RESUMO
The rare-earth telluride compound EuTe4 exhibits a charge density wave (CDW) and an unconventional thermal hysteresis transition. Herein, we report a comprehensive study of the CDW states in EuTe4 by using low-temperature scanning tunneling microscopy. Two types of charge orders are observed at 4 K, including a newly discovered spindle-shaped pattern and a typical stripe-like pattern. As an exotic charge order, the spindle-shaped CDW is off-axis and barely visible at 77 K, indicating that it is a hidden order developed at low temperature. Based on our first-principles calculations, we reveal the origins of the observed electronic instabilities. The spindle-shaped charge order stems from a subsequent transition based on the stripe-like CDW phase. Our work demonstrates that the competition and cooperation between multiple charge orders can generate exotic quantum phases.
RESUMO
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here, a general framework is proposed to perform density functional perturbation theory (DFPT) calculations by neural networks, greatly improving the computational efficiency. Automatic differentiation is applied on neural networks, facilitating accurate computation of derivatives. High efficiency and good accuracy of the approach are demonstrated by studying electron-phonon coupling and related physical quantities. This work brings deep-learning density functional theory and DFPT into a unified framework, creating opportunities for developing ab initio artificial intelligence.