Orbital- and atom-dependent linear dispersion across the Fermi level induces charge density wave instability in EuTe4

Abstract

In the Peierls description of a charge density wave (CDW), Fermi surface nesting (FSN)---defined by the divergence of the imaginary part of electronic susceptibility, i.e., $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$---leads to divergence of the real part, thus inducing CDW instability at wave vector ${\mathbf{q}}_{\mathrm{CDW}}$. Here we show that the divergence of $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$ implying a divergence of $\mathrm{Re}{{\ensuremath{\chi}}_{0}}$ at the same ${\mathbf{q}}_{\mathrm{CDW}}$ breaks down for three-dimensional Fermi surfaces and is particularly severe for linearly dispersing electronic bands across the Fermi level (${E}_{\mathrm{F}}$), as exemplified by rare-earth tellurides $R{\mathrm{Te}}_{n}$. By calculating the orbital-, atom-, and momentum-resolved contribution to ${\ensuremath{\chi}}_{0}$ of ${\mathrm{EuTe}}_{4}$, we find that FSN and CDW instability are not driven by the same atoms and orbitals but from different ones. This unique behavior is enabled by linearly dispersing bands across ${E}_{\mathrm{F}}$ with constant Fermi surface velocity that assists electron-hole pairs to form not only at ${E}_{\mathrm{F}}$ but also across ${E}_{\mathrm{F}}$ at ${\mathbf{q}}_{\mathrm{CDW}}$, hence allowing different orbitals to contribute to the divergence of $\mathrm{Re}{{\ensuremath{\chi}}_{0}}$ and $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$. The above scenario is general and applicable to recent observations of CDWs and spin density waves (SDWs) from linearly dispersing bands in several Dirac and Weyl semimetals and kagome metals. Moreover, as we demonstrate, such component-resolved analysis provides focused input to engineer CDW and SDW states.