A piezoelectric quantum spin Hall insulator VCClBr monolayer with a pure out-of-plane piezoelectric response

The combination of piezoelectricity with a nontrivial topological insulating phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall insulators (PQSHI), is intriguing for exploring novel topological states toward the development of high-speed and dissipationless electronic devices. In this work, we predict a PQSHI Janus monolayer VCClBr constructed from VCCl₂, which is dynamically, mechanically and thermally stable. In the absence of spin orbital coupling (SOC), VCClBr is a narrow gap semiconductor with a gap value of 57 meV, which is different from Dirac semimetal VCCl₂. The gap of VCClBr is due to a built-in electric field caused by asymmetrical upper and lower atomic layers, which is further confirmed by the external-electric-field induced gap in VCCl₂. When including SOC, the gap of VCClBr is increased to 76 meV, which is larger than the thermal energy of room temperature (25 meV). The VCClBr is a 2D topological insulator (TI), which is confirmed by Z₂ topological invariant and nontrivial one-dimensional edge states. It is proved that the nontrivial topological properties of VCClBr are robust against strain (biaxial and uniaxial cases) and external electric fields. Due to broken horizontal mirror symmetry, only an out-of-plane piezoelectric response can be observed, when a biaxial or uniaxial in-plane strain is applied. The predicted piezoelectric strain coefficients d₃₁ and d₃₂ are -0.425 pm V^-1 and -0.219 pm V^-1, respectively, and they are higher than or compared with those of many 2D materials. Finally, Janus monolayer VCFBr and VCFCl (dynamically unstable) are also constructed, and they are still PQSHIs. Moreover, the d₃₁ and d₃₂ of VCFBr and VCFCl are higher than those of VCClBr, and the d₃₁ (absolute value) of VCFBr is larger than one. According to out-of-plane piezoelectric coefficients of VCXY (X ≠ Y = F, Cl and Br), CrX_1.5Y_1.5 (X = F, Cl and Br; Y = I) and NiXY (X ≠ Y = Cl, Br and I), it is concluded that the size of the out-of-plane piezoelectric coefficient has a positive relation with the electronegativity difference of X and Y atoms. Our studies enrich the diversity of Janus 2D materials, and open a new avenue in the search for PQSHI with a large out-of-plane piezoelectric response, which provides a potential platform in nanoelectronics.