## Final Report Summary - USSU (UNCONVENTIONAL SUPERCONDUCTORS: FROM SYNTHESIS TO UNDERSTANDING)

The general framework of the research program:

“Unconventional superconductors: From synthesis to understanding” was focused on the study of the physical properties of unconventional superconductors. In contrast to conventional superconductors, such as Nb3Ge and elemental Hg, where weakly interacting electrons are paired by the electron–phonon interaction, unconventional superconductivity occurs in systems that exhibit strong correlations and where the pairing mechanism may not be phononic. Thus, besides the effects of reduced dimensions, the interplay of the magnetic correlations and of various charge orders with superconductivity observed in such systems are certainly of prime importance. Heavy-fermion compounds, low-dimensional organic conductors, cuprates and iron-pnictides discovered several years ago are excellent examples of such systems. Consequently, they were extensively explored in the effort of understanding the underlying mechanism for the superconductivity. Indeed, all of them exhibit certain types of magnetic/charge order in the close vicinity of a superconducting phase that at the first sight seems to be of unconventional nature.

Since these new materials are subject to strong correlations resulting in complex and subtle effects, a multidisciplinary effort was required. It relied on material science, including aspects from applied physics and chemistry, application of modern experimental techniques and the development of new theoretical ideas. Such a synergy is, if not the only then certainly the most efficient way for unraveling the complexity of physical properties in strongly correlated systems. The USSU project combined all of these components and turned out to be enlightening in many aspects. From the already published results perhaps the most exciting are those that clearly reveal the Fermi liquid aspects of the cuprate compounds, which we will briefly discuss in this report.

Our new findings for the metallic state of the cuprates, published in Proceedings of the National Academy of Sciences (N. Barišić et al., PNAS 110, 12235 (2013)) are both remarkably simple and profound. We have studied the high-quality crystals of Hg1201 (HgBa2CuO4+δ), arguably the most desirable cuprate superconductor for experimental study due to its high-symmetry crystal structure and high superconducting transition temperature. We first demonstrate that, in addition to the well-known linear resistive regime at higher temperature, the model cuprate Hg1201 exhibits a Fermi-liquid-like quadratic temperature regime at lower temperature. In other words, once the pseudogap has removed most of the quasi-particle spectral weight from the anti-nodal parts of the Fermi surface, the superconducting state actually emerges from a state that exhibits along the nodes metallic, in effect conventional behavior.

Second, motivated by our resistivity measurements for Hg1201, we have combined our data with published results for three structurally more complex cuprates and have been able to obtain the universal, quantitative resistivity per copper-oxygen plane (sheet resistance) throughout most of the temperature-doping phase diagram.

Finally, we demonstrated that the doping dependence of the sheet resistance in both the linear and the quadratic temperature regimes is remarkably simple, which lead us to propose the scenario that even outside of the pseudogap regime (both at high temperature and high hole concentrations) only the near-nodal states contribute to the planar transport. Conversely, it appeared that deep inside the pseudogap regime, close to the antiferromagnetic-insulating state at zero doping, the cuprates may in effect be nodal Fermi liquids. These insights imply the need for a dramatic paradigm shift for the phase diagram of the cuprates.

Our new insights already have inspired exciting collaborative work with the group of Prof. Dirk van Der Marel. By optical conductivity measurements we have revealed a Fermi-liquid-like quadratic frequency dependence and temperature-frequency scaling in Hg1201 samples in which the pure T2 behavior is demonstrated from dc transport was found before. This work confirms by an independent experimental probe our findings and has been separately published in PNAS (S. I. Mirzaei et al., PNAS 110, 5774 (2013)).

The observation of quantum oscillations (QO) for underdoped Y123 and Y124 implies the presence of a very small pocket (covering only ~2-3% of the Brillouin zone), in stark contrast to the situation at high hole concentrations, where a large Fermi surface (FS) was observed corresponding to approximately 65% of the first Brillouin zone. While this result can been taken as evidence for a dramatic change of the FS associated with the quintessential CuO2 planes, it could also be attributed to the existence of a non-universal FS piece related to the CuO chains in Y123 and Y124. Consequently, it has remained a pivotal open question whether the FS reconstruction has anything to do with aspects of the unidirectional structures, or if it is a universal property of the cuprates. We have settled this issue through the observation of QO in the magnetorestivity of Hg1201 at p≈0.09 in pulsed magnetic fields of up to 80 T (N. Barišić et al., Nature Physics 9, 761 (2013)).

In Fig. 1a the oscillatory part of the dc- magnetoresistivity resistivity, after removing a smooth non-oscillatory contribution, is plotted versus 1/B at different temperatures. The Fourier transforms in the limited field range [62 T; 81 T] exhibit a single peak at F = (840 ± 30) T (Fig. 1b). According to the Onsager relation, F = Ak0/22, where 0 is the magnetic flux quantum, and Ak the cross-sectional area of the FS perpendicular to the applied field, which corresponds to about 3 % of the Brillouin zone. Assuming that the FS is strictly two-dimensional, the Luttinger theorem yields n2D = 2Ak/(2)2 = F/0 = 0.061 ± 0.002 carriers per pocket. In a single-band model, the Hall coefficient RH = 1/n3De (n3D = n2D/c, where c is the lattice parameter perpendicular to the CuO2 planes) can be evaluated to be RH = 14.7 ± 0.6 mm3/C, in very good agreement with the value RH = 15 ± 5 mm3/C obtained at low temperatures and in high fields for a Hg1201 sample with a similar doping level (Tc = 65 K, p ≈ 0.075) (N. Doiron-Leyraud, et al., Phys. Rev. X 3, 021019 (2013)). By following the temperature dependence of the oscillation amplitude (inset of Fig. 3b), the quasiparticle effective mass m* = 2.45 ± 0.15 me is extracted (where me is the electron free mass). By performing a Lifshitz-Kosevich fit to the data (solid lines in Fig. 3a), the Dingle temperature could be evaluated to be TD = (18 ± 4) K, which corresponds to a mean free path of ~ 5 nm.

Figure 1 | Frequency of oscillations and effective mass. a, Oscillatory part of the isothermal magnetoresistivity data (obtained by subtracting a monotonic contribution) versus inverse field (symbols). Solid lines correspond to Lifshitz-Kosevich fit (see text). b, Fourier transform of the oscillatory part, from which only one peak is observed at F = (840 ± 30) T, with temperature-independent position. Inset: In accordance with the Lifshitz-Kosevich formula, the temperature dependence of the amplitude yields a cyclotron mass of m* = (2.45 ± 0.15) me, where me is the mass of a free electron. Solid red line: fit. Black dashed lines: error range.