[Paper Review] The Thermoelectric Effect and Its Natural Heavy Fermion Explanation in Twisted Bilayer and Trilayer Graphene

Dumitru Călugăru, Haoyu Hu+4 more|arXiv (Cornell University)|Feb 21, 2024

Graphene research and applicationsMaterials Science3 citations

TL;DR

This paper proposes the topological heavy-fermion (THF) model to explain the unconventional thermoelectric behavior in twisted bilayer and trilayer graphene (TBG), where localized, correlated f-electrons and itinerant c-electrons coexist. The model attributes the negative, sawtooth-oscillating Seebeck coefficient at positive fillings to lifetime asymmetry and strong correlations, with c-electrons dominating transport due to longer lifetimes and stronger dispersion, successfully matching new experimental data.

ABSTRACT

We study the interacting transport properties of twisted bilayer graphene (TBG) using the topological heavy-fermion (THF) model. In the THF model, TBG comprises localized, correlated $f$-electrons and itinerant, dispersive $c$-electrons. We focus on the Seebeck coefficient, which quantifies the voltage difference arising from a temperature gradient. We find that the TBG's Seebeck coefficient shows unconventional (strongly-interacting) traits: negative values with sawtooth oscillations at positive fillings, contrasting typical band-theory expectations. This behavior is naturally attributed to the presence of heavy (correlated, short-lived $f$-electrons) and light (dispersive, long-lived $c$-electrons) electronic bands. Their longer lifetime and stronger dispersion lead to a dominant transport contribution from the $c$-electrons. At positive integer fillings, the correlated TBG insulators feature $c$- ($f$-)electron bands on the electron (hole) doping side, leading to an overall negative Seebeck coefficient. Additionally, sawtooth oscillations occur around each integer filling due to gap openings. Our results highlight the essential importance of electron correlations in understanding the transport properties of TBG and, in particular, of the lifetime asymmetry between the two fermionic species (naturally captured by the THF model). Our findings are corroborated by new experiments in both twisted bilayer and trilayer graphene, and show the natural presence of strongly-correlated heavy and light carriers in the system.

Motivation & Objective

• To explain the unconventional thermoelectric transport in twisted bilayer and trilayer graphene (TBG), particularly the negative Seebeck coefficient and sawtooth oscillations at positive fillings.
• To address the limitations of conventional band theory in describing strongly correlated electron systems in twisted 2D materials.
• To establish the topological heavy-fermion (THF) model as a natural framework for describing the coexistence of heavy (f-electrons) and light (c-electrons) fermionic quasiparticles in TBG.
• To connect theoretical predictions with recent experimental measurements of thermopower in TBG, validating the role of electron correlations and lifetime asymmetry.

Proposed method

• Adopting the topological heavy-fermion (THF) model, which treats TBG as a system of localized, correlated f-electrons and itinerant, dispersive c-electrons.
• Using the THF framework to compute the Seebeck coefficient as a function of filling factor, incorporating electron correlation effects and lifetime differences between f- and c-electrons.
• Modeling the system’s electronic structure with gap openings at integer fillings, leading to sawtooth oscillations in the Seebeck coefficient.
• Analyzing transport contributions by weighting the Seebeck response according to quasiparticle lifetime and band dispersion, with c-electrons dominating due to longer lifetimes and stronger dispersion.
• Comparing theoretical predictions with experimental data from arXiv:2402.11749 and arXiv:2402.12296 to validate the model’s accuracy.
• Employing a 5+106 page theoretical framework with 3+36 figures and 6 tables to systematically explore the transport response across different fillings and correlation strengths.

Experimental results

Research questions

• RQ1 Why does the Seebeck coefficient in twisted bilayer graphene exhibit negative values with sawtooth oscillations at positive integer fillings, contrary to standard band theory predictions?
• RQ2 How do electron correlations and the lifetime asymmetry between heavy f-electrons and light c-electrons influence thermoelectric transport in twisted 2D materials?
• RQ3 To what extent can the topological heavy-fermion (THF) model quantitatively reproduce experimental thermopower measurements in twisted bilayer and trilayer graphene?
• RQ4 What is the role of gap openings at integer fillings in generating the observed sawtooth-like oscillations in the Seebeck coefficient?
• RQ5 How does the dominance of c-electrons in transport arise from their longer lifetimes and stronger dispersion, despite the presence of strongly correlated f-electrons?

Key findings

• The Seebeck coefficient in twisted bilayer graphene shows negative values with sawtooth oscillations at positive fillings, a behavior inconsistent with standard band theory but naturally explained by the THF model.
• The dominant transport contribution arises from c-electrons due to their longer lifetimes and stronger dispersion, even though f-electrons are more strongly correlated.
• At integer fillings, the system develops c-electron bands on the electron-doped side and f-electron bands on the hole-doped side, leading to an overall negative Seebeck coefficient.
• Sawtooth oscillations emerge around each integer filling due to gap openings, which are captured by the THF model’s description of correlated insulating states.
• The theoretical predictions of the THF model are in excellent agreement with new experimental measurements in both twisted bilayer and trilayer graphene, confirming the presence of strongly correlated heavy and light carriers.
• The model successfully accounts for the lifetime asymmetry between f- and c-electrons, which is essential for explaining the unconventional thermoelectric response.