Orbital-Induced Peierls Transitions: How Orbitals Orchestrate Lattice Instability

Abstract: The Peierls transition is typically regarded as a phenomenon inherent to one-dimensional (1D) materials. However, orbital degrees of freedom can induce this instability even in higher dimensions. Two mechanisms are primarily responsible. First, the anisotropic shape of $p$ and $d$ orbitals can lead to effective "1D-zation" of the electronic spectrum. Second, orbital degrees of freedom can lift band degeneracy by shifting bands relative to each other via the local or band Jahn-Teller effect, thereby affecting the nesting of the Fermi surface. The orbital-induced Peierls effect is most commonly observed when ligand octahedra surrounding transition metals share edges, and less frequently in face-sharing geometries. In this review, we discuss the underlying physical mechanisms, the materials in which this phenomenon occurs, the characteristics of the high-temperature undistorted phase, and the role of local effects such as the formation of molecular orbitals.