Collective Electrostatics and Band Alignment in Janus MoSTe nanotubes

Abstract

In this work, we investigate the collective electrostatic effects of one-dimensional (1D) Janus MoSTe nanotubes and their impacts on the band alignment of nanotube heterostructures. Using first-principles calculations based on Density Functional Theory, we find that the Janus nanotube generates a large and uniform electrostatic potential of over 1.3 V within the nanotube pores, which is accumulative for double wall nanotubes. We develop an analytical model to provide a quantitative understanding of the electrostatic potential and its dependence on the quadrupole moment and nanotube radius. For double wall MoSTe nanotube, we find a substantial band edge shift of about 1.0 eV for the inner tube originated from the electrostatic effects, leading to a type-II band alignment. These results demonstrate that the electrostatic effects of 1D nanotubes can be used to tune the electronic properties and band alignment of 1D nanotube heterostructures for optoelectronic and catalytic applications.

Figures (3)

• Figure 1: The atomic structure (a) and real-space electrostatic potential at the $z=1.0$ Å plane for (b) SW MoSTe nanotube ($n = 14$), and (d) DW MoSTe nanotube. (c) Electrostatic potential of the SW MoSTe nanotubes along the $y = 0$ Å line as labeled in (b). All potentials are referenced to the vacuum potential. $z$-axis is along the tube axis. The electrostatic potential in this work corresponds to the potential experienced by an electron.
• Figure 2: The quadrupole moment (a), and the electrostatic potential from DFT ($V_{DFT}$) and from Eq. \ref{['eq:V2']} ($V_{eq2}$) (b). Here, $Q$ and $V_{eq2}$ are computed using the radius-dependent effective charges as shown in Table S1. For comparison, the quadrupole moment and electrostatic potential for all nanotubes are also calculated using a common charge $q = 0.0298 e$, which are denoted as $Q'$ in (a) and $V'_{eq2}$ in (b), respectively. $q = 0.0298 e$ is the effective charge for 2D MoSTe monolayer. The inset in (a) is the nanotube structure with Mo (white), Te (blue), and S (red) atoms, with dipoles pointing from S to Te. The black dashed line connects the first and last $Q$ values. All the other dashed lines are just connecting the data points used as aid of the eye. For comparison, the electrostatic potential difference between the two sides of the 2D MoSTe monolayer (Fig. S7) is included in (b), assuming it’s a tube with infinite radius.
• Figure 3: (a) Radially-resolved local density of states (LDOS) of the DW MoSTe, where zero is the center of the nanotube. The dashed horizontal lines show the conduction band minimum (CBM) and valence band maximum (VBM). (b) The real-space CBM and VBM wavefunctions (charge density isosurfaces) of the double wall MoSTe view along the tube axis. The isosurface shown in (b) is the squared modulus of the wavefunction. The isosurface value of the VBM is $2.2\times 10^{-6}$$e/$Å$^3$, and that of the CBM is $1.6\times 10^{-6}$$e/$Å$^3$. (c) VBM and CBM band energies for the $n=6$ (red) and $n=14$ (blue) SW nanotubes and that in the DW nanotube. All energies are referenced to the vacuum energy.