Non-Fermi liquid behaviour at the orbital-ordering quantum critical point in the two-orbital model

The critical behaviour of a two-orbital model with degenerate d _xz and d_yz orbitals is investigated by multi-dimensional 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 behaviour 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 behaviour. 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 Sr₃Ru₂O₇.