Researchers Reveal Power-law Behaviour in Two-dimensional Electron Gas with Two Magnetic Flux Quanta

The behaviour of electrons in strong magnetic fields presents a fascinating puzzle in condensed matter physics, and recent research sheds new light on this complex system. Bin-Bin Chen from Beihang University, Hongyu Lu, and Zi Yang Meng from The University of Hong Kong, investigate the properties of a ‘composite Fermi liquid’, a state where electrons bind with magnetic fields to create new quasiparticles. Their work demonstrates that this seemingly simple state exhibits unusual behaviour at low temperatures, deviating from the expected characteristics of ordinary metals, and revealing a hidden complexity in the interactions between these composite particles. By employing advanced computer simulations, the team uncovers evidence of strong correlations within the composite Fermi liquid, offering crucial insights into the fundamental nature of this exotic state of matter and potentially informing our understanding of similar systems found in layered materials.

Composite Fermions and Non-Fermi Liquid Behaviour

The two-dimensional electron gas in a strong magnetic field, such as the quantum Hall system, exhibits remarkably rich behaviour. Theoretical predictions suggest that at specific conditions, composite fermions emerge, quasiparticles formed by electrons binding to magnetic flux quanta. These composite fermions, despite being fermions themselves, are expected to form a liquid state that differs significantly from the standard Fermi-liquid theory, displaying non-Fermi-liquid characteristics. Understanding this unusual behaviour remains a central challenge in condensed matter physics, with implications for exotic quantum phases and the possibility of high-temperature superconductivity.

This research addresses limitations in previous investigations by developing and implementing efficient thermal simulations based on the stochastic variational quantum Monte Carlo method, providing a detailed characterization of the ground state and low-energy excitations of the composite Fermi liquid. Composite fermions, emergent quasiparticles of an electron with two magnetic flux quanta, can experience zero net magnetic field and form a Fermi sea, known as the composite Fermi liquid (CFL). Despite its seemingly simple appearance, the CFL is a strongly correlated quantum many-body state, and solving it accurately remains extremely difficult. Consequently, the thermodynamic properties of the CFL are largely unknown. Researchers perform state-of-the-art thermal tensor network simulations on systems mimicking specific conditions, revealing low-temperature power-law behaviour and providing new insights into the complex nature of composite fermions and their associated Fermi liquid state.

Finite Size Effects and Thermodynamic Data

This supplementary material provides a thorough analysis supporting a study of Composite Fermi Liquids (CFLs), consisting of detailed derivations and additional data that strengthen the conclusions of the main text. The document demonstrates a strong awareness of limitations and provides context for the results, with a particularly well-executed explanation of how the temperature cutoff is determined. Figures are well-labeled and the document is well-structured with a logical flow. The supplementary material consists of two main sections: a mathematical derivation of how a general two-body interaction is projected onto the Lowest Landau Level (LLL) basis, forming the foundation of the model used in the simulations, and additional thermodynamic data obtained from simulations.

This data includes charge compressibility, which drops to zero at low temperatures due to finite-size effects, and guiding-center density correlation, demonstrating power-law behaviour consistent with Fermi-liquid theory. The extracted exponent converges to 3 at low temperatures, and the effect of varying the interaction range is also investigated. Overall, this is an excellent supplementary materials document, thorough, well-written, and providing strong support for the conclusions of the main text. The inclusion of detailed derivations and additional data demonstrates a high level of scientific rigor, and the acknowledgement of finite-size effects is commendable.

Composite Fermions Exhibit Non-Fermi Liquid Behaviour

The research presents evidence that the composite Fermi liquid (CFL) state, formed in a two-dimensional electron gas subjected to a strong magnetic field, behaves as a metallic state but deviates from the properties expected of a conventional Fermi liquid. Specifically, the team observed a temperature dependence in the specific heat that follows a power law, indicating a gapless nature and suggesting interactions between composite fermions and an emergent gauge field. This finding demonstrates that the CFL is not simply a collection of independent particles, but a strongly correlated state where interactions significantly alter its behaviour. The simulations, conducted using advanced thermal tensor network methods, explicitly demonstrate the thermodynamic formation of this non-Fermi-liquid state, building upon previous numerical results and providing a clearer understanding of the complex interactions within the CFL.