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

Abstract

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

Figures (4)

• Figure 1: Multiple layer-selective polar CDW configurations in ${\rm{EuTe}}_{4}$. (a) Crystal structure of non-CDW ${\rm{EuTe}}_{4}$ in $Pmmn$ symmetry, showing relatively weak couplings between Te layers. (b) Fermi surface of non-CDW ${\rm{EuTe}}_{4}$ from tight-binding model. (c) Lindhard function corresponding to (b), exhibiting a dominant peak around $\boldsymbol{q} = \frac{1}{3}\boldsymbol{b^*}$. (d) Schematics for the imaginary phonons $Q_{1,2,3}$ at $\boldsymbol{q} = \frac{1}{3}\boldsymbol{b^*}$ (left) and the three-layer CDW representations $[\nu_{1}\;\nu_{2}\;\nu_{3}]$ (right), where $\nu_{1,2,3}=\pm$ describes the polar order of each Te layer. (e) Three nonequivalent $1\times3\times1$ CDW configurations with overall positive polarization: $S(+1)$, $S(+2)$, and $S(+3)$. Their counterparts with negative polarization are $S(-1) = [---]$, $S(-2) = [-+-]$, and $S(-3) = [--+]=[+--]$, respectively.
• Figure 2: Framework for understanding ${\rm{EuTe}}_{4}$-like systems. (a) Multiple layer-selective polar CDW configurations with low interconversion energy barriers. (b) Schematic for the effective model, where each site hosts one $1\times3\times1$ CDW configuration among $S(\pm1)$, $S(\pm2)$, and $S(\pm3)$. (c) Schematics for the underlying order-disorder physics (left) and non-volatile state switching (right). The balls depict various possible paired configurations, while fan areas show their populations in the metastable CDW state.
• Figure 3: Thermal hysteresis and electrical state control. (a) Temperature-dependent Helmholtz free energy $H(\mathbf{S})$ (red) and configurational entropy $S_{\mathrm{config}}$ (blue), obtained from average-mode MC simulations SI. Here, the temperature ($T$) is normalized by critical temperature ($T_{\mathrm{C}}$). (b) Population ratios of the ground-state paired configuration ($S(+1)$+$S(-1)$) versus other configurations ("Others") upon heating and (then) cooling, obtained from heating-cooling-mode MC simulations SI with a sweep rate of $|\delta(T/T_{\mathrm{C}})| = 5.0\times 10^{-3}$. (c) Population ratios of paired configurations and (d) polarization under a $x$-directional electric field, obtained from average-mode MC simulations SI and initialized from the heating and cooling branches of (b) at $T/T_{\mathrm{C}} = 0.75$. In (b-d), the curves are smoothed to reduce fluctuations.
• Figure 4: Optical state control. (a) MC-simulated evolution of $H(\mathbf{S})$ (upper) under a Gaussian heat pulse with amplitude of 0.25 (bottom). (b) and (c) display the results under pulse amplitudes of 1.75 and 4, respectively. In (a-c), the curves are smoothed and are initialized from the heating and cooling branches of Fig. \ref{['fig3']}(b) at $T/T_{\mathrm{C}} = 0.75$. FS$\ast$ denote the final states, with their $H(\mathbf{S})$ shown in parentheses.