Valley Hall effect in graphene-like SnX (X=Si, Ge) buckled monolayers with high charge carrier mobility and low lattice thermal conductivity

A systematic analysis of the electronic and thermal properties of two semiconducting monolayers, SnSi and SnGe, is conducted through the lens of density functional theory. Unlike centrosymmetric graphene, these two monolayers are noncentrosymmetric and buckled in the structure; however, their band dispersion resembles that of graphene with a finite small band gap occurring at the $K$ point of the Brillouin zone. Unlike transition metal dichalcogenide (TMDC) monolayers, the band edges in the studied semiconducting monolayers are devoid of $d$ orbitals and contain $s$ and $p$ orbitals, and thus, the valley spin splitting occurring in these semiconductors is a nontrivial topological effect originating from broken inversion symmetry in the crystal structure, as observed earlier in bilayer graphene or graphene-based van der Waals heterostructures. The electronic properties are found to be tunable via external perturbations like an electric field and biaxial strain. These monolayers are highly flexible, as indicated by the small value of Young's modulus, $<50\phantom{\rule{0.28em}{0ex}}\mathrm{N}/\mathrm{m}$. The charge carrier mobility is calculated within the Boltzmann transport equation and found to be $\ensuremath{\sim}1000\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.28em}{0ex}}{\mathrm{V}}^{\ensuremath{-}}1\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The phonon dynamics study indicates a very low value of lattice thermal conductivity at room temperature (i.e., ${\ensuremath{\kappa}}_{l}<1.5\phantom{\rule{0.28em}{0ex}}\mathrm{W}\phantom{\rule{0.28em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.28em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$), which arises from the domination of Umklapp scattering, small group velocity, and low Debye temperature. Such a low value of ${\ensuremath{\kappa}}_{l}$ will facilitate better thermal control than TMDCs or graphene-based devices. In this paper, we indicate that the inherent properties of SnSi and SnGe monolayers, such as valley contrasting properties, high charge carrier mobility, low lattice thermal conductivity, and mechanical flexibility, surpass that of well-known TMDCs (${\mathrm{MoS}}_{2}, {\mathrm{WS}}_{2}$) and boron pnictides (BP, BAs, BSb), thereby motivating their synthesis.