Non-Fermi Liquid behavior at the Orbital Ordering Quantum Critical Point in the Two-Orbital Model

TL;DR

This paper investigates the quantum critical behavior of a two-orbital model with degenerate orbitals, revealing a non-Fermi liquid phase driven by overdamped collective modes near the orbital-ordering quantum critical point, with implications for materials like iron-based superconductors.

Contribution

It demonstrates that a two-orbital model exhibits a dominant overdamped mode with z=3, leading to non-Fermi liquid behavior and connecting orbital order to nematic order in a continuous model.

Findings

Presence of a z=3 overdamped collective mode near the quantum critical point

Non-Fermi liquid behavior occupies a sizable phase space in the model

Orbital order in the two-orbital model is analogous to nematic order in continuous models

Abstract

The critical behavior of a two-orbital model with degenerate $d_{xz}$ and $d_{yz}$ orbitals is investigated by multidimensional bosonization. We find that the corresponding bosonic theory has an overdamped collective mode with dynamical exponent $z=3$, which appears to be a general feature of a two-orbital model and becomes the dominant fluctuation in the vicinity of the orbital-ordering quantum critical point. Since the very existence of this $z=3$ overdamped collective mode induces non-Fermi liquid behavior near the quantum critical point, we conclude that a two-orbital model generally has a sizable area in the phase diagram showing non-Fermi liquid behavior. Furthermore, we show that the bosonic theory resembles the continuous model near the d-wave Pomeranchuk instability, suggesting that orbital order in a two-orbital model is identical to nematic order in a continuous model. Our results can be applied to systems with degenerate $d_{xz}$ and $d_{yz}$ orbitals such as iron-based superconductors and bilayer strontium ruthenates Sr$_3$Ru$_2$O$_7$.