Engineering Weyl Phases and Nonlinear Hall Effects in T_{d}-MoTe_{2}

MoTe_{2} has recently attracted much attention due to the observation of pressure-induced superconductivity, exotic topological phase transitions, and nonlinear quantum effects. However, there has been debate on the intriguing structural phase transitions among various observed phases of MoTe_{2} and their connection to the underlying topological electronic properties. In this work, by means of density-functional theory calculations, we investigate the structural phase transition between the polar T_{d} and nonpolar 1T^{'} phases of MoTe_{2} in reference to a hypothetical high-symmetry T_{0} phase that exhibits higher-order topological features. In the T_{d} phase we obtain a total of 12 Weyl points, which can be created/annihilated, dynamically manipulated, and switched by tuning a polar phonon mode. We also report the existence of a tunable nonlinear Hall effect in T_{d}-MoTe_{2} and propose the use of this effect as a probe for the detection of polarity orientation in polar (semi)metals. By studying the role of dimensionality, we identify a configuration in which a nonlinear surface response current emerges. The potential technological applications of the tunable Weyl phase and the nonlinear Hall effect are discussed.