Questioning the cuprate paradigm -- absence of superfluid density loss in several overdoped cuprates I

Abstract

It is long established that overdoped cuprate superconductors experience a loss of superfluid density (SFD) with increasing doping, p, along with the decline in T_c. Such behavior is unconventional and suggests a depletion of the condensate by increasing pairbreaking or the growth of a second non-pairing channel. This led to a recent suggestion that the condensate arises from an incoherent charge channel which progressively gives way with overdoping to a second, coherent non-pairing channel. Contra these ideas, we report analysis of the field-dependent electronic specific heat of several cuprates from which we find no apparent loss of SFD with overdoping. The SFD per CuO_2 plaquette is found to rise progressively with overdoping from p towards (1+p), undiminished and much the same as the Hall number, thus implying that all available carriers contribute to the condensate. We suggest this could be the underlying intrinsic behavior for all cuprates. Our samples include (Y,Ca)Ba_2Cu_3O_{7-δ}, Bi_2Sr_2CaCu_2O_{8+δ}, La_{2-x}Sr_xCuO_4 and Tl_2Ba_2CuO_6, with the latter being the only exception. Our results signal a possible return to a more conventional picture.

Figures (6)

• Figure 1: (a) The penetration depth at 13 tesla calculated from $\Delta F(13,T) = F(13,T)-F(0,T)$ shown in Fig. \ref{['YCa123_2']}(c) for Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$ using the London model (Eq. \ref{['FHaoPoly']}). The dashed divergences seen near $T_{\textrm{c}}$ occur because $H/H_{\textrm{c2}}$ diverges as $T\rightarrow T_{\textrm{c}}$. We extrapolate each curve from above this breakdown to smoothly approach zero at $T_{\textrm{c}}$. (b) The penetration depth at zero field calculated from $\lambda(13)^{-2}$ in panel (a) using the renormalization due to Amin et al. Amin given by Eq. \ref{['AminFit']}.
• Figure 2: (a) Uemura plot, $T_{\textrm{c}}(p)$ vs $\lambda_0(p)^{-2}$, for our results for (Y,Ca)123 (blue squares), Bi2212 (olive squares), La214 (red diamonds) Paradigm and (Y,Ca)123 obtained from $\mu$SR BernhardAnom (blue stars). Red crosses show the data of Božović et al. for La214 films Bozovic. (b) $\lambda_0^{-2}$ for Tl2201: this work (orange squares) and previous $\mu$SR results NiedermayerUemuraboomerang (orange stars) or microwave data (orange diamond).
• Figure 3: (a) $H_{\textrm{c2}}(T=0)$ calculated using the London model for (Y,Ca)123 (blue squares) along with values reported in ref. Grissonanche (open blue circles, open orange diamonds) and by Kokanović and Cooper Kokanovic (open blue stars). (b) $n_{\textrm{s}}(0)$ vs $p$ inferred from $\lambda_0^{-2}$: (Y,Ca)123 (blue squares), La214 (red diamonds) and Bi2212 (olive squares). The shaded strip summarises the carrier filling, $n_{\textrm{n}}$, for Bi2201 Putzke, Tl2201 Tam and La214 Legros2022 which matches our rising $n_{\textrm{s}}(0)$ values. In contrast, values of $n_{\textrm{s}}(0)$ for Tl2201 calculated from our measured $\gamma(H,T)$ (orange squares) and as reported by $\check{\textrm{C}}$ulo et al.Culo2021 (open orange squares) decline steadily with doping.
• Figure 4: (a) Schematic phase diagram for cuprates as a function of doping, $p$. $p^*$ denotes critical doping and the region, $p<p^*$, is the pseudogap domain. Note the vertical boundary at $p^*$. (b) electron mass enhancement deduced from specific heat as described in the text.
• Figure 5: (a) The change in $\gamma$ with field, $\Delta\gamma(13,T) = \gamma(13,T)-\gamma(0,T)$, for Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$. The transition is very sharp around optimal doping, but broadens with overdoping probably due to a random distribution of Ca pairs Naqib; (b) the magnetic entropy, $\Delta S(13,T) = S(13,T)-S(0,T)$, obtained by integrating $\Delta\gamma(13,T)$; and (c) the change in magnetic free energy $\Delta F(13)$ obtained by integrating $\Delta S(13)$. The curves cover seven doping states as annotated, one optimal, three underdoped and three overdoped.