Superfluid response in monolayer high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>cuprates

Panagopoulos, C.; Xiang, Tao; Anukool, Waranont; Cooper, J. R.; Wang, Y. S.; Chu, C. W.

doi:10.1103/physrevb.67.220502

Cited by 64 publications

(71 citation statements)

References 30 publications

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“…Moreover, based on our analysis, a plot of T c vs. ρ s (0) should rise more steeply in the underdoped regime than in the overdoped regime; a number of experiments appear to support this assertion at a qualitative level [19,20,21] (an effect known in the literature as the "boomerang" effect), although more data are necessary, especially because there are other experiments that do not fit into this picture [22].…”

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confidence: 89%

Criticality in correlated quantum matter

2005

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At quantum critical points (QCP) [1,2,3,4,5,6,7] there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, ρs(0), and the transition temperature, Tc, of the cuprates are related by Tc ∝ ρs(0) y , where the exponent y is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.Do quantum critical points (QCPs) provide a powerful framework for understanding complex correlated many body problems? Do they shed new light on quantum mechanics of macroscopic systems, providing, for example, a deeper understanding of entanglement? Answers to many such questions require a precise recognition of the experimentally observable regime of quantum criticality. An important class of QCPs are analogs of classical critical points, but in a dimension higher than the actual spatial dimension of the system; that is, a quantum critical point in d spatial dimensions is equivalent to a classical critical point in (d + z), dimensions, where z is the dynamic critical exponent. We shall be primarily concerned with z = 1, although an example involving z = 1 is given below. This extra dimension (imaginary time) is the sine qua non of the effect of quantum mechanics.It seems paradoxical that often the region of classical critical fluctuations is small and tends to zero as the temperature, T , tends to zero, while the region of quantum critical fluctuations fans out as T increases. The reason is that the quantum critical region is determined by the dominant microscopic energy scale in the Hamiltonian, whereas the classical critical region is determined by the ratio of the transition temperature, T c , to the same scale raised to a positive power (the dimensionality). Since this ratio is usually small compared to unity (it is 10 −5 in a conventional superonductor), the classical critical region is small as well. As a classical critical point is driven to zero by tuning a parameter to reach the QCP, T c itself vanishes as ξ −z , provided the T = 0 spatial correlation length, ξ, is large compared to the lattice spacing, further amplifying the contrast between classical and quantum criticalities.How high in temperature does the effect of a QCP persist? Consider perhaps the simplest possible example of a quantum phase transition described by the Hamiltonian of an Ising model in a transverse field [8] in one dimension,where the usual Pauli matrices,...

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confidence: 89%

Criticality in correlated quantum matter

2005

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“…Such a dimensional crossover is expected to occur at B 2D ∼ Φ 0 /(γc) 2 ∼ 1.4 T for Hg1201, where c = 9.6Å is the c-axis lattice constant and γ is ∼ 40 (Ref. 27). Both the estimated value of B 2D and the measured value of 0.4 T are substantially lower than B c2 = 100 T, 24 and than the magnetic field (B = 10.8 T) up to which the VL has been observed in the more isotropic compound YBCO, 9 for which B 2D is expected to be much larger than in Hg1201.…”

Section: Experimental Methodsmentioning

confidence: 99%

Magnetic vortex lattice in HgBa2CuO4+δobserved by small-angle neutron scattering

Egetenmeyer

Gavilano

et al. 2011

Phys. Rev. B

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We report the direct observation of the magnetic vortex lattice in the model high-temperature superconductor HgBa2CuO 4+δ . Using small-angle neutron scattering on high-quality crystals, we observe two equal domains of undistorted triangular vortex lattices well-aligned with the tetragonal crystallographic axes. The signal decreases rapidly with increasing magnetic field and vanishes above 0.4 Tesla, which we attribute to a crossover from a three-dimensional to a two-dimensional vortex system, similar to previous results for the more anisotropic compound Bi2.15Sr1.95CaCu2O 8+δ . Our result indicates that a triangular vortex lattice (with or without distortion) at low magnetic fields is a generic property of cuprates with critical temperatures above 80 K.

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“…A further problem arises [24] in that, for small particles, this relation does not satisfy the sum rule, µ 0 M (H)dH = U 0 ≡ the condensation energy. With a mean grain size of 25µm and λ ab (0) ranging from 0.2 to 0.32µm [25], we adopt the limit λ ≪ r g which is clearly satisfied up to a few K below T c . This yields…”

Section: Remain Unchangedmentioning

confidence: 99%

Isotope Effect in the Superfluid Density of High-Temperature Superconducting Cuprates: Stripes, Pseudogap, and Impurities

et al. 2005

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Underdoped cuprates exhibit a normal-state pseudogap, and their spins and doped carriers tend to spatially separate into 1-or 2-D stripes. Some view these as central to superconductivity, others as peripheral and merely competing. Using La2−xSrxCu1−yZnyO4 we show that an oxygen isotope effect in Tc and in the superfluid density can be used to distinguish between the roles of stripes and pseudogap and also to detect the presence of impurity scattering. We conclude that stripes and pseudogap are distinct, and both compete and coexist with superconductivity.PACS numbers: 71.10. Hf, 74.25.Dw, 74.62.Dh, 74.72.Dn High-T c superconductors (HTS) remain a puzzle. Various correlated states have been identified in HTS including antiferromagnetism, the pseudogap[1], nanoscale spin-charge stripes [2] and, of course, superconductivity (SC). (Here we generalise"stripes" to include possible 2D checkerboard structures [3]). The pseudogap is a nodal energy gap of uncertain origin that appears in the normal-state (NS) density of states (DOS). Its effects can be observed in many physical properties [1,4]. Several opposing views are still current. One is that stripes play a central role [5], forming the pseudogap correlation [6] and/or mediating the SC pairing. Another is that the NS pseudogap arises from incoherent superconducting fluctuations which set in well above T c [7]. Another is that these states are independently competing [8]. Here stripes and pseudogap play a secondary role and SC is mediated by some other pairing boson. An unambiguous test of these opposing views is urgently needed. We show here that isotope effects provide such a test.The isotope exponent α(E) in a given property E is defined as α(E) = − (∆E/E)/(∆M/M ), where M is the isotopic mass and E may be T c , the SC gap parameter, ∆ 0 , the pseudogap energy scale, E g , or the superfluid density ρ s = λ −2 ab = µ 0 e 2 (n s /m * ab ). (λ ab is the in-plane London penetration depth, n s is the carrier density and m * ab is the effective electronic mass for in-plane transport). An isotope effect on T c was first discovered in 1950 by Allen et al. for Sn [9]. They found α(T c ) ≈ 0.5 ± 0.05 which provided the central clue for the role of phonons in pairing and led 7 years later to the BCS theory of SC [10].The situation with HTS is more complex. The oxygen isotope effect on T c was found[11] to be small, with α(T c ) ≈ 0.06. However, with decreasing doping the effect rises and eventually diverges as T c → 0[12, 13]. Surprisingly, an isotope effect was also found in the superfluid density [14] (and attempts were made to resolve this into a dominant isotope effect just in m * [15,16]). We will show that both of these unusual effects can be understood in terms of a normal-state pseudogap which competes with SC [17]. We also predict and confirm an isotope effect in ρ s induced by impurity scattering. The isotope effects in T c and ρ s are mapped as a function of doping in La 2−x Sr x Cu 1−y Zn y O 4 and we observe a canonical pseudogap behavior as well as a huge an...

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Superfluid response in monolayer high-Tccuprates

Cited by 64 publications

References 30 publications

Criticality in correlated quantum matter

Criticality in correlated quantum matter

Magnetic vortex lattice in HgBa2CuO4+δobserved by small-angle neutron scattering

Isotope Effect in the Superfluid Density of High-Temperature Superconducting Cuprates: Stripes, Pseudogap, and Impurities

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