Siddharth Parameswaran

Abstract:

We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled-pair state calculations to investigate the ground-state phase diagram of the triangular-lattice Hubbard model at “half doping” relative to single occupancy, i.e., at fillings of $(1\pm \frac{1}{2})$ electrons per site. The electron-doped case has a nested Fermi surface in the noninteracting limit, and hence a weak-coupling instability toward density-wave orders whose wave vectors are determined by Fermi-surface nesting conditions. We find that at moderate-to-strong interaction strengths, other spatially modulated orders arise, with wave vectors distinct from the nesting vectors. In particular, we identify a series of closely competing, itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.

Abstract:

We link the presence of “unnecessary” quantum critical surfaces within a single gapped phase of matter to the nontrivial topology of of gapped Hamiltonians that encircle the critical surface. We study a specific set of one-dimensional spin models where each such family forms a one-parameter loop in a two-dimensional phase diagram. Foliating the noncritical region by such loops identifies “radial” and “angular” coordinates in the phase diagram that respectively parametrize different families and different members of a single family. We show that each one-parameter family is a generalized Thouless charge pump, all with the same topological index, and hence the gapped phase undergoes one or more nontrivial boundary phase transitions as we vary the angular coordinate in a loop through members of one family. Tuning the radial coordinate generates loci of boundary critical points that terminate at the end points of the bulk unnecessary critical line within the gapped phase. We discuss broader implications of our results and possible extensions to higher dimensions.

Abstract:

We review the theoretical modeling of moiré materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree–Fock mean-field theory. We first provide an elementary introduction to the continuum modeling of moiré bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized ‘chiral-flat’ strong-coupling limit, in which ground states at electron densities commensurate with the moiré superlattice are exactly captured by mean-field ansätze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekulé spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree–Fock manifold form our first ‘case study’. Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moiré systems.

Abstract:

SciPost Journals Publication Detail SciPost Phys. 19, 086 (2025) Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

Abstract:

Graphene moiré systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms that underlie them, as they permit controlled manipulation of electronic properties. Magic-angle twisted trilayer graphene has emerged as a key platform for exploring moiré superconductivity due to the robustness of its superconducting order and the ability to tune its energy bands with an electric field. Here we report the direct observation of two domes of superconductivity in the phase diagram of magic-angle twisted trilayer graphene. The dependence of the superconductivity of doped holes on the temperature, magnetic field and bias current shows that it is suppressed near a specific filling of the moiré flat band, leading to a double dome in the phase diagram within a finite range of the displacement field. The transport properties are also indicative of a phase transition and the potentially distinct nature of superconductivity in the two domes. Hartree–Fock calculations incorporating mild strain yield an incommensurate Kekulé spiral state whose effective spin polarization peaks in the regime where superconductivity is suppressed in the experiments.