Role of Fermi Surface Nesting and Hidden Nesting in Controlling Kohn Anomalies in α-Uranium

Charge density wave (CDW), the periodic modulation in electrons charge distribution, is accompanied by a simultaneous symmetry lowering and a finite gap opening near the Fermi level (<i>E</i>_F) in low dimensional metals. The Fermi surface topology of such systems allows Fermi surface nesting (FSN), resulting in divergence of the imaginary part of electronic susceptibility (<i>Im{χ</i>₀(<i><b>q</b></i>)}). The divergence in <i>Im{χ</i>₀(<i><b>q</b></i>)} is further carried over to the real part (<i>Re{χ</i>₀(<i><b>q</b></i>)}) under specific scenarios that drives the electronic instability. Kohn extended the implications of electronic instability to the lattice explicitly showing anomalous phonon behavior at <b>q</b>_CDW. A finite resolution of momentum transfer (<b>Q</b>) in x-ray or neutron scattering experiments often fails to capture the Kohn anomalies owing to its localized nature in the <i>k</i>-space. Hence, such phenomena are challenging to realize in experiments.<br/>In this work, we use comprehensive <i>ab-initio</i> simulations of electrons and phonons [1] and earlier inelastic neutron scattering (INS) measurements [2] to understand the governing mechanism of CDW instability in <i>α</i>-Uranium (<i>α</i>-U) that displays pronounced Kohn anomalies in multiple phonon branches. <i>α</i>-U undergoes CDW transition (<i>T</i>_CDW = 43 K) along with a symmetry lowering and unit-cell doubling along the a-axis. Initially, we capture the Kohn anomalies in multiple phonon branches. Subsequently, we map it to the electronic origin by calculating <i>Re{χ</i>₀(<i><b>q</b></i>)}. The results display a diverging peak in <i>Re{χ</i>₀(<i><b>q</b></i>)} indicating electronic instability. Finally, we project the contribution of <i>Re{χ</i>₀(<i><b>q</b></i>)} in the entire <i>k</i>-space. The result highlights that besides the FSN features where contributions coincide with the Fermi surface, many <i>k</i>-points away from the Fermi surface also display a finite contribution to the divergence in <i>Re{χ</i>₀(<i><b>q</b></i>)}. This phenomenon is called hidden nesting and manifests by the nesting of the electronic states above and below near <i>E</i>_F. Hence, our study demonstrates that the combined effect of FSN and hidden nesting drives the Kohn anomalies in multiple phonon branches and results in the CDW transition in <i>α</i>-U. Understanding such systems with coupled FSN and hidden nesting opens avenues to exploit electronic and lattice states of topological Weyl semimetals and superconductors.<br/><br/>Authors acknowledge financial support from BRNS–DAE under Project No. 58/14/30/2019-BRNS/ 11117, and MoE-STARS under Project No. STARS/ APR2019/PS/345/FS. We acknowledge the use of the SPACETIME-II supercomputing facility at IITB and ANUPAM supercomputing facility at BARC.<br/><br/><b>References </b><br/>[1] Roy et al., Phys. Rev. Lett. 126, 096401 (2021)<br/>[2] Crummett et al., Phys. Rev. B 19, 6028 (1979