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Register a new userGiant thermal Hall conductivity from neutral excitations in the pseudogap phase of cuprates
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The nature of the pseudogap phase of cuprates remains a major puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature. Although Fermi-surface, transport and thermodynamic signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order, there is no evidence for an associated long-range magnetic order. Here we report measurements of the thermal Hall conductivity $kappa_{rm xy}$ in the normal state of four different cuprates (Nd-LSCO, Eu-LSCO, LSCO, and Bi2201) and show that a large negative $kappa_{rm xy}$ signal is a property of the pseudogap phase, appearing with the onset of that phase at the critical doping $p^*$. Since it is not due to charge carriers -- as it persists when the material becomes an insulator, at low doping -- or magnons -- as it exists in the absence of magnetic order -- or phonons -- since skew scattering is very weak, we attribute this $kappa_{rm xy}$ signal to exotic neutral excitations, presumably with spin chirality. The thermal Hall conductivity in the pseudogap phase of cuprates is reminiscent of that found in insulators with spin-liquid states. In the Mott insulator LCO, it attains the highest known magnitude of any insulator.
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The opening of the pseudogap in underdoped cuprates breaks up the Fermi surface, which may lead to a breakup of the d-wave order parameter into two subband amplitudes and a low energy Leggett mode due to phase fluctuations between them. This causes a large increase in the temperature range of superconducting fluctuations with an overdamped Leggett mode. Almost resonant scattering of inter-subband phonons to a state with a pair of Leggett modes causes anomalously strong damping. In the ordered state, the Leggett mode develops a finite energy, suppressing the anomalous phonon damping but leading to an anomaly in the phonon dispersion.
Motivated by a previous $sd^2$-graphene study, the pairing symmetry in the superconducting state and the thermal Hall conductivity are investigated by a self-consistent Bogoliubov--de Gennes approach on the kagome lattice with intrinsic spin-orbit coupling near van Hove fillings. While the topologically trivial state with broken time-reversal symmetry appears in the absence of spin-orbit coupling, the highest flat band becomes dispersive with a hexagonal symmetry due to spin-orbit coupling, which leads to a topological superconducting state. Since the thermal Hall conductivity in the low-temperature limit is associated with the topological property of time-reversal symmetry breaking superconductors, we study its temperature dependence near van Hove fillings. In particular, the pairing symmetry in the highest flat band is sensitive to the amplitudes of spin-orbit coupling and the attractive interaction, which is reflected remarkably in the thermal Hall conductivity. The obtained result may enable us to investigate the stable superconducting state on the kagome lattice.
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.
The conjecture made recently by the group at Sherbrooke, that their observed anomalous thermal Hall effect in the pseudo-gap phase in the cuprates is due to phonons, is supported on the basis of an earlier result that the observed loop-current order in this phase must induce lattice distortions which are linear in the order parameter and an applied magnetic field. The lowered symmetry of the crystal depends on the direction of the field. A consequence is that the elastic constants change proportional to the field and are shown to induce axial thermal transport with the same symmetries as the Lorentz force enforces for the normal electronic Hall effect. Direct measurements of elastic constants in a magnetic field are suggested to verify the quantitative aspects of the results.
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.
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