The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene

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The gist

The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene explores how phonon scattering events in subsonic fermions lead to unique

In short

The kinetic theory of ultra-subsonic fermion systems explores unique low-temperature transport physics in two-band systems with subsonic fermions ($v_F < v_p$). It predicts linear-in-$T$ resistivity down to very low temperatures, offering a new explanation for 'strange metal' behavior in flat band materials like magic angle twisted bilayer graphene.

Key concepts

Kinematic Constraints and Scattering Mechanisms
For subsonic fermions, the only allowed phonon scattering events are interband transitions between different energy bands. This kinematic rule dictates that all single-phonon scattering must occur between these distinct bands, fundamentally changing how transport behaves compared to supersonic systems.
Ultrasubsonic (USS) Limit
The theory develops a framework for an 'ultrasubsonic' limit where the system is accurately described by small ratios of Fermi velocity to phonon velocity ($v_F/v_p$) and small band separation. In this limit, relaxation times exhibit an exponential divergence at low temperatures, which balances thermodynamic state suppression.
Strange Metal Behavior
This refers to a non-Fermi liquid transport regime observed in certain materials where resistivity scales linearly with temperature ($ ho ho imes T$). The paper suggests that the unique phonon scattering physics in subsonic fermion systems can provide a microscopic explanation for this 'strange metal' behavior seen in flat band systems like MATBLG.

Terminology used across episodes

This episode discusses

The paper

The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene · Read on arXiv

Seth M. Davis, Sankar Das Sarma

Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland · Joint Quantum Institute

The only kinematically-allowed phonon-scattering events for bands of subsonic fermions (v F < v p) are interband transitions, leading to different low- T transport physics than in the typical supersonic case. We apply a kinetic theory of phonon-limited transport to a generic two-band system of subsonic fermions, deriving formulae for relaxation times and resistivity that are accurate in the limit of close bands and small v F/v p. We predict regimes of ρ proportional to T, ρ proportional to T squared, and perfect conductivity. Our theory predicts linear-in- T resistivity down to a crossover temperature that is suppressed from its supersonic analogue by a factor of v F/v p, offering a new explanation for low- T "strange metal" behavior observed in flat band systems.

DOI: 10.1103/PhysRevB.109.195105

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene".

Mira: The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene explores how phonon scattering events in subsonic fermions lead to unique low-temperature transport…

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So to recap, this paper sets up a kinetic theory for ultra-subsonic fermion systems and shows how their unique scattering rules dictate their low-temperature transport properties.

Mira: The core thesis is that because of kinematic constraints, phonon scattering in subsonic fermions must be interband transitions, which leads to different low- T transport physics than the typical supersonic case.

Lev: It’s important to note that they apply this kinetic theory to a generic two-band system of these subsonic fermions and derive the formulae for relaxation times and resistivity under conditions of close bands and small v F / v p.

Kai: And what they claim is that their theory predicts specific regimes: rho proportional to T, rho proportional to T squared, and perfect conductivity <ref:2305.09120#pg1,T^2$, and perfect conductivity>.

Mira: The most interesting part seems to be the prediction that the linear-in- T resistivity scaling goes down to a crossover temperature that is suppressed by v F / v p.

Lev: That suppression factor for the crossover temperature is key, because it offers a new explanation for the low- T "strange metal" behavior we see in flat band systems.

Conclusion: Kai: The paper, "The kinetic theory of ultra-subsonic fermion systems and applications to flat band magic angle twisted bilayer graphene," by Seth M. Davis and Sankar Das Sarma, is fundamentally about how the nature of phonon scattering dictates transport in these specific materials.

Mira: It’s not just about finding new scattering rates; it’s about showing that for subsonic fermions, the physics at very low temperatures is governed by interband transitions, which leads to linear-in- T resistivity scaling down to a lower temperature than you might expect.

Lev: For those of us building real hardware, the implication is that we have to be careful how we model these systems because the relaxation time divergence in this regime isn't like the standard T-four behavior for supersonic fermions; it’s exponential <ref:2305.09120#pg3>.

Kai: So, when you look at MATBLG or other flat band systems, this paper suggests that those low-temperature transport features might be caused by this specific subsonic phonon scattering physics.

Mira: It connects the microscopic details of the fermion band structure—specifically the close bands and small v F / v p limit—to macroscopic transport phenomena like linear resistivity.

Lev: The paper notes a limitation, though, and it does say that while this theory is general for NFB systems, applying it directly to a specific model like the BM model might be limited due to possible band renormalizations.

Kai: So the main thing is that this kinetic theory provides a framework where we can expect rho proportional to T scaling in these flat band systems based on the way phonons interact with subsonic fermions.

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