Competition between spin density wave order and superconductivity in the underdoped cuprates

Moon, Eun-Gook; Sachdev, Subir

doi:10.1103/physrevb.80.035117

Cited by 103 publications

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“…the spectrum of the Bogoliubov quasiparticle excitations of the d-wave superconductor can lose signature of the Fermi pockets. Note that superconductivity competes mainly with SDW order, and will have a weaker suppression effect on the associated tendencies to VBS/nematic ordering [15]. Indeed, these orderings can survive at T = 0, as has been discussed in some toy models [19].…”

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confidence: 86%

“…Now, let us consider the onset of superconductivity at H = 0. This occurs in a dome-shaped region around x = x m [15]. Here a crucial effect is that the competition between the SC and SDW orders shifts the position of the SDW-ordering QCP to x = x s (the subscript s refers to the presence of superconductivity).…”

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confidence: 99%

“…Loosely speaking, the competition is for the Fermi surface: both the SDW and SC orders want to induce gaps in the same regions of the Fermi surface. We have presented a theory [15] which shows how such a competition leads to the shift in the position of the QCP.…”

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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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Quantum criticality and the phase diagram of the cuprates

Sachdev

2010

Physica C: Superconductivity and its Applications

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“…The antiferromagnetic moment is then allowed spacetime fluctuations in orientation, and these lead to an emergent U(1) gauge field which is coupled to the electron pockets. The simplest form of such a theory has a pair of fermions, f ± ; these are sometimes called 'doublons' because they represent doubly-occupied sites in a derivation from a lattice Hubbard model (the doublons were denoted g ± in the earlier work [34][35][36]). These doublons are coupled with opposite charges to the U(1) gauge field (A τ , A), as described by the Lagrangian [35][36][37][38][39][40] …”

Section: Doublon Metalmentioning

confidence: 99%

“…[34][35][36] This is a model of a fluctuating doped antiferromagnet, with applications to the cuprate superconductors. The theory begins with an ordered antiferromagnet and re-expresses the electrons in terms of the pocket Fermi surfaces created by the antiferromagnetic order.…”

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confidence: 99%

Fermi surfaces and gauge-gravity duality

2011

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Where is the quantum critical point in the cuprate superconductors?

Sachdev

2010

Physica Status Solidi (b)

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The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Transport measurements in the hole-doped cuprates show a 'strange metal' normal state with an electrical resistance which varies linearly with temperature. This strange metal phase is often identified with the quantum critical region of a zero temperature quantum critical point (QCP) at hole density x = x m , near optimal doping. A long-standing problem with this picture is that low temperature experiments within the superconducting phase have not shown convincing signatures of such a optimal doping QCP (except in some cuprates with small superconducting critical temperatures). I review theoretical work which proposes a simple resolution of this enigma.The crossovers in the normal state are argued to be controlled by a QCP at x m linked to the onset of spin density wave (SDW) order in a "large" Fermi surface metal, leading to small Fermi pockets for x < x m . A key effect is that the onset of superconductivity at low temperatures disrupts the simplest canonical quantum critical crossover phase diagram. In particular, the competition between superconductivity and SDW order shifts the actual QCP to a lower doping x s < x m in the underdoped regime, so that SDW order is only present for x < x s . I review the phase transitions and crossovers associated with the QCPs at x m and x s : the resulting phase diagram as a function of x, temperature, and applied magnetic field consistently explains a number of recent experiments.Copyright line will be provided by the publisher 1 Introduction The strange metal phase of the holedoped cuprates is often regarded as the central mystery in the theory of high temperature superconductivity. This appears near optimal doping, and exhibits a resistivity which is linear in temperature (T ) over a wide temperature range. A useful review of the transport data has been provided recently by Hussey [1]: we show his crossover phase diagram in Fig. 1.It is tempting to associate the strange metal with the finite temperature quantum critical region linked to a T = 0 quantum critical point (QCP) [2]: this is the regime where k B T is the most important perturbation away from the QCP. From the sketch in Fig. 1, we see that such a QCP should be at a hole doping x = x m , near optimal doping [3]. However, experiments have not so far revealed any

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Competition between spin density wave order and superconductivity in the underdoped cuprates

Cited by 103 publications

References 56 publications

Quantum criticality and the phase diagram of the cuprates

Quantum criticality and the phase diagram of the cuprates

Fermi surfaces and gauge-gravity duality

Where is the quantum critical point in the cuprate superconductors?

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