Pawel Hawrylak

We demonstrate here that a chain of bilayer graphene quantum dots (BLGQDs) can realize topological quantum matter by effectively simulating a spin-1 chain that hosts the Haldane phase within a specific range of parameters. We describe a chain of BLGQDs with two electrons per dot using an atomistic tight-binding model combined with exact diagonalization to solve the interacting few-electron problem. Coulomb interactions and valley-mixing effects are treated within a single microscopic framework, allowing us to systematically investigate spin and valley polarization transitions as functions of interaction strength and external tuning parameters. We calculate the low energy states for single and double QDs as a function of the number of electrons, identifying regimes of highly correlated multielectron states. We confirm the presence of a spin-1 ground state for two electrons. Then, we explore two coupled QDs with four electrons and extend the analysis to QD arrays. Using a mapping of the BLGQD chain to an effective bilinear-biquadratic (BLBQ) spin model, we demonstrate that BLGQD arrays can work as a quantum simulator for one-dimensional spin chains with emergent many-body topological phases.

Monolayer transition metal dichalcogenides have emerged as prominent candidates to explore the complex interplay between spin and valley degrees of freedom. Their strong spin-orbit interaction and broken inversion symmetry lead to the spin-valley locking effect, in which carriers occupying the K and K ′ valleys of the reciprocal space must have opposite spins. This effect is particularly strong for holes due to a larger spin-orbit gap in the valence band. By reducing the dimensionality of a monolayer of WSe ₂ to 1D via electrostatic confinement, we demonstrate that spin-valley locking and strong hole-hole interactions lead to a ferromagnetic state where hole transport is spin-valley polarized, even without an applied magnetic field. A massive Dirac fermion model in the Hartree-Fock approximation reveals that many-body hole-exchange interactions lead to this polarized ground-state. This observation opens the possibility of implementing a robust and stable valley-polarized system, essential in valleytronic applications.

We present here a theory of Majorana excitons, photo-excited conduction electron-valence band hole pairs, interacting with Majorana Fermions in a Kitaev chain of semiconductor quantum dots embedded in a nanowire. Using analytical tools and exact diagonalization methods, we identify the presence of Majorana zero modes in the nanowire absorption spectra.

We present here a theory of Majorana excitons, photo-excited conduction electron-valence band hole pairs, interacting with Majorana Fermions in a Kitaev chain of semiconductor quantum dots embedded in a nanowire. Using analytical tools and exact diagonalisation methods we identify the presence of Majorana Zero Modes in the nanowire absorption spectra.

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS₂, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron–electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe–Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

DOI: https://doi.org/10.1103/PhysRevX.11.019901