Session A3: Invited Session: Superconducting Fluctuations in Cuprates

Decrease of pairing strength with underdoping in cuprate superconductors

The transition temperature $T_{c}$ of cuprate superconductors decreases at low hole doping $p$, but it is still unclear whether the pairing strength decreases or increases. Different interpretations of the pseudogap lead to opposite conclusions. Different estimates of the upper critical field $H_{c2}$ are in sharp contradiction. In this talk, we resolve the latter contradiction by showing that superconducting fluctuations in the underdoped cuprate Eu-LSCO, measured via the Nernst effect, obey the theory of Gaussian fluctuations, as in conventional superconductors [1, 2]. The extracted critical field $H_{c2}$ is small, and it dips at $p$ = 0.11, showing that pairing strength is weak where stripe order is strong. In the archetypal cuprate superconductor YBCO, $H_{c2}$ extracted from other measurements~[3] has the same doping dependence, also with a minimum at $p$ = 0.11, again where stripe order is present [4, 5]. We conclude that competing states such as stripe order weaken the pairing strength and this, rather than phase fluctuations, is the predominant cause for the low $T_{c}$ of underdoped cuprates. Work done in collaboration with N. Doiron-Leyraud, E. Hassinger, J.-Ph. Reid, O. Cyr-Choini\`{e}re,~F. Lalibert\'{e}, R. Daou, S. Pyon, T. Takayama, H. Takagi,~~and Louis Taillefer. \\[4pt] [1] M. N. Serbyn \textit{et al}., Phys. Rev. Lett. \textbf{102}, 067001 (2009). \\[0pt] [2] K. Michaeli and A. M. Finkel'stein, Europhys. Lett. \textbf{86}, 27007 (2009).\\[0pt] [3] Y. Ando and K. Segawa, Phys. Rev. Lett. \textbf{88}, 167005 (2002).\\[0pt] [4] F. ~Lalibert\'{e}~\textit{et al.}, Nature Comm. \textbf{2}, 432 (2011).\\[0pt] [5] T. Wu \textit{et al}., Nature \textbf{477}, 191 (2011).   

Pseudogap phase and superconducting fluctuation regime of the cuprate superconductors

The pseudogap phenomenon in the cuprates is one of the most investigated topics in the field of correlated materials. A related question is the extent to which superconducting fluctuation persist between the pseudogap temperature (\textit{T*}) and superconducting transition temperature (\textit{T$_c$}). We have addressed this question by combining several experimental probes: planar dc-resistivity [1], microwave conductivity [2,3], and torque mangetometry [4]. dc-resistivity measurements in the simple tetragonal model compound HgBa$_2$CuO$_{4+\delta}$ [5], which features the highest \textit{T$_c$} (97 K) among all single-layer cuprates, reveal four characteristic temperatures: \textit{T*}, coincident with the onset of novel \textbf{q}=0 magnetic order revealed by neutron diffraction [6]; a second, lower pseudogap temperature \textit{T**} associated with a further rearrangement of the sates at the Fermi level; \textit{T'}, which marks the onset of superconducting fluctuations; and finally \textit{T$_c$}. Notably, \textit{T'} lies only 10-20 K above \textit{T$_c$} and closely tracks the superconducting dome with doping. The superconducting fluctuation regime is further investigated by microwave conductivity and torque magnetometry, and these results confirm the latter conclusion. The results for HgBa$_2$CuO$_{4+\delta}$ are complemented by a comprehensive investigation of other cuprates (La$_{2-x}$Sr$_x$CuO$_4$, YBa$_2$Cu$_3$O$_{6+\delta}$, Bi$_2$Sr$_{2-z}$La$_z$CuO$_{6+\delta}$), which leads to new insights into the phase diagram of cuprate superconductors.\\[4pt] [1] N. Bari\v{s}i\'{c} \textit{et al.}, \textit{preprint}.\\[0pt] [2] M.S. Grbi\'{c} \textit{et al.}, \textit{Phys. Rev. B} \textbf{80}, 094511 (2009).\\[0pt] [3] M.S. Grbi\'{c} \textit{et al.}, \textit{Phys. Rev. B} \textbf{83}, 144508 (2011).\\[0pt] [4] G. Yu \textit{et al.}, \textit{preprint}.\\[0pt] [5] N. Bari\v{s}i\'{c} \textit{et al.}, \textit{Phys. Rev. B} \textbf{78}, 054518 (2008).\\[0pt] [6] Y. Li \textit{et al.}, \textit{Nature} \textbf{455}, 372 (2008).   

Fluctuations of Superconductivity in La$_{2-x}$Sr$_x$CuO$_4$: A Terahertz Conductivity Study

In the underdoped pseudogap regime of the high-temperature superconductors, one expects that due to low superfluid densities and short correlation lengths, superconducting fluctuations will be significant for transport and thermodynamic properties. However, there has been disagreement about how high in temperature they may persist, their role in the phenomenology of the pseudogap regime, and their significance for understanding high-temperature superconductivity. We use THz time-domain spectroscopy (TTDS) to probe the temporal fluctuations of superconductivity above the critical temperature (T$_C$) in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) thin films over a doping range that spans almost the entire superconducting dome. Signatures of the fluctuations persist in the conductivity in a narrow temperature range above T$_C$. Our measurements show that superconducting correlations do not make an appreciable contribution to the charge transport anomalies of the pseudogap in LSCO at tempera tures well above T$_C$.\footnote{L.S. Bilbro \textit{et al.}, Nature Physics 7, 298 (2011).} I will compare our results for an underdoped (x=0.095) sample with measurements of diamagnetism in a similarly doped crystal of La$_{1.905}$Sr$_{0.095}$CuO$_4$. I will show, through a vortex-plasma model, that if the fluctuation diamagnetism originates solely in vortices, then these vortices must exhibit an anomalously large vortex diffusion constant, more than two orders of magnitude larger than the Bardeen-Stephen estimate.\footnote{L.S. Bilbro \textit{et al.}, Phys. Rev. B 84, 100511 (2011).} This points to either the extremely unusual properties of vortices in the underdoped d-wave Cuprates or a contribution to the diamagnetic response that is not superconducting in origin. Finally, I will introduce preliminary results of THz conductivity measurements of critically underdoped LSCO films, where superconductivity is fully suppressed.   

Distinct Ranges of Superconducting Fluctuations and Pseudogap in YBa$_2$Cu$_3$O$_{6+x}$

The contribution of superconducting fluctuations (SCF) to the ab-plane conductivity has been determined accurately in a series of YBa$_2$Cu$_3$O$_{6+x}$ single crystals using high magnetic fields to restore the normal state behavior [1]. This allows us to determine within the same set of transport measurements both the field $H^{\prime}_c(T)$ and the temperature $T^{\prime}_c$ above which the SCFs are fully suppressed, and the pseudogap temperature $T^{\star}$. A careful investigation near optimal doping shows that $T^{\star}$ becomes smaller than $T^{\prime}_c$, which unambiguously evidences that the pseudogap cannot be assigned to preformed pairs [2]. In the nearly optimally doped samples, the SCF contribution to conductivity can be accounted for by Gaussian Aslamazov-Larkin fluctuations in the Ginzburg-Landau approach [3]. A phase fluctuation contribution might be invoked in the most underdoped sample in a $T$ range which increases when controlled disorder is introduced by electron irradiation. The analysis of the fluctuation magnetoconductance allows us to determine the critical fields $H_{c2}(0)$ which are found to be very similar to $H^{\prime}_c(0)$ and to increase with hole doping. These two depairing fields which are directly connected to the magnitude of the superconducting gap therefore follow the evolution of $T_c$, which is at odds with the sharp decrease of the pseudogap with increasing hole doping. \\[4pt] [1] F. Rullier-Albenque, H. Alloul, Cyril Proust, P. Lejay, A. Forget, and D. Colson, Phys. Rev. Lett. \textbf{99}, 027003 (2007). \\[0pt] [2] H. Alloul, F. Rullier-Albenque, B. Vignolle, D. Colson, A. Forget, Europhys. Lett. \textbf{91}, 37005 (2010). \\[0pt] [2] F. Rullier-Albenque, H. Alloul, G. Rikken, Phys. Rev. B \textbf{84}, 014522 (2011).   

Fluctuoscopy of Superconductors

The study of superconducting fluctuations (SF) is a subject of fundamental and practical importance. Since the moment of discovery SF became a noticeable part of research in the field of superconductivity (SC) and a variety of fluctuation effects have been detected. The interest to SF in SC was regenerated by the discovery of HTS, where, due to extremely short coherence length and low effective dimensionality of the electron system, SF manifest themselves in a wide range of temperatures. The characteristic feature of SF is their strong dependence on temperature and magnetic field. This allows to separate SFs from other contributions and to use them as a tool for characterization of SC systems (``fluctuoscopy'') for example to extract the values of $T_c$, $H_{c2}(T)$ and phase-breaking time from experimental data. We present the complete results for fluctuation magneto-conductivity (FMC) and Nernst signal (FNS) of impure 2D superconductor in the whole phase diagram above the transition line $H_{c2}(T)$, including the domain of quantum fluctuations. Along some line $H_0(T)$, in agreement with experimental findings, FMC becomes zero and beyond it remains small and negative. The corresponding surface in coordinates $(T,H)$ becomes in particular non-trivial at low temperatures and close to $H_{c2}(0)$, where it is trough-shaped. The observation of large FNS in HTS and conventional SC above $T_c(H)$, has attracted much attention recently. The idea to attribute it to the entropy transport by analogy to vortices was proposed. On the other hand this giant effect, close to $T_c(0)$, was explained in terms of SF. Our general results allow to successfully fit the available experimental data in a wide range of magnetic fields and temperatures, to extract the value of the ``ghost'' field and other parameters of SC. We offer also a qualitative consideration, which gives a natural explanation for the giant value of FNS attributing it to a strong dependence of the fluctuation Cooper pair (FCP) chemical potential on temperature. Close to zero temperature, when the magnetic field approaches $H_{c2}(0)$, a peculiar dynamic state consisting of clusters of coherently rotating FCP forms. We estimate the characteristic size and lifetime of such clusters and present the scenario of fluctuation nucleation of Abrikosov's lattice.