Mehrshad Mehboudi

Two-dimensional disorder in black phosphorus and monochalcogenide monolayers

Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given materials melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

Strain and the optoelectronic properties of nonplanar phosphorene monolayers

Significance Phosphorene is a new 2D atomic material, and we document a drastic reduction of its electronic gap when under a conical shape. Furthermore, geometry determines the properties of 2D materials, and we introduce discrete differential geometry to study them. This geometry arises from particle/atomic positions; it is not based on a parametric continuum, and it applies across broad disciplinary lines. Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene––a new 2D atomic material––in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum.

Intrinsic Defects, Fluctuations of the Local Shape, and the Photo- Oxidation of Black Phosphorus

Black phosphorus is a monatomic semiconducting layered material that degrades exothermically in the presence of light and ambient contaminants. Its degradation dynamics remain largely unknown. Even before degradation, local-probe studies indicate non-negligible local curvature—through a nonconstant height distribution—due to the unavoidable presence of intrinsic defects. We establish that these intrinsic defects are photo-oxidation sites because they lower the chemisorption barrier of ideal black phosphorus (>10 eV and out of visible-range light excitations) right into the visible and ultraviolet range (1.6 to 6.8 eV), thus enabling photoinduced oxidation and dissociation of oxygen dimers. A full characterization of the material’s shape and of its electronic properties at the early stages of the oxidation process is presented as well. This study thus provides fundamental insights into the degradation dynamics of this novel layered material.

Quantitative chemistry and the discrete geometry of conformal atom-thin crystals.

When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional and ideal crystal structure evolves into arbitrary shapes, providing a direct and dramatic link among geometry and material properties due to the larger structural flexibility when compared to bulk three-dimensional materials. We describe methods to understand the local geometrical information of two-dimensional conformal crystals quantitatively and directly from atomic positions, even in the presence of atomistic defects. We then discuss direct relations among the discrete geometry and chemically relevant quantities--mean bond lengths, hybridization angles, and σ-π hybridization. These concepts are illustrated for carbon-based materials and ionic crystals. The pyramidalization angle turns out to be linearly proportional to the mean curvature for relevant crystalline configurations. Discrete geometry provides direct quantitative information on the potential chemistry of conformal two-dimensional crystals.

Photostrictive Two-Dimensional Materials in the Monochalcogenide Family

Photostriction is predicted for group-IV monochalcogenide monolayers, two-dimensional ferroelectrics with rectangular unit cells (the lattice vector a_{1} is larger than a_{2}) and an intrinsic dipole moment parallel to a_{1}. Photostriction is found to be related to the structural change induced by a screened electric polarization (i.e., a converse piezoelectric effect) in photoexcited electronic states with either p_{x} or p_{y} (in-plane) orbital symmetry that leads to a compression of a_{1} and a comparatively smaller increase of a_{2} for a reduced unit cell area. The structural change documented here is 10 times larger than that observed in BiFeO_{3}, making monochalcogenide monolayers an ultimate platform for this effect. This structural modification should be observable under experimentally feasible densities of photexcited carriers on samples that have been grown already, having a potential usefulness for light-induced, remote mechano-optoelectronic applications.

Structural Phase Transition and Material Properties of Few-Layer Monochalcogenides

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a critical temperature T_{c} well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above T_{c}. As the in-plane lattice transforms from a rectangle into a square at T_{c}, the electronic, spin, optical, and piezoelectric properties dramatically depart from earlier predictions. Indeed, the Y and X points in the Brillouin zone become effectively equivalent at T_{c}, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at T_{c}. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement is drawn by theoretical predictions of giant piezoelectricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about 3×10^{-12}  C/K m here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenides.

Layered material GeSe and vertical GeSe/MoS2 p-n heterojunctions

Group-IV monochalcogenides are emerging as a new class of layered materials beyond graphene, transition metal dichalcogenides (TMDCs), and black phosphorus (BP). In this paper, we report experimental and theoretical investigations of the band structure and transport properties of GeSe and its heterostructures. We find that GeSe exhibits a markedly anisotropic electronic transport, with maximum conductance along the armchair direction. Density functional theory calculations reveal that the effective mass is 2.7 times larger along the zigzag direction than the armchair direction; this mass anisotropy explains the observed anisotropic conductance. The crystallographic orientation of GeSe is confirmed by angleresolved polarized Raman measurements, which are further supported by calculated Raman tensors for the orthorhombic structure. Novel GeSe/MoS2 p-n heterojunctions are fabricated, combining the natural p-type doping in GeSe and n-type doping in MoS2. The temperature dependence of the measured junction current reveals that GeSe and MoS2 have a type-II band alignment with a conduction band offset of ∼0.234 eV. The anisotropic conductance of GeSe may enable the development of new electronic and optoelectronic devices, such as high-efficiency thermoelectric devices and plasmonic devices with resonance frequency continuously tunable through light polarization direction. The unique GeSe/MoS2 p-n junctions with type-II alignment may become essential building blocks of vertical tunneling field-effect transistors for low-power applications. The novel p-type layered material GeSe can also be combined with n-type TMDCs to form heterogeneous complementary metal oxide semiconductor (CMOS) circuits.