Molecular Dynamics Study of The Heat Transport Mechanism of Cu_2-δSe Using Machine Learning Potential

Cu_2-δSe is a material that exhibits the high thermoelectric performance of <i>zT</i>=1.5 at 1000 K [1]. This high thermoelectric performance is due to its extremely low lattice thermal conductivity at high temperatures. For example, 0.5 W/m/K at 1000 K was reported for Cu₂Se [1]. This value is comparable to that of liquid and amorphous materials. Cu_2-δSe superionic conduction causes such low lattice thermal conductivity. At high temperatures (&gt;410 K), Cu ions move between the fcc-structured selenium [1,2]. Such a material with liquid-like properties for phonon transport and crystal-like properties for electrons is called "phonon-liquid electron-crystal (PLEC)”. It has been explored for candidate thermoelectric materials.<br/>The "liquid-like" nature of Cu ions in PLEC materials makes it hard to treat heat transport in a perturbative manner. Thus, it requires computationally demanding <i>ab initio</i> molecular dynamics (AIMD) simulation. On the other hand, the use of machine learning potentials in calculating thermal conductivity has been increasing in recent years [3,4]. Machine learning potentials are developed to approximate interatomic potentials using machine learning. They can reduce the computational cost to the same extent as empirical potentials while maintaining the accuracy of <i>ab initio</i> calculations. The Beheler-Parrinello type potential using Neural Networks is one of the machine learning potentials [5].<br/>In this study, we constructed the interatomic potential of Cu_2-δSe based on Moment Tensor Potential [6] and calculated thermal properties by MD simulations. We tested our potential, and MD trajectories on our potential showed Cu ions' liquid-like properties. We performed the Non-equilibrium Molecular Dynamics (NEMD) method for calculating the lattice thermal conductivity, and we got the calculated thermal conductivity of 0.5 W/m/K at 700 K. Moreover, we derived the relation between thermal conductivity and diffusion coefficient. From this relation, we investigated the contribution of Cu ions transport and found that the hopping transport of Cu ions is dominant in heat transport.<br/>[1] Huili Liu, et al., <i>Nat. Mater</i>., <b>11</b>, 422–425, 2012. [2] Hyoungchul Kim, et al., <i>Acta Mater.</i>, <b>86</b>, 247–253, 2015.<br/>[3] R. Li, et al., <i>Mater. Today Phys.</i>, <b>12</b>, 100181, 2020. [4] Pavel Korotaev, et al., <i>Phys. Rev. B</i>, <b>100</b>, 144308, 2019.<br/>[5] Jörg Behler, et al., <i>Phys. Rev. Let., </i>98, 146401, 2007. [6] Novikov Ivan S, et. al. <i>ML: Sci. & Tech.</i>, <b>2</b>, 025002, 2021