Multiple Layer-Selective Polar Charge Density Waves in ${\rm{EuTe}}_{4}$

${\rm{EuTe}}_{4}$ is a polar charge density wave (CDW) material, with giant thermal hysteresis and non-volatile state switching under electric and optical fields, attracting great attention in recent years. However, the in-depth understanding of these anomalous phenomena remains elusive. Herein, via first-principles calculations, we reveal that the polar CDW state in ${\rm{EuTe}}_{4}$ hosts a novel layer-selective nature, wherein multiple energetically close CDW configurations coexist and exhibit low interconversion energy barriers. Monte Carlo simulations indicate that the giant thermal hysteresis in ${\rm{EuTe}}_{4}$ originates from a phase transition mainly driven by the change of configurational entropy, around which the material hosts a metastable CDW state characterized by diverse local polar configurations breaking the out-of-plane translational symmetry. The configurational composition of this metastable CDW state can be effectively controlled by electric and optical fields, thereby enabling non-volatile state switching. Our theoretical findings align well with recent experimental observations in ${\rm{EuTe}}_{4}$ and pave the way for exploring the emerging phenomena and applications of polar CDW in multilayered systems.