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

${\rm{EuTe}}{4}$ 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.

💡 Research Summary

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This paper provides a comprehensive theoretical investigation of the polar charge‑density‑wave (CDW) phenomena observed in the layered material EuTe₄, focusing on the origin of its giant thermal hysteresis and non‑volatile electric/optical switching. Using density‑functional theory (DFT) together with a tight‑binding model that faithfully reproduces the electronic structure of the two tellurium layers (a monolayer, ML‑Te, and a bilayer, BL‑Te), the authors identify a pronounced nesting feature at the wave vector q ≈ 1/3 b* in the Lindhard susceptibility. This nesting, amplified by strong electron‑phonon coupling, gives rise to three imaginary phonon modes (Q₁, Q₂, Q₃) at the same q‑point. Each mode involves a‑axis (x‑direction) polar displacements confined to either the ML‑Te or the BL‑Te layer, establishing a “layer‑selective” CDW: each Te layer can independently adopt a + or – polar distortion.

DFT structural relaxations within a 1 × 3 × 1 supercell reveal six symmetry‑inequivalent ferro‑electric CDW configurations, denoted S(±1), S(±2) and S(±3), where the sign indicates the overall polarization direction. Energy differences among these configurations are minute (≤ 1.26 meV per atom when the supercell is doubled along the out‑of‑plane direction), and the barriers for inter‑conversion are even lower (< 5.4 meV/atom). Consequently, at finite temperature the system can readily fluctuate among these states, leading to a manifold of nearly degenerate CDW patterns that break translational symmetry only along the stacking direction.

To capture the statistical mechanics of this manifold, the authors construct a one‑dimensional effective Hamiltonian. Each lattice site represents a 1 × 3 × 1 block that can occupy any of the six CDW states. The internal energy consists of a Landau‑Devonshire expansion in the local polarization (quadratic, quartic, sextic terms) plus a nearest‑neighbor coupling term proportional to the square of the polarization difference. Parameters (A, B, C, D) are extracted directly from the DFT calculations. The Helmholtz free energy adds a configurational entropy term, S_conf = −k_B ∑ n_C ln n_C, where n_C is the population of each paired configuration across neighboring sites.

Monte‑Carlo simulations of this model reveal a first‑order order‑disorder transition at a critical temperature T_C ≈ 652 K, consistent with the experimentally observed CDW transition. Below T_C the ground state S_g is an antiferroelectric stacking of S(+1) and S(−1) layers. As temperature approaches T_C, the configurational entropy sharply rises, driving the system into a metastable CDW state S_ms that contains a random mixture of the six layer‑selective configurations. The free energy drops while the entropy spikes, characteristic of a configurational‑entropy‑driven transition. When the system is cycled through heating and cooling, the populations of the ground‑state paired configuration and the “other” configurations follow distinct paths, producing a pronounced thermal hysteresis loop centered on T_C. This theoretical hysteresis quantitatively reproduces the experimentally reported resistance hysteresis spanning more than 400 K, offering a new mechanism distinct from impurity pinning, sliding, or metal‑insulator transitions traditionally invoked for CDW hysteresis.

The authors further incorporate an electric‑field coupling term (−∑ P_i·E/N) into the free energy. Simulations at T/T_C = 0.75 show that an increasing in‑plane electric field gradually reorders the mixed CDW domains, with the heating and cooling branches responding differently. This field‑induced reconfiguration provides a microscopic explanation for the observed non‑volatile electric switching: the system can be driven from one metastable configuration to another and retain the new state after the field is removed. A similar argument applies to optical excitation, where photo‑induced changes in the electron‑phonon subsystem can modify the configurational entropy and thus toggle the CDW pattern.

In summary, the paper establishes that EuTe₄ hosts a novel layer‑selective polar CDW in which multiple energetically close configurations coexist with low interconversion barriers. The giant thermal hysteresis originates from a configurational‑entropy‑driven first‑order transition that creates a metastable, translation‑symmetry‑broken CDW state. Electric and optical fields can selectively bias the configurational ensemble, enabling reversible, non‑volatile switching. These insights not only resolve longstanding questions about EuTe₄’s anomalous behavior but also suggest a general design principle for exploiting layer‑selective polar CDWs in other multilayered van‑der‑Waals systems for future optoelectronic and memory applications.