Elusive Exciton Insulator States in 1T-HfTe2: Exciton softening, and Symmetry Breaking by Ab Initio Methods
Recent experiments have provided evidence for excitonic insulator (EI) states in 1T HfTe2. In this work, we investigate EI states in monolayer, bilayer, trilayer, and bulk 1T HfTe2 using advanced meta generalized gradient approximation (meta GGA) calculations and a model Bethe-Salpeter equation (BSE) approach, together with structural and electronic symmetry breaking analyses. Our results show that both the monolayer and bilayer exhibit negative exciton energies, leading to the spontaneous formation of bound excitons and EI states, whereas the trilayer and bulk display positive exciton energies and do not support EI states. Structural symmetry-breaking calculations show very small in-plane displacements of the Hf atoms from their symmetric positions in the monolayer and multilayers, consistent with experimental observations. Interestingly, electronic symmetry-breaking calculations for the monolayer, performed using a symmetric structure and a hybrid functional, show a pronounced unfolded valence-band feature at the M point and no unfolded conduction-band states near the Fermi level at Gamma, in good agreement with experimental results. Overall, our findings support the existence of EI states in low dimensional 1T HfTe2. The methodology developed here can be readily extended to investigate EI behavior in other related quantum material systems.