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Register a new userEffect of the pseudogap on T$_c$ in the cuprates and implications for its origin
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One of the most intriguing aspects of cuprates is a large pseudogap coexisting with a high superconducting transition temperature. Here, we study pairing in the cuprates from electron-electron interactions by constructing the pair vertex using spectral functions derived from angle resolved photoemission data for a near optimal doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ sample that has a pronounced pseudogap. Assuming that that the pseudogap is {it not} due to pairing, we find that the superconducting instability is strongly suppressed, in stark contrast to what is actually observed. Using an analytic approximation for the spectral functions, we can trace this suppression to the destruction of the BCS logarithmic singularity from a combination of the pseudogap and lifetime broadening. Our findings strongly support those theories of the cuprates where the pseudogap is instead due to pairing.
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The penetration depth is calculated over the entire doping range of the cuprate phase diagram with emphasis on the underdoped regime. Pseudogap formation on approaching the Mott transition, for doping below a quantum critical point, is described within a model based on the resonating valence bond spin liquid which provides an ansatz for the coherent piece of the Greens function. Fermi surface reconstruction, which is an essential element of the model, has a strong effect on the superfluid density at T=0 producing a sharp drop in magnitude, but does not change the slope of the linear low temperature variation. Comparison with recent data on Bi-based cuprates provides validation of the theory and shows that the effects of correlations, captured by Gutzwiller factors, are essential for a qualitative understanding of the data. We find that the Ferrell-Glover-Tinkham sum rule still holds and we compare our results with those for the Fermi arc and the nodal liquid models.
It is argued that the unusual non-states-conserving fermion density of states, deduced from the specific heat of several families of hole-doped cuprates, points towards interpretations of the pseudogap based on the suppression of a Kondo or heavy fermion-like density of states by antiferromagnetic spin fluctuations.
We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $ u(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_ u$ at which $ u/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^star$- in agreement with gap opening detected in ARPES data. We track $T^star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^star(p)$ to $p=0$ yields $T^star(pto 0)simeq T_N(0)$, the Neel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^star(p)$ extrapolates linearly to zero at $psimeq p_{rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{rm c}$, and not $T^star$. This confirms that the pseudogap phase is not a form of precursor superconductivity.
The nature of the pseudogap phase of cuprates remains a major puzzle. One of its new signatures is a large negative thermal Hall conductivity $kappa_{rm xy}$, which appears for dopings $p$ below the pseudogap critical doping $p^*$, but whose origin is as yet unknown. Because this large $kappa_{rm xy}$ is observed even in the undoped Mott insulator La$_2$CuO$_4$, it cannot come from charge carriers, these being localized at $p = 0$. Here we show that the thermal Hall conductivity of La$_2$CuO$_4$ is roughly isotropic, being nearly the same for heat transport parallel and normal to the CuO$_2$ planes, i.e. $kappa_{rm zy}(T) approx kappa_{rm xy} (T)$. This shows that the Hall response must come from phonons, these being the only heat carriers able to move as easily normal and parallel to the planes . At $p > p^*$, in both La$_{rm 1.6-x}$Nd$_{rm 0.4}$Sr$_x$CuO$_4$ and La$_{rm 1.8-x}$Eu$_{rm 0.2}$Sr$_x$CuO$_4$ with $p = 0.24$, we observe no c-axis Hall signal, i.e. $kappa_{rm zy}(T) = 0$, showing that phonons have zero Hall response outside the pseudogap phase. The phonon Hall response appears immediately below $p^* = 0.23$, as confirmed by the large $kappa_{rm zy}(T)$ signal we find in La$_{1.6-x}$Nd$_{rm 0.4}$Sr$_x$CuO$_4$ with $p = 0.21$. The microscopic mechanism by which phonons become chiral in cuprates remains to be identified. This mechanism must be intrinsic - from a coupling of phonons to their electronic environment - rather than extrinsic, from structural defects or impurities, as these are the same on both sides of $p^*$. This intrinsic phonon Hall effect provides a new window on quantum materials and it may explain the thermal Hall signal observed in other topologically nontrivial insulators.
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.
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