PbTe's local polar order survives without anharmonicity: machine-learned potential simulations trace it to long-range harmonic forces
Synopsis
Cubic PbTe keeps a centrosymmetric average structure yet hosts finite-range local polar correlations, which were often attributed to lattice anharmonicity. Machine-learned interatomic potentials trained on density functional theory data drive 100,000-atom-scale molecular dynamics, and mapping them onto an interpretable force-constant model lets third- and fourth-order terms be switched off. The nanoscale correlations persist without those anharmonic terms, but vanish when harmonic interactions are cut to the third nearest neighbor; at low temperature the correlation range exceeds 50 Å.
Interpretation
Finite-range local polar correlations in PbTe are supported by long-range harmonic interactions rather than by the higher-order lattice anharmonicity usually tied to polar nanoregion formation. Earlier interpretations treated the non-Gaussian broadening of Pb–Te bond lengths and the optical phonon peak splitting as direct consequences of lattice anharmonicity, and inferred the origin of local dipole correlations from that. At 200 K, force-constant molecular dynamics trajectories with and without third- and fourth-order force constants are compared; removing the anharmonic terms leaves the nanoscale polar correlation maps in place, with no qualitative difference between 10 K and 200 K.
The approach translates machine-learned potential trajectories into an interatomic force-constant model truncated by neighbor shell, so interactions of a given order and distance can be kept or deleted separately. A machine-learned potential delivers large-scale, high-accuracy molecular dynamics but does not by itself say which interactions produce the observed correlations. The force-constant trajectories reproduce the local correlation behavior of the machine-learned potential trajectories only when second-order harmonic interactions extend to the 14th nearest neighbor (12.9 Å in the undisplaced symmetric configuration); truncating to the eighth nearest neighbor (9.7 Å) shrinks the correlation range, and truncating to the third (5.6 Å) removes correlations in every direction.
In reciprocal space this long-range harmonic action appears as high curvature of the transverse optical phonon branch near the Γ point, with a low Γ-point frequency that hardens rapidly with wavevector. The Γ-point transverse optical frequency alone does not set the correlation range, because uniformly scaling short-range force constants can also bring that frequency to the same value. Scaling the force constants up to the third nearest neighbor by a factor of 0.05 reproduces the 0.5 THz transverse optical frequency obtained with 14th-nearest-neighbor force constants, yet the resulting trajectories show no discernible spatial correlations in local polarization.
Perspective
The conclusions come from machine-learned potential molecular dynamics and force-constant molecular dynamics of cubic PbTe at temperatures from 10 K to 300 K, compared with density functional force constants and potential profiles of isostructural NaCl; the authors treat the captured correlation range as a lower bound.
The authors note that the maximum interaction range of current machine-learned potentials is limited by factors such as training-cell size and cutoff range, even with enough message-passing layers; they hope later experimental and theoretical work will resolve low-temperature local symmetry breaking and related material responses.