Abstract
Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors (SCs) and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here, we introduce the form factor that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the density-wave equation that gives the thermodynamically stable form factor, like the SC gap equation. In addition, a rigorous expression of the Ginzburg-Landau free energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based SC FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron pocket) due to the bond orbital order below ; (ii) Curie-Weiss (CW) behavior of the nematic susceptibility at higher , and the deviation from the CW behavior at lower near the nematic quantum critical point; and (iii) scaling relation of the specific heat jump at with . (Note that in the Bardeen-Cooper-Schrieffer theory.) These results lead to a conclusion that the nematicity in FeSe is the bond orbital order due to the paramagnon interference mechanism. The present theory paves the way for solving various unconventional phase transition systems.
3 More- Received 12 April 2022
- Revised 2 September 2022
- Accepted 29 November 2022
DOI:https://doi.org/10.1103/PhysRevB.107.035137
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