Excitonic insulators as a model of $d-d$ and Mott transitions in strongly correlated materials

Abstract

We show how strongly correlated materials could be described within the framework of an excitonic insulator formalism, and delineate the relationship between inter-and intra-band ordering phenomena. Our microscopic model of excitons clarifies the fundamental role of Van-Hove-singularitynesting in driving both inter-and intra-band ordering transitions, and uncovers an interesting connection with resonating-valence-bond physics.

Landscape of coexisting excitonic states in the insulating single-layer cuprates and nickelates

“…The theoretical investigation of excitons in strongly correlated matter has a long history starting around the time of BCS theory. Questions regarding exciton condensation, [16][17][18][19][20][21][22] propagation, 23,24 electron-hole pairing pathways, [25][26][27][28][29][30] and their possible link to the mechanism of high-termperature superconductivity 19,[31][32][33][34][35] have been pursued. In particular, several calculations have been put forth classifying the excitons as charge-transfer, where the electron and hole site on neighboring Cu and O sites, along with justifying their dispersive nature in La 2 CuO 4 .…”

“…25,26,28 Additionally, Mott and d − d excitons, where electron and holes originate from the Cu-d x 2 −y 2 bands and the d x 2 −y 2 /d z 2 orbitals, respectively, have also been suggested. 20 However, a detailed characterization of the dispersion and nature of the excitons -Mott vs. d-d vs. charge-transfer -in the real materials requires approaches that are not restricted to simple bases-sets and limiting cases.…”

Excitonic insulators and Gross-Neveu models

“…Therefore, this instability may appear near to the SM-SMC transition at sufficiently low temperatures [19][20][21][22][23] . Thus, one can infere that, for solids with small band overlap or with small energy gaps, there may exist a new low temperature phase of matter, the excitonic insulator [24][25][26][27][28][29][30] .…”

“…Besides the usual chiral order parameter (COP), we also introduce an excitonic order parameter (EOP) that characterizes the EI phase. When using the generalized GN model to describe our system, we keep in mind the familiar two-band picture of valence and conduction electrons, assuming that Coulomb interactions between electrons in a given band are taken into account by renormalizing these bands [21][22][23][24][25]29,30 . For simplicity, the spin of the electrons is not taken into account and we consider the case that the EI phase emerges from a direct gap system, as for the EI candidate Ta 2 NiSe 5 28,[34][35][36]38,40 .…”