From first-principles calculations, we make a comparison study of the structural, electronic, elastic, dielectric and dynamical properties of Zr-based monolayer dioxides (ZrO₂) and dichalcogenides (ZrX₂; X = S, Se or Te) as well as their Janus structures (ZrXY; X, Y = O, S, Se or Te, $\text{Y}\ne \text{X}$). Regardless the constituents, the bond length between Zr⁺⁴ cation and its nearest-neighbor X⁻² anions d_Zr-X equals the sum of ionic radii of Zr⁺⁴ and X⁻² ions (X = O, S, Se or Te) reflects a p-d hybridized ionic bond instead of a sp² hybridized covalent bond in graphene. For six O-free monolayers ZrS₂, ZrSe₂, ZrTe₂, ZrSSe, ZrSTe, ZrSeTe, the conduction band minimum (CBM) and valence band maximum (VBM) are located at the M and Γ points, respectively, while for four O-containing monolayers ZrO₂, ZrOS, ZrOSe, ZrOTe, the CBM and VBM are located at K (except ZrOSe between MΓ) and Γ (except ZrO₂ between ΓK) points. The decreasing indirect band gaps of semiconductor 4.41, 1.88, 1.06 eV and 1.19, 0.76, 0.50 eV are obtained for three Te-free and O-containing monolayers ZrO₂, ZrOS, ZrOSe and three Te-free and O-free monolayers ZrS₂, ZrSSe, ZrSe₂ respectively due to increasing the sum of d_Zr-X and d_Zr-Y, while the metal characteristics are obtained for four Te-containing monolayers ZrTe₂, ZrOTe, ZrSTe, ZrSeTe due to the larger radius of 2.21 Å for Te⁻² anion. The large dielectric permittivity, mechanical stability and dynamical stability show three Te-free and O-free monolayers ZrSSe, ZrS2 and ZrSe2 are the promising dielectric materials.

从第一性原理计算，我们对基于 Zr 的单层二氧化物 (ZrO ₂ ) 和二硫属化物 (ZrX ₂ ; X = S、Se 或 Te)的结构、电子、弹性、介电和动力学特性进行了比较研究，以及他们的 Janus 结构 (ZrXY; X, Y = O, S, Se 或 Te,$\text{是}\ne \text{X}$）。不管成分如何，Zr ⁺⁴阳离子与其最近邻 X ^-2阴离子 d _Zr-X之间的键长等于 Zr ⁺⁴和 X ^-2离子的离子半径之和（X = O、S、Se 或 Te ) 反映了 pd 杂化离子键而不是石墨烯中的 sp ²杂化共价键。对于六个无 O 单层 ZrS ₂、ZrSe ₂、ZrTe ₂ 、ZrSSe、ZrSTe、ZrSeTe，导带最小值 (CBM) 和价带最大值 (VBM) 分别位于 M 和 Γ 点，而对于四个 O -含单分子层ZrO ₂、ZrOS、ZrOSe、ZrOTe，CBM 和 VBM 位于 K（MΓ 之间的 ZrOSe 除外）和 Γ（ΓK 之间的 ZrO ₂除外）点。对于三个不含 Te 和 O 的单层 ZrO ₂、ZrOS、ZrOSe 和三个不含 Te 和 O 的单层 ZrS ₂获得了半导体 4.41、1.88、1.06 eV 和 1.19、0.76、0.50 eV 的间接带隙减小, ZrSSe, ZrSe ₂分别是由于增加了 d _Zr-X和 d _Zr-Y的总和，而四个含 Te 单层 ZrTe ₂ , ZrOTe, ZrSTe, ZrSeTe 由于 2.21 Å 的较大半径获得了金属特性对于 Te ^-2阴离子。大的介电常数、机械稳定性和动态稳定性表明三种不含 Te 和 O 的单层 ZrSSe、ZrS2 和 ZrSe2 是很有前途的介电材料。