Controlling the Quantum Spin Hall Edge States in Two-Dimensional Transition Metal Dichalcogenides.

Two-dimensional transition metal dichalcogenides (TMDs) of Mo and W in their 1T' crystalline phase host the quantum spin Hall (QSH) insulator phase. We address the electronic properties of the QSH edge states by means of first-principles calculations performed on realistic models of edge terminations of different stoichiometries. The QSH edge states show a tendency to have complex band dispersions and coexist with topologically trivial edge states. We nevertheless identify two stable edge terminations that allow isolation of a pair of helical edge states within the band gap of TMDs, with monolayer 1T'-WSe2 being the most promising material. We also characterize the finite-size effects in the electronic structure of 1T'-WSe2 nanoribbons. Our results provide guidance to the experimental studies and possible practical applications of QSH edge states in monolayer 1T'-TMDs.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

Manipulating Topological Domain Boundaries in the Single-Layer Quantum Spin Hall Insulator 1T'-WSe2.

We report the creation and manipulation of structural phase boundaries in the single-layer quantum spin Hall insulator 1T'-WSe2 by means of scanning tunneling microscope tip pulses. We observe the formation of one-dimensional interfaces between topologically nontrivial 1T' domains having different rotational orientations, as well as induced interfaces between topologically nontrivial 1T' and topologically trivial 1H phases. Scanning tunneling spectroscopy measurements show that 1T'/1T' interface states are localized at domain boundaries, consistent with theoretically predicted unprotected interface modes that form dispersive bands in and around the energy gap of this quantum spin Hall insulator. We observe a qualitative difference in the experimental spectral line shape between topologically "unprotected" states at 1T'/1T' domain boundaries and protected states at 1T'/1H and 1T'/vacuum boundaries in single-layer WSe2.

Identifying substitutional oxygen as a prolific point defect in monolayer transition metal dichalcogenides.

Chalcogen vacancies are generally considered to be the most common point defects in transition metal dichalcogenide (TMD) semiconductors because of their low formation energy in vacuum and their frequent observation in transmission electron microscopy studies. Consequently, unexpected optical, transport, and catalytic properties in 2D-TMDs have been attributed to in-gap states associated with chalcogen vacancies, even in the absence of direct experimental evidence. Here, we combine low-temperature non-contact atomic force microscopy, scanning tunneling microscopy and spectroscopy, and state-of-the-art ab initio density functional theory and GW calculations to determine both the atomic structure and electronic properties of an abundant chalcogen-site point defect common to MoSe2 and WS2 monolayers grown by molecular beam epitaxy and chemical vapor deposition, respectively. Surprisingly, we observe no in-gap states. Our results strongly suggest that the common chalcogen defects in the described 2D-TMD semiconductors, measured in vacuum environment after gentle annealing, are oxygen substitutional defects, rather than vacancies.

Observation of topologically protected states at crystalline phase boundaries in single-layer WSe2.

Transition metal dichalcogenide materials are unique in the wide variety of structural and electronic phases they exhibit in the two-dimensional limit. Here we show how such polymorphic flexibility can be used to achieve topological states at highly ordered phase boundaries in a new quantum spin Hall insulator (QSHI), 1T'-WSe2. We observe edge states at the crystallographically aligned interface between a quantum spin Hall insulating domain of 1T'-WSe2 and a semiconducting domain of 1H-WSe2 in contiguous single layers. The QSHI nature of single-layer 1T'-WSe2 is verified using angle-resolved photoemission spectroscopy to determine band inversion around a 120 meV energy gap, as well as scanning tunneling spectroscopy to directly image edge-state formation. Using this edge-state geometry we confirm the predicted penetration depth of one-dimensional interface states into the two-dimensional bulk of a QSHI for a well-specified crystallographic direction. These interfaces create opportunities for testing predictions of the microscopic behavior of topologically protected boundary states.

Atomic scale microstructure and properties of Se-deficient two-dimensional MoSe2.

We study the atomic scale microstructure of nonstoichiometric two-dimensional (2D) transition metal dichalcogenide MoSe2-x by employing aberration-corrected high-resolution transmission electron microscopy. We show that a Se-deficit in single layers of MoSe2 grown by molecular beam epitaxy gives rise to a dense network of mirror-twin-boundaries (MTBs) decorating the 2D-grains. With the use of density functional theory calculations, we further demonstrate that MTBs are thermodynamically stable structures in Se-deficient sheets. These line defects host spatially localized states with energies close to the valence band minimum, thus giving rise to enhanced conductance along straight MTBs. However, electronic transport calculations show that the transmission of hole charge carriers across MTBs is strongly suppressed due to band bending effects. We further observe formation of MTBs during in situ removal of Se atoms by the electron beam of the microscope, thus confirming that MTBs appear due to Se-deficit, and not coalescence of individual grains during growth. At a very high local Se-deficit, the 2D sheet becomes unstable and transforms to a nanowire. Our results on Se-deficient MoSe2 suggest routes toward engineering the properties of 2D transition metal dichalcogenides by deviations from the stoichiometric composition.