Bandgap Modulated by Electronic Superlattice in Blue Phosphorene Jincheng Zhuang,,,# Chen Liu,,# Qian Gao, Yani Liu,, Haifeng Feng,, Xun Xu, Jiaou Wang, Shi Xue Dou,, Zhenpeng Hu, and Yi Du*,, Institute for Superconducting and Electronic Materials (ISEM), Australian Institute for Innovative Materials (AIIM), University of Wollongong, Wollongong, NSW 2525, Australia BUAA-UOW Joint Centre, Department of Physics, Beihang University, Haidian District, Beijing 100091, China Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China School of Physics, Nankai University, Tianjin, 300071, China * To whom correspondence should be addressed: yi_du@uow.edu.au
S1. The initial growth dynamics of phosphorene on Au(111). Figure S1. STM images of sub-monolayer phosphorene with (a) 0.1 monolayer (ML) (V bias = 2.0 V, I = 50 pa, 100 nm 100 nm), (b) 0.4 ML (V bias = 2.0 V, I = 30 pa, 100 nm 100 nm), and (c) 0.6 ML (V bias = 3.0 V, I = 30 pa, 100 nm 100 nm). The red Ps label the positions of phosphorene. The close-packed Au(111) surface shows a 22 3 reconstruction with a long-range herringbone pattern on the scale of a few hundred nanometers. It could be clearly identified that the phosphorene prefers to emerge at the terrace edge of the Au(111) substrate.
S2. Ordered and reversible P adatoms on 4 4 phosphorene surface. Figure S2 (a) STM image of P adatoms on monolayer phosphorene (V bias = 100 mv, I = 30 pa, 30nm 30 nm). (b) The clean 4 4 phosphorene surface is fully recovered after annealing the surface at 300 C V bias = 2.0 V, I = 30 pa, 30nm 30 nm).
S3. Band dispersion of bare Au(111) and P/Au(111). Figure S3. (a) and (b) ARPES spectra of bare Au(111) along the - direction. The Shockley surface state (SS) and the sp band of Au(111) are indicated. (c) ARPES spectra of 4 4 phosphorene on the Au(111) surface along the S -K S -K S - S direction. The blue R with the arrows stands for the replicas of the sp band of Au(111). The calculated Fermi velocities for the sp band of Au(111) and the replicas are close to each other with values around 1.0 10 6 m/s.
S4. Carrier effective masses, deformation potentials, elastic moduli, and carrier mobilities. Figure S4. Structural model of 4 4 phosphorene with strain. The X and Y are correlated with the armchair direction and zigzag direction, respectively. Figure S5 (a) Deformation potential constants and (b) elastic modulus along armchair direction, based on the structural model in Figure S4. (c) Deformation potential constants and (d) elastic modulus along the zigzag direction, based on the structural model in Figure S4.
Figure S6. Structural model of 4 4 phosphorene without strain. The X and Y are correlated with the armchair direction and zigzag direction, respectively. Figure S7. (a) Deformation potential constants and (b) elastic modulus along the armchair direction based on the structural model in Figure S6. (c) Deformation potential constants and (d) elastic modulus along the zigzag direction based on the structural model in Figure S6.
Table S1. Calculated carrier effective masses, deformation potentials, elastic moduli, and carrier mobilities along the x and y direction in 4 4 phosphorene with different lattice constants at T = 300 K. The room temperature carrier mobilities of phosphorene on Au(111) based on the so-called acoustic phonon limited approach are determined by using the following expression 1,2 : (1) Where e is the electron charge, is the reduced Planck s constant, is the effective mass along the transport direction, and is the average effective mass determined by. The x and y are correlated with the armchair direction and the zigzag direction, respectively. The term Δ / Δ / represents the deformation potential constant of the valence-band minimum for holes or the conduction-band maximum for electrons along the transport direction, where Δ is the energy change of the i th band under compression and dilatation from the equilibrium distance by a distance of Δ along the transport direction. The term is the elastic modulus of the longitudinal strain in the propagation directions (both x and y) of the longitudinal acoustic wave, derived from / Δ / /2, where is the total energy and is the lattice volume at equilibrium for a 2D system. We calculated the longitudinal strain from -1.0% to 1.0% with a step size of 0.5% to fit the values for and, and then to obtain the value of the carrier mobility. 1. Qiao, J. S.; Kong, X. H.; Hu, Z. X.; Yang, F.; Ji, W. High-Mobility Transport Anisotropy and Linear Dichroism in Few-Layer Black Phosphorus. Nat. Commun. 2014, 5, 4475. 2. Fei, R.; Faghaninia, A.; Soklaski, R.; Yan, J. A.; Lo, C.; Yang, L.; Enhanced Thermoelectric Efficiency via
Orthogonal Electrical and Thermal Conductances in Phosphorene. Nano Lett. 2014, 14, 6393-6399.