Session V3: Invited Session: Spin Fluctuations and Cooper Pairing in Unconventional Superconductors

Linear-T scattering and pairing from spin fluctuations in organic superconductors

The (TMTSF)$_2$X series of organic superconductors, with X=PF$_6$ or ClO$_4$, are clean single-band metals that exhibit unconventional superconductivity in the vicinity of a pressure-induced spin-density wave (SDW) quantum critical point. As such, they epitomize the interplay between magnetism and superconductivity observed in heavy fermion, cuprate, and iron-pnictide superconductors. We have recently examined the electrical resistivity $\rho(T)$ of (TMTSF)$_2$X materials as a function of temperature and pressure. At the SDW quantum critical point, we observed a strictly linear temperature dependence of the resistivity over two decades in temperature [1,2]. Moving away from SDW order with increasing pressure, this linear resistivity was found to decrease in parallel with the weakening superconductivity, such that $A$, the coefficient of the linear contribution to $\rho(T)$, directly correlates with the superconducting $T_c$ [1,2]. This shows that linear-$T$ scattering and superconducting pairing share a common origin. A similar correlation was also found between $A$ and the spin fluctuations seen by NMR experiments [2]. Owing to the quasi-1D nature of the (TMTSF)$_2$X system, this connection between spin fluctuations, scattering, and superconductivity is well described theoretically by a model that considers the hitherto overlooked mutual reinforcement of SDW and pairing correlations [3]. In particular, the feedback of pairing correlations on SDW fluctuations appears to be decisive for the strength of the linear resistivity and its extent in temperature and pressure. The fact that the same empirical correlation between linear-$T$ resistivity and $T_c$ is observed in the hole-doped [4,5] and electron-doped [6] cuprates, as well as in iron-pnictides [1,4], shows that the same mechanism is at play in these materials. This points to a common, magnetic origin to the superconducting pairing. Work done in collaboration with S. Ren\'e de Cotret, P. Auban-Senzier, D. J\'er\^ome, C. Bourbonnais, K. Bechgaard, and L. Taillefer. \\[4pt] [1] N. Doiron-Leyraud et al., Phys. Rev. B 80, 214531 (2009).\\[0pt] [2] N. Doiron-Leyraud et al., Eur. Phys. J. B 78, 23 (2010).\\[0pt] [3] C. Bourbonnais and A. Sedeki, Phys. Rev. B 80, 085105 (2009).\\[0pt] [4] N. Doiron-Leyraud et al., arXiv:0905.0964.\\[0pt] [5] L. Taillefer, Annu. Rev. Condens. Matter Phys. 1, 51 (2010).\\[0pt] [6] K. Jin et al., Nature 476, 73 (2011).   

Link between spin fluctuations and Cooper pairing in copper oxide superconductors

Although it is generally accepted that superconductivity is unconventional in the high-\textit{T}$_{c}$ cuprates, the relative importance of phenomena such as spin and charge (strip) order, superconductivity fluctuations, proximity to Mott insulator, a pseudogap phase and quantum criticality are still a matter of debate. In electron-doped cuprates, the absence of $``$anomalous\textquotedblright\ pseudogap phase in the underdoped region of the phase diagram and weaker electron correlations suggest that Mott physics and other unidentified competing orders are less relevant and that antiferromagnetic (AFM) spin fluctuations are the dominant feature. In this talk, I will report results of low temperature magnetotransport experiments in optimal to overdoped (non-superconducting) thin films of the electron-doped cuprate La$_{2-x}$Ce$_{x}$CuO$_{4}$ (LCCO). We find that a linear-in-\textit{T} scattering rate is correlated with the superconductivity (\textit{T}$_{c}$). Our results show that an envelope of such scattering surrounds the superconducting phase, surviving to 20 mK (the limit of our experiments) when superconductivity is suppressed by magnetic fields [1]. Comparison with similar behavior found in organic superconductors [2] strongly suggests that the linear-in-\textit{T} resistivity in the electron-doped cuprates is caused by spin-fluctuation scattering. Because linear-in-T scattering has also been linked to \textit{T}% $_{c}$ in some hole-doped cuprates [2], our results suggest a fundamental connection between AFM spin fluctuations and the pairing mechanism of high temperature superconductivity in all cuprates. In addition, I will discuss how quantum criticality plays a significant role in shaping the anomalous properties of the electron-doped cuprate phase diagram. We identify quantum critical scaling in LCCO with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping [3]. \\[4pt] [1] K. Jin, N.P. Butch, K. Kirshenbaum, J. Paglione, and R.L. Greene, Nature 476, 73 (2011).\\[0pt] [2] L. Taillefer, Annu. Rev. Cond. Matter Phys. 1, 51 (2010). \\[0pt] [3] N.P. Butch, K. Jin, K. Kirshenbaum, R.L. Greene, and J. Paglione, submitted.   

Intense paramagnon excitations in a large family of high-temperature superconductors

Motivated by the search for the mechanism of high-temperature superconductivity, an intense research effort has been focused on the evolution of the spin excitation spectrum upon doping from the antiferromagnetic insulating to the superconducting states of the cuprates. Because of technical limitations, however, the experimental investigation of doped cuprates has been largely focused on excitations with energies $\bf \leq 100$ meV in a small range of momentum space~[1]. Here we take advantage of the recent developments of high-resolution resonant inelastic x-ray scattering~[2,3] to show that a large family of superconductors, encompassing the model compounds YBa$_2$Cu$_4$O$_8$ and YBa$_2$Cu$_3$O$_{7}$, exhibits damped spin excitations - or paramagnons - with dispersions and spectral weights closely similar to those of magnons in undoped, antiferromagnetically ordered cuprates over much of the Brillouin zone. The results are in excellent agreement with the spin excitations obtained by exact diagonalization of the $\bf t-J$ Hamiltonian on finite-sized clusters. A numerical solution of the Eliashberg equations based on the experimental spin excitation spectrum of YBa$_2$Cu$_3$O$_{7}$ reproduces its superconducting transition temperature $\bf T_c$ within a factor of two. The discovery of a well-defined, surprisingly simple spin excitation branch over a wide range of doping levels thus strongly supports magnetic Cooper pairing models for the cuprates~[4]. \\[4pt] [1] M. Fujita \textit{et al.} arXiv/condmat:1108.4431\\[0pt] [2] G. Ghiringhelli \textit{et al.}, Review of Scientific Instruments, \textbf{77}, (2006).\\[0pt] [3] L. Braicovich \textit{et al.}, Phys. Rev. Lett., \textbf{104}, 077002 (2010).\\[0pt] [4] M. Le Tacon \textit{et al.}, Nature Physics \textbf{7}, 725 (2011).   

Magnetically driven superconductivity in CeCu$_2$Si$_2$

The origin of unconventional superconductivity, including high-temperature and heavy-fermion superconductivity, is still discussed controversially. Spin excitations instead of phonons are thought to be responsible for the formation of Cooper pairs. Unconventional superconductivity is quite often observed in the vicinity of a magnetic quantum critical point (QCP), i.e., a continuous magnetic phase transitions occurring at $T = 0$. Such a QCP can be approached when tuning a continuous finite temperature phase transition to $T = 0$ by means of a non-thermal control parameter like doping, pressure or magnetic field. As a result of the quantum-critical spin fluctuations unusual low-temperature properties are observed. The heavy-fermion compound CeCu$_2$Si$_2$ displays unconventional superconductivity and is already at ambient pressure located in the vicinity of a QCP where long-range antiferromagnetism vanishes. Using elastic and inelastic neutron scattering we studied in detail the antiferromagnetic order and the spin excitations spectrum around the QCP. Antiferromagetism and superconductivity exclude each other on a microscopic scale. While for magnetically ordered samples critical slowing down of the spin fluctuations above $T_{\rm N}$ is observed, shows the normal state response of superconducting CeCu$_2$Si$_2$ an almost critical slowing down for $T \rightarrow 0$. Its temperature dependence and scaling behavior are in line with the expectations for an itinerant spin-density-wave QCP. This interpretation is substantiated by an analysis of specific heat data and the momentum dependence of the magnetic excitation spectrum. The magnetic response in the superconducting state is characterized by a transfer of spectral weight to energies above a spin excitation gap. Compared to the condensation energy there is a larger saving of magnetic exchange energy as the system condenses into a superconducting state. Our results strongly imply that the coupling of Cooper pairs in CeCu$_2$Si$_2$ is mediated by overdamped spin fluctuations.   

2012 IUPAP C10 Young Scientist Prize on the Structure and Dynamics of Condensed Matter Lecture: Spin Fluctuations and Pairing in Fe-based Superconductors

The origin of superconductivity in the Fe-based superconductors, like that in other unconventional superconductors, remains shrouded in mystery. How the pairing bosons emerge either due to or in spite of the strong magnetic interactions found in the Fe-based superconductors is one of the most thoroughly investigated questions in the field. A prominent example of the interplay of superconductivity and magnetism is the dramatic shift of spectral weight from the low energy spin excitations to an energy which is related to the superconducting gap resulting in a peak in the spin excitation spectrum localized in both momentum and energy which occurs at the onset of superconductivity. The appearance of the new peak in the spin excitation spectrum below the superconducting transition temperature is referred to as s spin resonance and is most commonly interpreted as indicating a sign change of the superconducting order parameter on different portions of the Fermi surface and thus is consistent with an extended s-wave or s$\pm $ pairing symmetry in many Fe-based superconductors. We will review the observations and implications of the spin resonance across the Fe-based superconductors. In particular we will examine the relationship between the resonance energy and the superconducting transition temperature as a function of chemical doping and pressure. While the spin resonance provides important information about pairing symmetry, there does not appear to be sufficient spectral to explain the pairing strength. Thus the remainder of the spin excitation spectrum must be examined to determine if spin fluctuations are ultimately responsible for pairing in the Fe-based materials. Consequently, we will discuss in detail the way in which the spin excitations evolve from the nonsuperconducting compounds to their superconducting relatives as a function of chemical doping.