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Energy bandgap largely determines the optical and electronic properties of a semiconductor. Variable bandgap therefore makes versatile functionality possible in a single material. In layered material black phosphorus, the bandgap can be modulated by the number of layers; as a result, few-layer black phosphorus has discrete bandgap values that are relevant for opto-electronic applications in the spectral range from red, in monolayer, to mid-infrared in the bulk limit. Here, we further demonstrate continuous bandgap modulation by mechanical strain applied through flexible substrates. The strain-modulated bandgap significantly alters the charge transport in black phosphorus at room temperature; we for the first time observe a large piezo-resistive effect in black phosphorus field-effect transistors (FETs). The effect opens up opportunities for future development of electro-mechanical transducers based on black phosphorus, and we demonstrate strain gauges constructed from black phosphorus thin crystals.

Phosphorene, a single atomic layer of black phosphorus, has recently emerged as a new twodimensional (2D) material that holds promise for electronic and photonic technology. Here we experimentally demonstrate that the electronic structure of few-layer phosphorene varies significantly with the number of layers, in good agreement with theoretical predictions. The interband optical transitions cover a wide, technologically important spectrum range from visible to mid-infrared. In addition, we observe strong photoluminescence in few-layer phosphorene at energies that match well with the absorption edge, indicating they are direct bandgap semiconductors. The strongly layer-dependent electronic structure of phosphorene, in combination with its high electrical mobility, gives it distinct advantages over other twodimensional materials in electronic and opto-electronic applications., Comment: 17 pages, 4 figures, Likai Li, Jonghwan Kim, Chenhao Jin contributed equally to this work

Development of new, high quality functional materials has been at the forefront of condensed matter research. The recent advent of two-dimensional black phosphorus has greatly enriched the material base of two-dimensional electron systems. Significant progress has been made to achieve high mobility black phosphorus two-dimensional electron gas (2DEG) since the development of the first black phosphorus field-effect transistors (FETs)$^{1-4}$. Here, we reach a milestone in developing high quality black phosphorus 2DEG - the observation of integer quantum Hall (QH) effect. We achieve high quality by embedding the black phosphorus 2DEG in a van der Waals heterostructure close to a graphite back gate; the graphite gate screens the impurity potential in the 2DEG, and brings the carrier Hall mobility up to 6000 $cm^{2}V^{-1}s^{-1}$. The exceptional mobility enabled us, for the first time, to observe QH effect, and to gain important information on the energetics of the spin-split Landau levels in black phosphorus. Our results set the stage for further study on quantum transport and device application in the ultrahigh mobility regime.

Two-dimensional electron gases (2DEG) have been an important source of experimental discovery and conceptual development in condensed matter physics for decades. When combined with the unique electronic properties of two-dimensional (2D) crystals, rich new physical phenomena can be probed at the quantum level. Here, we create a new 2DEG in black phosphorus, a recent member of the two-dimensional atomic crystal family, using a gate electric field. We achieve high carrier mobility in black phosphorus 2DEG by placing it on a hexagonal boron nitride substrate (h-BN). This allows us, for the first time, to observe quantum oscillations in this material. The temperature and magnetic field dependence of the oscillations yields crucial information about the system, such as cyclotron mass and lifetime of its charge carriers. Our results, coupled with the fact that black phosphorus possesses anisotropic energy bands with a tunable, direct bandgap, distinguishes black phosphorus 2DEG as a novel system with unique electronic and optoelectronic properties.

Two-dimensional crystals have emerged as a new class of materials with novel properties that may impact future technologies. Experimentally identifying and characterizing new functional two-dimensional materials in the vast material pool is a tremendous challenge, and at the same time potentially rewarding. In this work, we succeed in fabricating field-effect transistors based on few-layer black phosphorus crystals with thickness down to a few nanometers. Drain current modulation on the order of 10E5 is achieved in samples thinner than 7.5 nm at room temperature, with well-developed current saturation in the IV characteristics, both are important for reliable transistor performance of the device. Sample mobility is also found to be thickness dependent, with the highest value up to ~ 1000 cm2/Vs obtained at thickness ~ 10 nm. Our results demonstrate the potential of black phosphorus thin crystal as a new two-dimensional material for future applications in nano-electronic devices., Comment: 23 pages, 4 figures