- In a set of substantial manuscripts, we have achieved a substantial fraction of the proposed work in the first part of the ERC (referred to as (i) above):
In most solids, heat is carried by phonons, which are the elastic waves in the lattice. The speed of heat transport is typically controlled by scattering. We have shown that phonons scattering off of electronic degrees of freedom can induce novel phenomena like thermal Hall effect when phonons scatter more "to the left" than "to the right" or vice versa.
We have provided a very general formulation to calculate the scattering of phonons with an arbitrary quantum degree of freedom Q, and from it we derived the consequences on the thermal conductivity tensor of the phonons, i.e. both its longitudinal and Hall components. This should apply to any material—conductor, insulator, magnet etc—for any correlations of the degrees of freedom (the Q may in particular be a strongly interacting field), provided only that the material is not too disordered. A central result is that the thermal Hall conductivity is proportional to a four-point correlation function of Q, which we gave explicitly. This shows how chiral/handed scattering probes highly non-trivial structure of correlations.
As an illustration of the method, we applied our results to the case where the fluctuating field Q arises from magnon excitations of an ordered antiferromagnet. For a reasonable set of parameters, we found that the Hall angle can be of the order of magnitude of that in systems where it is lauded as "large", and obtained various power-law regimes of the longitudinal and Hall thermal conductivities.
- In a related project we have provided methodology, symmetry constraints etc to understand the phonon Hall viscosity, which is another mechanism through which a nonzero thermal Hall effect can appear, and shown that its size will generally be small compared with experimental measurements.
- We have also investigated how unusual magnetic phases could arise in several materials, both two- and three-dimensional, and with spin-1 and spin-1/2. In the first case, we showed that the phase diagram for a small set of parameters was particularly rich and in particular observed that a macroscopically-degenerate phase arose at the mean-field level, which could signal a quantum spin liquid in a more "quantum" calculation. Developing new methodology, we also derived the neutron scattering excitation spectra, to which experiments can be directly compared. In the second case, we showed that an antisymmetric (Dzyaloshinskii-Moriya) interaction arose in the half-Heusler compounds and contributed to the appearance of noncollinear/noncoplanar phases, which we expect will yield an anomalous Hall effect in the compounds in this class where there exist itinerant electrons.
- We have established unbiased methodology to carry out renormalization group calculations in flat band systems, and applied it to twisted bilayer graphene (TBG), where a number of correlated phases have been shown to appear. We found that at half-filling TBG ought to favor nematic order, consistent with experimental observations, and moreover showed that our procedure was "controlled", a rare occurrence of such calculations.
