This review article provides a birds-eye view of what first-principles based methods can contribute to next-generation device design and simulation. After a brief overview of methods and capabilities in the area, we focus on published work by our gro
up since 2015 and current work on $textrm{CrI}_3$. We introduce both single- and dual-gate models in the framework of density functional theory and the constrained random phase approximation in estimating the Hubbard $U$ for 2D systems vs. their 3D counterparts. A wide range of systems, including graphene-based heterogeneous systems, transition metal dichalcogenides, and topological insulators, and a rich array of physical phenomena, including the macroscopic origin of polarization, field effects on magnetic order, interface state resonance induced peak in transmission coefficients, spin filtration, etc., are covered. For $textrm{CrI}_3$ we present our new results on bilayer systems such as the interplay between stacking and magnetic order, pressure dependence, and electric field induced magnetic phase transitions. We find that a bare bilayer $textrm{CrI}_3$, graphene$,|,$bilayer $textrm{CrI}_3,|,$graphene, $h$-BN$,|,$bilayer $textrm{CrI}_3,|,h$-BN, and $h$-BN$,|,$bilayer $textrm{CrI}_3,|,$graphene all have a different response at high field, while small field the difference is small except for graphene$,|,$bilayer $textrm{CrI}_3,|,$graphene. We conclude with discussion of some ongoing work and work planned in the near future, with the inclusion of further method development and applications.
In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$mathrm{Mn}_{3}$]$_{2}$ dimers of $mathrm{Mn}_3$ SM
Ms, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.
Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability a
nd computational effectiveness. Most remarkably for the Hubbard model in 2-d, a highly unconventional quadruple-fermion non-Cooper-pair order parameter is discovered.
Following the discovery of the potentially very high temperature superconductivity in monolayer FeSe we investigate the doping effect of Se vacancies in these materials. We find that Se vacancies pull a vacancy centered orbital below the Fermi energy
that absorbs most of the doped electrons. Furthermore we find that the disorder induced broadening causes an effective hole doping. The surprising net result is that in terms of the band structure Se vacancies behave like hole dopants rather than electron dopants. Our results exclude Se vacancies as the origin of the large electron pockets measured by angle resolved photoemission spectroscopy.
