Extreme anharmonicity and thermal contraction of 1D wires

TL;DR

The paper investigates the thermodynamics of exfoliable one-dimensional wires CuC$_2$, TaSe$_3$, and AuSe$_2$, focusing on strong anharmonic effects and extreme negative thermal expansion. It employs the stochastic self-consistent harmonic approximation (SSCHA) enhanced with machine-learning interatomic potentials to capture quantum and temperature-driven phonon fluctuations, enabling accurate calculations of $C_V$ and the linear expansion coefficient $\alpha$ across temperatures. Key findings include pronounced anharmonicity and colossal negative $\alpha$ values (contractions) for CuC$_2$ and AuSe$_2$, with TaSe$_3$ showing a high-temperature instability via imaginary phonons around $T \approx 650$ K, and a substantial temperature-driven reduction of band gaps in AuSe$_2$. The results suggest these 1D wires share general thermodynamic features driven by soft transverse modes, underscoring the importance of anharmonicity in low-dimensional materials and informing design principles for nanoelectronic applications.

Abstract

Ultrathin nanowires could play a central role in next-generation downscaled electronics. Here, we explore some of the most promising candidates identified from previous high-throughput screening: CuC$_2$, TaSe$_3$, and AuSe$_2$, to gain insight into the thermodynamic and anharmonic behaviors of nanowires that could be exfoliated from weakly-bonded three-dimensional materials. We analyze thermal stability, linear thermal expansion, and anharmonic heat capacity using the stochastic self-consistent harmonic approximation. Notably, our work unveils exotic features common among all the 1D wires: a colossal record negative thermal expansion and very large deviations from the Dulong-Petit law due to strong anharmonicity.

Figures (4)

• Figure 1: CuC$_2$ (Cu: red, C: gray). (a) Phonon dispersions (Hessian of the positional free energy bianco_2017_structural) at different temperatures within the SSCHA for the wire in the configuration as exfoliated from the 3D. Dashed black lines represent harmonic phonons from DFPT. (b) Anharmonic heat capacity calculated within SSCHA with eq. (\ref{['eq:cv_sscha']}) (blue line) and harmonic heat capacity (brown line) using eq. (\ref{['eq:cv']}) with temperature-independent harmonic DFPT $\omega$. (c) Linear thermal expansion coefficient $\alpha(T)$ using QHA. In the inset, $\alpha(T)$ per phonon branch. A and O refer to acoustic and optical modes, T and L to transversal and longitudinal modes. Within the same group of modes, lighter colors correspond to lower frequencies.
• Figure 2: TaSe$_3$ (Ta: blue, Se: green). (a) Phonon dispersions (Hessian of the positional free energy) at different temperatures within the SSCHA for TaSe$_3$ in the configuration as exfoliated from the 3D1. Dashed black lines represent harmonic phonons from DFPT. The blue arrow highlights the unstable modes appearing from 700K. (b) Anharmonic heat capacity calculated within SSCHA with eq. (\ref{['eq:cv_sscha']}) (blue line) and harmonic heat capacity (brown line) using eq. (\ref{['eq:cv']}) with temperature-independent harmonic DFPT $\omega$. (c) Linear thermal expansion coefficient $\alpha(T)$ using QHA. In the inset, $\alpha(T)$ per phonon branch. A and O refer to acoustic and optical modes. Within the same group of modes, lighter colors correspond to lower frequencies. 1Note that the small wings around $\Gamma$ are interpolation defects and sensitive to the ASR imposition, in contrast to the genuine instability at 700K, which aligns with an explicit q-point in the sampling mesh.
• Figure 3: Au$_2$Se$_2$ (Au: pink, Se: brown). (a) Band gap behavior with temperature in the stable insulating double cell phase. (b) Anharmonic heat capacity calculated within SSCHA with eq. (\ref{['eq:cv_sscha']}) (blue line) and harmonic heat capacity (brown line) using eq. (\ref{['eq:cv']}) with temperature-independent harmonic DFPT $\omega$. (c) Linear thermal expansion coefficient $\alpha(T)$ using QHA. In the inset, $\alpha(T)$ per phonon branch. A and O Within the same group of modes, lighter colors correspond to lower frequencies.
• Figure 4: Comparison of negative thermal expansion (NTE) coefficients for different materials: a) Ref. kwon2004thermal; b) Ref. jiang2010thermal; c) Ref. yoon2011negativebao2009controlled; d) Ref. kriegel2023incommensurability; e) Ref. demiroglu2021extraordinary; f) Ref. ernst1998phononmary1996negative; g) Ref. sanson2006negative; h) rottger1994latticefortes2018accurate; i) Ref. chapman2005direct; j) Ref. greve2010pronounced. We plot the highest $\alpha$ value found for the material at the corresponding temperature. In blue points, the temperature-behavior of $\alpha$ for the three wires studied in this work, using SSCHA and eq. (\ref{['eq:alpha_v']}) (more details can be found in SI).