[Paper Review] Nematic electron states enhanced by orbital band hybridization

Wei-Cheng Lee, Congjun Wu|arXiv (Cornell University)|Feb 9, 2009

Advanced Condensed Matter Physics24 citations

TL;DR

This paper proposes that orbital band hybridization in transition metal oxides drives nematic electron states by shifting Landau interaction weight from s-wave to non-s-wave channels, inducing anisotropic Fermi surface distortions even with conventional interactions. In a multi-band Hubbard model with hybridized d_{xz} and d_{yz} bands, it demonstrates that nematic order can be stabilized via metamagnetic coupling, explaining anisotropic states in Sr₃Ru₂O₇ under high magnetic fields.

ABSTRACT

We extend the study of the Fermi surface instability of the Pomeranchuk type into systems with orbital band structures, which are common features in transition metal oxides. Band hybridization significantly shifts the spectra weight of the Landau interactions from the conventional s-wave channel to unconventional non-s-wave channels, which results in anisotropic (nematic) Fermi surface distortions even with ordinary interactions in solids. The Ginzburg-Landau free energy is constructed by coupling the charge-nematic, spin-nematic and ferromagnetic order parameters together, which shows that nematic electron states can be induced by metamagnetism. The connection between this mechanism to the anisotropic metamagnetc states observed in Sr$_3$Ru$_2$O$_7$ at high magnetic fields is studied in a multi-band Hubbard model with the hybridized quasi-one dimensional $d_{xz}$ and $d_{yz}$-bands.

Motivation & Objective

• To investigate the role of orbital band hybridization in driving Fermi surface instabilities beyond conventional s-wave Pomeranchuk instabilities.
• To understand how hybridization alters the channel dominance of Landau interactions, leading to anisotropic (nematic) Fermi surface distortions.
• To establish a connection between metamagnetism and nematic order in correlated electron systems like Sr₃Ru₂O₇.
• To construct a Ginzburg-Landau free energy framework coupling charge-nematic, spin-nematic, and ferromagnetic order parameters to explore emergent nematicity.

Proposed method

• Construct a multi-band Hubbard model incorporating hybridized quasi-one-dimensional d_{xz} and d_{yz} bands relevant to Sr₃Ru₂O₇.
• Analyze the spectral weight redistribution of Landau interactions due to band hybridization, shifting dominance from s-wave to non-s-wave channels.
• Derive a Ginzburg-Landau free energy functional that couples charge-nematic, spin-nematic, and ferromagnetic order parameters.
• Use the Ginzburg-Landau framework to explore the stability and interplay of nematic order under metamagnetic conditions.
• Perform analytical and numerical analysis to identify the emergence of nematic states driven by hybridization and magnetic field-induced effects.

Experimental results

Research questions

• RQ1 How does orbital band hybridization alter the channel structure of Landau interactions in correlated electron systems?
• RQ2 Can nematic Fermi surface distortions emerge from conventional electron-electron interactions when band hybridization shifts interaction weight to non-s-wave channels?
• RQ3 What is the role of metamagnetism in stabilizing nematic electron states in high-field phases of Sr₃Ru₂O₇?
• RQ4 How do charge-nematic, spin-nematic, and ferromagnetic order parameters couple in the Ginzburg-Landau description to enable nematicity?
• RQ5 To what extent can the observed anisotropic metamagnetic states in Sr₃Ru₂O₇ be explained by hybridization-induced nematicity?

Key findings

• Orbital band hybridization shifts the dominant channel of Landau interactions from s-wave to non-s-wave, enabling anisotropic Fermi surface distortions even with ordinary interactions.
• The Ginzburg-Landau free energy framework confirms that nematic order can be induced via coupling to metamagnetic states, particularly through spin-nematic and ferromagnetic fluctuations.
• In the multi-band Hubbard model with d_{xz} and d_{yz} bands, hybridization leads to a significant enhancement of nematic susceptibility.
• The model reproduces key features of the anisotropic metamagnetic state observed in Sr₃Ru₂O₇ under high magnetic fields, linking it to hybridization-driven nematicity.
• The coexistence and coupling of charge-nematic, spin-nematic, and ferromagnetic order parameters stabilize nematic electron states in the absence of explicit nematic interactions.