Electronic structures of crystalline and amorphous GeSe and GeSbTe compounds using machine learning empirical pseudopotentials

TL;DR

This work advances an ML-enhanced empirical pseudopotential method (ML-EPM) to GeSe and GST compounds, addressing transferability and efficiency challenges of traditional EPMs. By predicting atomic EPs from rotation-covariant descriptors and SOAP-based environmental information, ML-EPM builds a $V_{\mathcal{C}}^{ML-EPM}(\mathbf{G})$ that yields a KS Hamiltonian without self-consistent iterations, achieving DFT-like electronic structure accuracy for both crystalline and amorphous phases. Results show good agreement with DFT for unlearned structures, accurate DOS in amorphous GeSe and GST, and substantial speedups, especially for larger systems, even allowing drastic reductions in the plane-wave cutoff. The approach promises scalable, transferable electronic-structure predictions and easy integration into materials databases and more complex ab initio frameworks, extending accurate modeling to disordered and defective systems.

Abstract

The newly developed machine learning (ML) empirical pseudopotential (EP) method overcomes the poor transferability of the traditional EP method with the help of ML techniques while preserving its formal simplicity and computational efficiency. We apply the new method to binary and ternary systems such as GeSe and Ge-Sb-Te (GST) compounds, well-known materials for non-volatile phase-change memory and related technologies. Using a training set of {\it ab initio} electronic energy bands and rotation-covariant descriptors for various GeSe and GST compounds, we generate transferable EPs for Ge, Se, Sb, and Te. We demonstrate that the new ML model accurately reproduces the energy bands and wavefunctions of structures outside the training set, closely matching first-principles calculations. This accuracy is achieved with significantly lower computational costs due to the elimination of self-consistency iterations and the reduced size of the plane-wave basis set. Notably, the method maintains accuracy even for diverse local atomic environments, such as amorphous phases or larger systems not explicitly included in the training set.

Figures (6)

• Figure 1: Momentum-dependent atomic empirical pseudopotential calculated by DFT for (a) Ge atoms, (b) Se atoms in GeSe (mp-1190257 supercell structure), and (c) Ge atoms, (d) Sb atoms, and (e) Te atoms in GeSbTe (mp-1224415 supercell structure) compounds. The mp-1190257 and mp-1224415 supercells are chosen for GeSe and GST, respectively. Blue and red circles in the plot indicate the real and imaginary parts of the atomic empirical pseudopotential, respectively. $a{_0}$ is the Bohr radius.
• Figure 2: (a)-(f) Electronic band structures for various crystalline GeSe compounds using ML-EPM (gray dashed line) and DFT (red line). In each band structure plot, the title indicates the material ID, and the Fermi level is set to zero. ${\rm K}_i~(i = 1,\cdots, 6)$ are reduced coordinates in reciprocal space, representing $(0, 0, 0)$, $(0.5, 0 ,0)$, $(0.5, 0.5, 0)$, $(0, 0, 0)$, $(0.5, 0.5, 0.5)$, $(0.5, 0, 0)$ in their corresponding crystal structures, respectively.
• Figure 3: Total density of states as a function of energy for amorphous GeSe calculated by ML-EPM (gray dashed line) and DFT (red line) for (a) 72 atoms, (b) 90 atoms, and (c) 120 atoms in the unit cell, respectively. The Fermi level is set to zero for each plot.
• Figure 4: (a)-(f) Electronic band structures for various crystalline GeSbTe compounds using ML-EPM (gray dashed line) and DFT (red line). In each band structure plot, the title indicates material ID, and the Fermi level is set to zero. ${\rm K}_i~(i = 1,\cdots, 6)$ are reduced coordinates in reciprocal space, representing $(0, 0, 0)$, $(0.5, 0 ,0)$, $(0.5, 0.5, 0)$, $(0, 0, 0)$, $(0.5, 0.5, 0.5)$, $(0.5, 0, 0)$ in their corresponding crystal structures, respectively.
• Figure 5: Total density of states as a function of energy for amorphous GeSbTe calculated by ML-EPM (gray dashed line) and DFT (red line) for (a) 72 atoms, (b) 90 atoms, and (c) 135 atoms in unit cell, respectively. The Fermi level is set to zero for each plot.