Two dimensional materials including graphene, silicene, MoS2 and so forth represent ideal materials composed of a single layer of atoms organized in a lattice form. Their unique geometry and intriguing mechanical and thermal properties make them perfect candidates for nano scale engineering applications. The robustness of the materials, especially those with defects is important to prevent their catastrophic failure and contribute to their durability in usage. Here we combine both large-scale molecular dynamics simulations based on reactive force fields and experiments via transmission electron microscopy to investigate their fracture behavior under extreme mechanical loading conditions. We focus on how defects and grain boundaries in 2D materials affect the critical conditions and the dynamics process of their fracture. Our results reveal that certain forms of atomic defects and grain boundaries are beneficial to enhance the mechanical strength of 2D materials that are subjected to cracks. For example, we find that poly-crystalline graphene under fracture releases up to 50% more energy than the pristine graphene. We find that grain boundaries increase the critical energy release rate to fracture by reducing stress concentration and making branches near the crack tip. We find atomic defects can cause crack deflections during crack propagation, effectively extending the crack length during propagation and thus increase the energy dissipation. Together, these molecular irregularities taking place at the atomic scale level can significantly affect the lattice characteristics of the 2D materials at larger scale levels and thereafter enhance their fracture toughness, making its crack propagation different from pristine ones, and such a mechanism explains the reduced crack propagation speed by adding vacancies as what is seen in experiments.

The optical excitations in semiconductors are substantially influenced by electron-hole interactions resulting in formation of excitons. Although the exciton binding energies in the bulk are much smaller that the fundamental band gaps, the excitonic effects in 2D materials are significantly amplified due to combined effect of quantum confinement and non-local screening of electron-hole interactions in two dimensions. An effective mass theory of 2D excitons, which takes into account the combined effect of the anisotropy and non-local 2D screening, is used to systematically investigate the variation of monolayer exciton binding energies E_x across a representative set of layered chalcogenides, both isotropic, such as MoTe₂, MoSe₂, WSe2, and WS₂, and anisotropic including phosphorene, TiS₃, ReS₂, and SnSe₂. The markedly different values of E_x are correlated with corresponding variations in atomic polarizabilities of constituent atoms.

A recent addition to low-dimensional materials are monolayer transition metal dichalcogenides (TMDs), such as WSe₂, with an atomically thin, honeycomb lattice and optical band gaps. In addition to spin, charge carriers in TMDs exhibit a “valley” degree of freedom which can be optically addressed using circularly polarized light, opening up exciting possibilities for “valleytronics". Another curious aspect of TMDs lies in the non-trivial geometry of their band structure which gives rise to equal but opposite Berry curvature, an effective magnetic field in the momentum space. Owing to unusually strong Coulomb interactions in truly 2D limit, optical spectra of monolayer TMDs is dominated by tightly bound excitons which are expected to strongly couple to light and form stable polaritons - half light, half matter excitations.

In this talk, I will begin by presenting our recent results on valley Zeeman effect, where in analogy to spins, valleys shift in energy with magnetic field. Next, I will discuss our theoretical results on how the non-trivial geometry of Bloch bands modifies the excitonic fine structure of TMDs resulting in an orbital Zeeman effect in reciprocal space and a Lamb-like shift of levels. Finally, I will present our recent results on the observation of microcavity polaritons confirming the strong light-matter interactions in these materials. The presence of valley degree of freedom, non-trivial geometry of bands, and the possibility of introducing non-linearities in form of quantum emitters makes polaritons in TMDs particularly appealing for studying correlated many-body physics and topological states of matter.

[1] C.D. Cress, et al. ACS Nano 10, 3714 (2016).

[2] A.L. Friedman, et al. Phys. Rev. B, 93 161409(R) (2016).

We utilize a combination of X-ray photoelectron spectroscopy, transport measurements and optical as well as acoustic excitation to study the impact of the formation of metal contacts to transition metal dichalcogenide films on the electronic structure of the films. Photoelectron spectroscopy permits us to follow the formation of a Schottky-like barriers with increasing metal film thickness on the Angstrom scale. We utilize core level spectroscopy to indicate the evolution of the MoS₂ valence band during metal deposition. Our findings indicate that single layer MoS₂ films adopt the character of the metal (Fermi-level pinning) resulting in a Fermi-level position in the MoS₂ semiconducting gap that is – depending on the metal work function –indicative of a p-type semiconductor, even though the native carriers in an MoS₂ film are electrons. As a consequence, metal-TMD-metal junctions may best be understood as p-n-p junctions. Numerous ancillary measurements support this hypothesis.

Layered transition metal dichalcogenides (TMDs) are ideal systems for exploring the effects of dimensionality on correlated electronic phases such as charge density wave (CDW) order and superconductivity. In bulk NbSe₂ a CDW sets in at T_CDW = 33 K and superconductivity sets in at T_c = 7.2 K. Below T_c these electronic states coexist but their microscopic formation mechanisms remain controversial. In this tal I will present the electronic characterization study of a single 2D layer of NbSe₂ by means of low temperature scanning tunneling microscopy/spectroscopy (STM/STS), angle-resolved photoemission spectroscopy (ARPES), and electrical transport measurements (1). I will show that 3x3 CDW order in NbSe₂ remains intact in 2D. Superconductivity also still remains in the 2D limit, but its onset temperature is depressed to 1.9 K. Our STS measurements at 5 K reveal a CDW gap of Δ = 4 meV at the Fermi energy, which is accessible via STS due to the removal of bands crossing the Fermi level for a single layer. Our observations are consistent with the simplified (compared to bulk) electronic structure of single-layer NbSe₂, thus providing insight into CDW formation and superconductivity in this model strongly-correlated system. Furthermore I will show that CDW order is also present in 2D semiconducting TMDs around 1D mirror twin boundaries (2).

(1) M. M. Ugeda, et al., Nature Physics 12, 92 (2016).

(2) S. Barja, et al., Nature Physics, in press (2016).