Superexchange Mechanism in Coupled Triangulenes Forming Spin-1 Chains.

We show that the origin of the antiferromagnetic coupling in spin-1 triangulene chains, which were recently synthesized and measured by Mishra et al. ( Nature 2021, 598, 287-292), originates from a superexchange mechanism. This process, mediated by intertriangulene states, opens the possibility to control parameters in the effective bilinear-biquadratic spin model. We start from the derivation of an effective tight-binding model for triangulene chains using a combination of tight-binding and Hartree-Fock methods fitted to hybrid density functional theory results. Next, correlation effects are investigated within the configuration interaction method. Our low-energy many-body spectrum for NTr = 2 and NTr = 4 triangulene chains agree well with the bilinear-biquadratic spin-1 chain antiferromagnetic model when indirect coupling processes and superexchange coupling between triangulene spins are taken into account.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot.

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Theory of Excitons in Gated Bilayer Graphene Quantum Dots.

We present a theory of excitons in gated bilayer graphene (BLG) quantum dots (QDs). Electrical gating of BLG opens an energy gap, turning this material into an electrically tunable semiconductor. Unlike in laterally gated semiconductor QDs, where electrons are attracted and holes repelled, we show here that lateral structuring of metallic gates results in a gated lateral QD confining both electrons and holes. Using an accurate atomistic approach and exact diagonalization tools, we describe strongly interacting electrons and holes forming an electrically tunable exciton. We find these excitons to be different from those found in semiconductor QDs and nanocrystals, with exciton energy tunable by voltage from the terahertz to far infrared (FIR) range. The conservation of spin, valley, and orbital angular momentum results in an exciton fine structure with a band of dark low-energy states, making this system a promising candidate for storage, detection and emission of photons in the terahertz range.

Edge States and Strain-Driven Topological Phase Transitions in Quantum Dots in Topological Insulators.

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band k→·p→ Hamiltonian or by a four-band k→·p→ Bernevig-Hughes-Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir-Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots.