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Register a new userEvidence for a Fermi liquid in the pseudogap phase of high-Tc cuprates
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Cuprate high-T_c superconductors on the Mott-insulating side of optimal doping (with respect to the highest T_cs) exhibit enigmatic behavior in the non-superconducting state. Near optimal doping the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. For carrier concentrations below optimal doping a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface, and causes a break-up of the Fermi surface into disconnected nodal and anti-nodal sectors. Here we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. Our optical measurements reveal that the dynamical relaxation rate 1/tau(omega,T) collapses on a universal function proportional to (hbar omega)^2+(1.5 pi k_B T)^2. Hints at possible Fermi liquid behavior came from the recent discovery of quantum oscillations at low temperature and high magnetic field in underdoped YBa2Cu3O6+d and YBa2Cu4O8, from the observed T^2-dependence of the DC ({omega}=0) resistivity for both overdoped and underdoped cuprates, and from the two-fluid analysis of nuclear magnetic resonance data. However, the direct spectroscopic determination of the energy dependence of the life-time of the excitations -provided by our measurements- has been elusive up to now. This observation defies the standard lore of non-Fermi liquid physics in high T_c cuprates on the underdoped side of the phase diagram.
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Angle-resolved photoemission on underdoped La$_{1.895}$Sr$_{0.105}$CuO$_4$ reveals that in the pseudogap phase, the dispersion has two branches located above and below the Fermi level with a minimum at the Fermi momentum. This is characteristic of the Bogoliubov dispersion in the superconducting state. We also observe that the superconducting and pseudogaps have the same d-wave form with the same amplitude. Our observations provide direct evidence for preformed Cooper pairs, implying that the pseudogap phase is a precursor to superconductivity.
We show that the resistivity in each phase of the High-Tc cuprates is a special case of a general expression derived from the Kubo formula. We obtain, in particular, the T-linear behavior in the strange metal (SM) and upper pseudogap (PG) phases, the pure $T^2$, Fermi liquid (FL) behavior observed in the strongly overdoped regime as well as the $T^{1+delta}$ behavior that interpolates both in the crossover. We calculate the coefficients: a) of $T$ in the linear regime and show that it is proportional to the PG temperature $T^*(x)$; b) of the $T^2$-term in the FL regime, without adjusting any parameter; and c) of the $T^{1.6}$ term in the crossover regime, all in excellent agreement with the experimental data. From our model, we are able to infer that the resistivity in cuprates is caused by the scattering of holes by excitons, which naturally form as holes are doped into the electron background.
Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave (CDW)) order parameter, competing with superconductivity. We explicitly demonstrate the evolution from Fermi arcs (on the large Fermi surface) observed in ARPES experiments at relatively high temperatures (when both the amplitude and phase of density waves fluctuate randomly) towards formation of typical small electron and hole pockets, which are apparently observed in de Haas - van Alfen and Hall resistance oscillation experiments at low temperatures (when only the phase of density waves fluctuate, and correlation length of the short-range order is large enough). A qualitative criterion for quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of cyclotron frequency, correlation length of fluctuations and Fermi velocity.
We have used pulsed magnetic fields up to 60Tesla to suppress the contribution of superconducting fluctuations(SCF)to the conductivity above Tc in a series of YBa2Cu3O6+x from the deep pseudogapped state to slight overdoping. Accurate determinations of the SCF conductivity versus temperature and magnetic field have been achieved. Their joint quantitative analyses with respect to Nernst data allow us to establish that thermal fluctuations following the Ginzburg-Landau(GL) scheme are dominant for nearly optimally doped samples. The deduced coherence length xi(T) is in perfect agreement with a gaussian (Aslamazov-Larkin) contribution for 1.01Tc<T<1.2Tc. A phase fluctuation contribution might be invoked for the most underdoped samples in a T range which increases when controlled disorder is introduced by electron irradiation. For all dopings we evidence that the fluctuations are highly damped when increasing T or H. The data permits us to define a field Hc^prime and a temperature Tc^prime above which the SCF are fully suppressed. The analysis of the fluctuation magnetoconductance in the GL approach allows us to determine the critical field Hc2(0). The actual values of Hc^prime(0) and Hc2(0) are found quite similar and both increase with hole doping. These depairing fields, which are directly connected to the magnitude of the SC gap, do therefore follow the Tc variation which is at odds with the sharp decrease of the pseudogap T* with increasing hole doping. This is on line with our previous evidence that T* is not the onset of pairing. We finally propose a three dimensional phase diagram including a disorder axis, which allows to explain most peculiar observations done so far on the diverse cuprate families.
The experimental investigations done in our paper Phys.Rev.B84,014522(2011) allowed us to establish that the superconducting fluctuations (SCF) always die out sharply with increasing T. But contrary to the claim done in the comment of Ramallo et al., this sharp cutoff of SCF measured in YBa2Cu3O{6+x} depends on hole doping and/or disorder. So our data cannot be used to claim for a universality of the extended gaussian Ginzburg Landau theory proposed by the authors of the comment. Furthermore, to explain quantitatively our data near optimal doping using this model they need to consider that fluctuations in the two CuO2 planes of a bilayer are totally decoupled, which is not physically well justified. On the contrary a consistent interpretation of all our data (paraconductivity, Nernst effect and magnetoresistance) has been done by considering that the coupling between the two layers of the unit cell is dominant at least up to 1.1Tc.
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