Charge density, atomic bonding and band structure of two-dimensional Sn, Sb, and Pb semimetals

Electrostatic shielding effects and binding energy shifts and topological phases of bilayer molybdenum chalcogenides

“…The potential energy surface and phase operator can be calculated as follows: [44] 33 $$$\vcenter{\openup.5em\halign{$\displaystyle{#}$\cr \left\{ \begin{matrix} {\widetilde V}_i \left( {\overrightarrow {r_{ij} } } \right){\rm{ = }}V_0 \left( {\overrightarrow {r_{ij} } } \right){\rm{e}}^{ - \mu _i r_{ij} } \cos k_1 a \hfill \\ {\widetilde V}_i \left( {\overrightarrow {r_{ij} } } \right){\rm{ = }}V_0 \left( {\overrightarrow {r_{ij} } } \right){\rm{e}}^{ - \mu _i r_{ij} } (\cos k_1 a + \cos k_2 a) \hfill \\ {\widetilde V}_i \left( {\overrightarrow {r_{ij} } } \right){\rm{ = }}V_0 \left( {\overrightarrow {r_{ij} } } \right){\rm{e}}^{ - \mu _i r_{ij} } (\cos k_1 a + \cos k_2 a{\rm{ + }}\cos k_3 a) \hfill \\ \end{matrix} \right.\hfill\cr}}$$$ …”