallic (hence the subscript m) Fermi liquid phases. At x > x m we have the full symmetry of the square lattice, and a "large" Fermi surface metal consisting of a hole-like Fermi surface enclosing the area 1 + x expected from the Luttinger theorem (this is for hole doping; with electron doping, x, the area enclosed is 1 − x). At x < x m we have the onset of spin density wave (SDW) order, and this breaks apart the large Fermi surface into "small" Fermi pockets. Nevertheless the Luttinger theorem continues to be obeyed, after accounting for the large unit cell created by the SDW order. The ultimate theory of this quantum critical point is not fully understood, despite much theoretical attention [2].Strong evidence for the QCP at x = x m , and its associated T > 0 crossovers comes from recent experiments on Nd-LSCO [3,4]. They detected the crossover between "Strange Metal" and "Fl...

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Section: H C2mentioning

confidence: 94%

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confidence: 99%

Quantum criticality and the phase diagram of the cuprates

Sachdev

2010

Physica C: Superconductivity and its Applications

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“…6. In particular, we have compared two samples of Nd-LSCO, respectively at p = 0.20 and p = 0.24 [33]. In Fig.…”

Section: Stripe Ordermentioning

confidence: 99%

Fermi surface reconstruction in high-T_csuperconductors

Taillefer

2009

J. Phys.: Condens. Matter

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143

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Abstract. The recent observation of quantum oscillations in underdoped high-T c superconductors, combined with their negative Hall coefficient at low temperature, reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This strongly suggests that the large hole Fermi surface characteristic of the overdoped regime undergoes a reconstruction caused by the onset of some order which breaks translational symmetry. Here we consider the possibility that this order is "stripe" order, a form of combined charge / spin modulation observed most clearly in materials like Eu-doped and Nd-doped LSCO. In these materials, the onset of stripe order coincides with major changes in transport properties, providing strong evidence that stripe order is indeed the cause of Fermi-surface reconstruction. We identify the critical doping where this reconstruction occurs and show that the temperature dependence of transport coefficients at that doping is typical of metals at a quantum critical point. We discuss how the pseudogap phase may be a fluctuating precursor of the stripeordered phase. Phase diagramThe doping phase diagram of hole-doped cuprates is sketched in Fig. 1a. With increased doping p, the materials go from being antiferromagnetic insulators at zero doping to more or less conventional metals at high doping. The overdoped metallic state is characterized by a single large hole Fermi surface whose volume contains 1 + p holes per Cu atom, as determined by angle-dependent magnetoresistance (ADMR) [1] and angle-resolved photoemission spectroscopy (ARPES) [2]. The lowtemperature Hall coefficient R H is positive and equal to V / e (1 + p) [3], as expected for a single-band metal with a hole density n = 1 + p. The electrical resistivity ρ(T) exhibits the standard T 2 temperature dependence of a Fermi liquid [4].At intermediate doping, between the insulator and the metal, there is a central region of superconductivity, delineated by a critical temperature T c which can rise to values of order 100 K. Above the maximal T c , near optimal doping, the normal state is a "strange metal", characterized by a resistivity which is linear in temperature instead of quadratic. In the midst of this strange-metal region, the enigmatic "pseudogap phase" sets in, below a crossover temperature T* where most physical properties undergo a smooth yet significant change [5].Elucidating the nature of the pseudogap phase is key to understanding high-temperature superconductivity. Two main scenarios have been proposed [6]: fluctuating superconductivity -a precursor to the long-range coherence which sets in below T c -versus some other ordered state. For hole-doped cuprates, a number of different types of order have been proposed, including "stripe order"

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“…The linear resistivity in the marginal Fermi liquid region is consistent with experiments. [44][45][46][47] For n = 0.75, both t ′ = 0 and t ′ /t = −0.1 show Fermi liquid character, with a resistivity which goes to zero quadratically when T approaches zero. The fact that doping region with marginal Fermi liquid character increases with negative t ′ has consequences for the phase diagram near the quantum critical point, which we will discuss in Section IV.…”

Section: Transport Propertiesmentioning

confidence: 99%

“…42,43 Above the quantum critical point, in a range of doping associated with marginal Fermi liq-uid behavior, the in-plane resistivity is known to vary linearly with T over a wide range of temperatures. [44][45][46][47][48][49][50] In the Fermi liquid region the low temperature resistivity varies as T 2 . The resistivity increases as the doping decreases from the Fermi liquid into the pseudogap region.…”

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confidence: 99%

Role of the van Hove singularity in the quantum criticality of the Hubbard model

et al. 2011

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A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase separation transition, and it separates the non-Fermi liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare d-wave pairing susceptibility exhibits an algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et al., Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the single-particle and transport properties near the quantum critical point using high quality estimates of the self energy obtained by direct analytic continuation of the self energy from Continuous-Time Quantum Monte Carlo. We focus mainly on a van Hove singularity coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping t ′ in the model. For comparison, we calculate the bare d-wave pairing susceptibility for non-interacting models with the usual two-dimensional tight binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare d-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A negative next-near-neighbor hopping t ′ increases the doping region with marginal Fermi liquid character. Both T and negative t ′ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.

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Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor

Cited by 232 publications

References 30 publications

Quantum criticality and the phase diagram of the cuprates

Quantum criticality and the phase diagram of the cuprates

Fermi surface reconstruction in high-T_csuperconductors

Role of the van Hove singularity in the quantum criticality of the Hubbard model

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Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor

Cited by 232 publications

References 30 publications

Quantum criticality and the phase diagram of the cuprates

Quantum criticality and the phase diagram of the cuprates

Fermi surface reconstruction in high-Tcsuperconductors

Role of the van Hove singularity in the quantum criticality of the Hubbard model

Contact Info

Product

Resources

About

Fermi surface reconstruction in high-T_csuperconductors