Siddharth Parameswaran

Abstract:

We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric ${\mathsf{Z}}_2$ and $\mathsf{U}\left(1\right)$ QSLs on the trillium lattice. We find two ${\mathsf{Z}}_2$ spin-liquids, and a single $\mathsf{U}\left(1\right)$ spin-liquid that is proximate to one of the ${\mathsf{Z}}_2$ states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two ${\mathsf{Z}}_2$ QSLs is nodal, while the $\mathsf{U}\left(1\right)$ case hosts a spinon Fermi surface. One of our ${\mathsf{Z}}_2$ spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.

Abstract:

We explore the phase diagrams of moiré materials in search of a class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper [Kwan , .], breaks valley <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>U</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </math> symmetry in a nontrivial fashion wherein the valley order parameter is forced to texture in momentum space as a consequence of band topology. Using detailed Hartree-Fock studies, we establish that the CTI emerges as an energetically competitive intermediate-coupling ground state in several moiré systems that lack a twofold rotation symmetry that forbids the single-particle topology essential to the formation of the CTI valley texture. Published by the American Physical Society 2025

Abstract:

We introduce and study interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the U(1) valley symmetry linked to independent charge conservation in each time-reversal sector is spontaneously broken, the corresponding “excitonic” order parameter is forced to form a topologically nontrivial texture across the Brillouin zone. We show that the resulting phase, which we dub a textured exciton insulator, cannot be given a local-moment description because of a form of delicate topology. Using toy models of bands with Chern or Euler obstructions to localization, we construct explicit examples of the Chern or Euler texture insulators (CTIs or ETIs) they support, and demonstrate that these are generically competitive ground states at intermediate coupling. We construct field theories that capture the response properties of these new states. Finally, we identify the incommensurate Kekulé spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.