Unconventional Discontinuous Transitions in Isospin Systems

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Two-dimensional (2D) electron systems are crucial for understanding novel quantum phenomena.
• The Stoner transition describes the onset of ferromagnetism in metals due to spin-polarization.
• Electron band structure and dispersion relations significantly influence electronic properties.

Purpose of the Study:

• To investigate the nature of the Stoner transition in 2D fermions with specific dispersion relations (k^2, k^4).
• To explore instabilities and potential fractional-metal states in generalized 2D systems (k^{2α}) with spin and valley isospin.
• To analyze the behavior of spin susceptibility near critical points and transitions.

Main Methods:

• Theoretical analysis of two-dimensional fermion systems.
• Calculation of electronic band structures and dispersion relations.
• Investigation of spin susceptibility and phase transitions.

Main Results:

• First-order Stoner transitions to fully spin-polarized states were identified for dispersions k^2 and k^4, even with diverging spin susceptibility.
• A cascade of instabilities into fractional-metal states, characterized by depleted electron bands, was found for generalized dispersions k^{2α}.
• Narrow intermediate ranges with partially depleted bands exist for specific values of α (α<1 or α>2).
• Spin susceptibility increases significantly near these transitions.

Conclusions:

• The Stoner transition can be first-order in 2D systems, contrary to some expectations based on diverging susceptibility.
• Fractional-metal states are a likely outcome in tunable 2D electronic systems with specific band structures.
• These findings have implications for understanding and designing materials like biased bi- and trilayer graphene and moiré systems.