Layer-Dependent Pressure Effect on the Electronic Structure of 2D Black Phosphorus

Through infrared spectroscopy, we systematically study the pressure effect on electronic structures of few-layer black phosphorus (BP) with layer number ranging from 2 to 13. We reveal that the pressure-induced shift of optical transitions exhibits strong layer dependence. In sharp contrast to the bulk counterpart which undergoes a semiconductor to semimetal transition under $\sim 1.8\mathrm{GPa}$, the band gap of 2 L increases with increasing pressure until beyond 2 GPa. Meanwhile, for a sample with a given layer number, the pressure-induced shift also differs for transitions with different indices. Through the tight-binding model in conjunction with a Morse potential for the interlayer coupling, this layer- and transition-index-dependent pressure effect can be fully accounted. Our study paves a way for versatile van der Waals engineering of two-dimensional BP.

Figure 1

Pressure effect on electronic structures of few-layer BP. (a) Schematic illustration of the experimental setup for band structure engineering in few-layer BP through diamond anvil cell (DAC). (b) Optical image of a BP flake which contains 3 and 6 L in DAC. The region inside the red box is where the IR light shines. Scale bar is $20\mu \mathrm{m}$. (c) Schematic illustration of optical transitions between different subbands in bilayer BP. (d) Infrared extinction spectra of sample shown in Fig. 1 under different pressure. The spectra are offset vertically for clarity. (e) Peak position versus pressure for $E_{11}$ of 3 L, $E_{11}$ and $E_{22}$ of 6 L, and band gap of a bulk BP from top to bottom, respectively. Dashed lines are a guide to the eye.

Figure 2

Pressure effect on electronic structures of 11 L BP. (a) Infrared extinction spectra of a 11 L BP under different pressure. Silicone oil has strong absorption between 0.35 to 0.37 eV (shaded region). The spectra are offset vertically for clarity. (b) Peak position versus pressure for $E_{11}$, $E_{22}$, and $E_{33}$ of 11 L.

Figure 3

Pressure effect on the interlayer interaction of few-layer BP. (a) Schematic illustration for the evolution of the atomic structure of trilayer BP with pressure. (b) The relative changes of $\gamma$ versus pressure. Dots are data extracted from $E_{22}\text{−}{E}_{11}$ of 6 L, 7 L, 9 L, and $E_{33}\text{−}{E}_{22}$ of 11 L. The solid curve is the fitting based on Eq. (3).

Figure 4

The relative change of optical band gaps of BP versus pressure. Dots are experiment data and solid curves are the fitting curves. The thickness of the thin film and bulk shown in the figure are $\sim 50\mathrm{nm}$ and $1\mu \mathrm{m}$, respectively.