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

Abstract

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...

Comment on “Isotope effect in high-Tcsuperconductors”

“…20,21 Nevertheless, OIE on the penetration depth is nearly constant from the optimally doped sample to the substituted samples with a large amount of Pr, 14 which is inconsistent with the theoretical prediction. 20 We would like to emphasize here that since the pairbreaking effect in optimally doped cuprates is negligibly small and the carrier concentrations of the two oxygenisotope samples have been consistently proved to be the same within Ϯ0.0002 per Cu, 2,23 the observed large oxygenisotope effect on the penetration depth must be caused by the large oxygen-isotope effect on the supercarrier mass. The origin of this unconventional isotope effect could arise from strong EPI that causes the breakdown of the Migdal approximation.…”

“…20,21 Two different groups 20,21 have consistently shown that the isotope effects on T c and the penetration depth are almost proportional to each other provided that the strong pair-breaking effect exists. These theoretical models may be able to explain the observed large oxygen-isotope effects on both T c and the penetration depth in underdoped cuprates if the scattering rate were large enough.…”

Intrinsic and structural isotope effects in iron-based superconductors

“…5,6 The cuprate high-temperature superconductors (HTS) are characterized by a vanishingly small but positive isotope effect exponent in optimally doped compounds which increases in a monotonic way upon decreasing doping. [7][8][9][10][11][12][13][14] For the optimally doped cuprate HTS the smallest value of the oxygen-isotope exponent α O ≃ 0.02 was obtained for YBa 2 Cu 3 O 7−δ and Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ , while it reaches α O ≃ 0.25 for Bi 2 Sr 1.6 La 0.4 CuO 6+δ . [7][8][9]13,14 In addition, it was demonstrated that in underdoped materials α O exceeds substantially the BCS limit α BCS ≡ 0.5.…”

Isotope effects in high-Tccuprate superconductors as support for the bipolaron theory of superconductivity

“…Also the low value of α O n = 0.146 in [25] is in sharp contrast to the observed very large OIE on the lowtemperature magnetic-field penetration depth, λ ab ∝ (m * * ab /n) 1/2 , in both La 1.94 Sr 0.06 CuO 4 (see [9]) and Y 0.55 Pr 0.45 Ba 2 Cu 3 O 7−y (see [26]), which would lead to α O n 2 if one assumed that the supercarrier mass is independent of the oxygen mass. Another model based on the pair-breaking effects due to impurities, disorder and/or pseudogap can also explain the observed OIEs on the penetration depth and critical temperature in deeply underdoped samples [27]. But this model cannot consistently explain the negligibly small α O but large OIE on the penetration depth in optimally doped samples [10].…”