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Register a new userThermal Hall effect in the pseudogap phase of cuprates
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Authors
Chandra M. Varma
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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.
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A recent observation of thermal Hall effect of magnetic origin in underdoped cuprates calls for critical re-examination of low-energy magnetic dynamics in undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce non-zero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of Born approximation. Local formation of skyrmion defects is also found incapable of generating magnon thermal Hall effect. Turning to spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known {pi}-flux model of spinons. The resulting two-band model has Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependences mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a first step towards reaching some level of understanding.
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.
We study the quantum transition from an antiferromagnet to a superconductor in a model for electron- and hole-doped cuprates by means of a variational cluster perturbation theory approach. In both cases, our results suggest a tendency towards phase separation between a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at larger doping. However, in the electron-doped case the energy scale for phase separation is an order of magnitude smaller than for hole doping. We argue that this can explain the different pseudogap and superconducting transition scales in hole- and electron-doped materials.
The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the $p$ (hole doping) to $1+p$ jump measured in the Hall number $n_H$ at a doping $p^*$. Here we explore {it collinear} incommensurate SDW as another possible explanation of this phenomenon, distinct from the incommensurate {it spiral} SDW proposal. We examine the effect of different SDW strengths and wavevectors and we find that the $n_Hsim p$ behavior is hardly reproduced at low doping. The calculated $n_H$ and Fermi surfaces give characteristic features that should be observed, thus the lack of these features in experiment suggests that the incommensurate collinear SDW is unlikely to be a good candidate to explain the $n_Hsim p$ observed in the pseudogap regime.
We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.
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