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Polar metals are challenging to identify spectroscopically because the fingerprints of electric polarization are often obscured by the presence of screening charges. Here, we unravel unambiguous signatures of a distortive polar order buried in the Fermi sea by probing the nonlinear optical response of materials driven by tailored terahertz fields. We apply this strategy to investigate the topological crystalline insulator Pb_1−xSn_xTe, tracking its soft phonon mode in the time domain and observing the occurrence of inversion symmetry breaking as a function of temperature. By combining measurements across the material’s phase diagram with ab initio calculations, we demonstrate the generality of our approach. These results highlight the potential of terahertz driving fields to reveal polar orders coexisting with itinerant electrons, thus opening additional avenues for material discovery. 

Recent studies have reported the experimental discovery that nanoscale specimens of even a natural material, such as diamond, can be deformed elastically to as much as 10% tensile elastic strain at room temperature without the onset of permanent damage or fracture. Computational work combining ab initio calculations and machine learning (ML) algorithms has further demonstrated that the bandgap of diamond can be altered significantly purely by reversible elastic straining. These findings open up unprecedented possibilities for designing materials and devices with extreme physical properties and performance characteristics for a variety of technological applications. However, a general scientific framework to guide the design of engineering materials through such elastic strain engineering (ESE) has not yet been developed. By combining first-principles calculations with ML, we present here a general approach to map out the entire phonon stability boundary in six-dimensional strain space, which can guide the ESE of a material without phase transitions. We focus on ESE of vibrational properties, including harmonic phonon dispersions, nonlinear phonon scattering, and thermal conductivity. While the framework presented here can be applied to any material, we show as an example demonstration that the room-temperature lattice thermal conductivity of diamond can be increased by more than 100% or reduced by more than 95% purely by ESE, without triggering phonon instabilities. Such a framework opens the door for tailoring of thermal-barrier, thermoelectric, and electro-optical properties of materials and devices through the purposeful design of homogeneous or inhomogeneous strains.