Coulomb Drag Drives Electron-hole Bifluidity in Doped Graphene, Violating the Wiedemann-Franz Law

The behaviour of electrons and holes within graphene, a material with exceptional electronic properties, continues to reveal surprising phenomena, and recent work by Dwaipayan Paul and Nakib H. Protik, both from Humboldt-Universität zu Berlin, demonstrates a remarkable example of this. The researchers investigate how electrons and holes interact within doped graphene, focusing on the significant role of Coulomb interactions, the electrical forces between charged particles. Their calculations reveal that these interactions can induce a state of ‘bifluidity’, where electrons and holes behave as interpenetrating fluids, and even lead to negative conductivity, a counterintuitive result where increasing voltage reduces current. This discovery elucidates the fundamental mechanisms driving hydrodynamic behaviour in graphene and challenges established principles like the Wiedemann-Franz law, potentially paving the way for novel electronic devices and a deeper understanding of charge transport in two-dimensional materials.

Scientists solved the Boltzmann transport equation to investigate charge carrier dynamics in materials, revealing how strong Coulomb interactions influence transport behavior. Their calculations demonstrate that, under specific conditions, these interactions induce phenomena like negative conductivity and a unique state where electrons and holes behave as separate, interacting fluids, known as bifluidity. The research also identifies conditions where either electrons or holes alone exhibit hydrodynamic behavior, a low-dissipation mode of transport, and elucidates the roles of microscopic scattering mechanisms that drive these phenomena, offering insights into the fundamental physics governing charge carrier movement.

Coulomb Interactions and Charge Carrier Transport

Researchers developed a sophisticated method to study charge carrier transport in doped graphene, focusing on the potential for hydrodynamic behavior arising from strong Coulomb interactions. They employed an ab initio Boltzmann transport equation (BTE) approach, extending the capabilities of the elphbolt code to incorporate a screened Coulomb collision integral that accounts for bidirectional momentum transfer between electrons and holes, known as Coulomb drag. This builds upon previous work with three-dimensional semiconductors. The team meticulously implemented this collision integral within the BTE framework and fully solved the BTE to self-consistency using an iterative approach, moving beyond simpler relaxation time approximations to ensure a comprehensive understanding of the momentum feedback loop between charge carriers.

The screened Coulomb interaction was calculated using a two-dimensional formulation, incorporating the dielectric response of an hBN substrate with a value of 4. 1 to replicate experimental conditions, and the Thomas-Fermi dielectric function accounted for the screening of the Coulomb interaction by the charge carriers themselves. The researchers combined the Coulomb collision integral with the established electron-phonon counterpart, adhering to Matthiesen’s rule to treat scattering channels as independent, allowing for a detailed analysis of charge carrier dynamics under both electric fields and temperature gradients. Calculated results were then compared with experimental measurements of resistivity at various temperatures, including 200 K, 300 K, and 400 K, demonstrating strong agreement with recent data.

Coulomb Interactions Drive Hydrodynamic Charge Transport

This work presents a detailed ab initio calculation of charge carrier transport properties in doped materials, revealing hydrodynamic phenomena driven by strong Coulomb interactions. Researchers extended the elphbolt code to incorporate a screened Coulomb collision integral, enabling the investigation of bidirectional momentum transfer between electrons and holes. The team’s calculations demonstrate that these interactions induce effects such as negative conductivity and bifluidity, where electrons and holes behave as separate, interacting fluids. The study focused on calculating resistivity as a function of charge carrier concentration, comparing results to recent measurements at 300 K.

Without accounting for Coulomb interactions, the calculations deviated significantly from experimental data. However, including these interactions, the calculated resistivity closely matched the measured values across a range of concentrations, validating the importance of Coulomb effects in this system. Specifically, the calculations accurately reproduce the measured resistivity for majority carrier concentrations ranging from 1. 6x 10 11 to 1. 7x 10 12 cm -2 . Further analysis revealed a strong violation of the Wiedemann-Franz law, a fundamental principle relating electrical and thermal conductivity, close to the bifluid state, and spectral conductivity calculations at 200 K for hole-doped cases demonstrate the impact of Coulomb interactions on the valence and conduction bands. These findings demonstrate that standard phonon-limited carrier transport theory fails to capture the essential physics, both quantitatively and qualitatively, and that accurate modeling requires a full consideration of Coulomb interactions.

Coulomb Interactions Drive Hydrodynamic Bifluidity

This research presents a detailed investigation into charge carrier transport within doped graphene, employing a sophisticated theoretical framework that incorporates both phonon and Coulomb interactions. The findings demonstrate that strong Coulomb interactions can induce several hydrodynamic transport regimes, including exclusive electron or hole hydrodynamics and, notably, a coupled electron-hole bifluidity at low temperatures. These results align with recent experimental observations of negative conductivity in strongly interacting electron-hole systems. Furthermore, the study reveals a significant violation of the Wiedemann-Franz law, directly attributable to the Coulomb interactions between electrons and holes. The team established that conventional theories neglecting Coulomb interactions fail to capture these observed phenomena, highlighting the crucial role of these interactions in determining the material’s transport properties. The authors acknowledge limitations within their model, specifically the exclusion of the exchange term in the collision integral and the use of a static screening approximation, and suggest that future work could incorporate these elements, alongside a more comprehensive treatment of electron-phonon interactions, potentially extending the applicability of this approach to other materials.