Interaction phenomena in graphene seen through quantum capacitance

Abstract: Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-quality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron-electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.

• The paper demonstrates that quantum capacitance measurements reveal strong many-body interactions in graphene with renormalized Fermi velocities.
• The study employs high-quality graphene capacitors supported by hBN to accurately map the density of states in both zero and finite magnetic fields.
• Interaction-induced phenomena such as Landau level splitting and negative compressibility provide evidence for novel quantum states in graphene.

Quantum Capacitance and Interaction Phenomena in Graphene

The paper entitled "Interaction phenomena in graphene seen through quantum capacitance" presents an insightful examination of the quantum capacitance in graphene, focusing on how interaction effects manifest in the material's density of states (DoS) in both zero and finite magnetic fields. The study utilizes large-area, high-quality graphene capacitors that offer a refined look at the many-body phenomena occurring within this robust two-dimensional material.

The authors have extensively leveraged capacitance measurements, a technique useful for investigating electron systems' DoS, to probe interaction effects in graphene. The unique properties of graphene, which include its Dirac-like spectrum and the substantial ratio between kinetic and Coulomb energies, result in a strong relativistic-like coupling regime. This is characterized by interactions that significantly renormalize the Fermi velocity around the Dirac point.

In non-quantizing magnetic fields, a clear renormalization of the linear spectrum due to electron-electron interactions is observed, which analogously plays a significant role in quantum field theory. Under high magnetic fields, the study reports an interaction-induced splitting of the Landau levels. This results in quartets with interaction-enhanced energy gaps that, at specific filling factors, form many-body states exhibiting negative compressibility. However, intriguingly, this compressibility transitions back to positive values at ultrahigh magnetic fields, which the authors attribute to a complex interplay between field-enhanced interactions and emerging fractional states.

The experimental structure consists of graphene layers supported by hexagonal boron nitride (hBN), substantially reducing charge inhomogeneity and allowing pronounced quantum oscillations in magnetic fields as low as 1 T. This setup has enabled accurate measurements of the DoS, which reveals the expected vF renormalization in zero fields and interaction-induced states at finite fields. The authors identify additional gaps at filling factors ν = 0 and ±1, supporting the SU(4) isospin symmetry model proposed for graphene—which have substantive analogies in theories involving strongly correlated electron systems.

The negative compressibility is particularly noteworthy and presents evidence of interaction effects in graphene that are not typical of conventional two-dimensional systems. Typically, potential energy scaling as n versus the kinetic energy scaling as n^1/2 in traditional systems leads to negative compressibility at low carrier concentrations. In contrast, both energies in graphene scale as n, indicating uniqueness in the observation of negative compressibility—a phenomenon likely enabled by quantizing magnetic fields.

From a methodological perspective, the analysis employed several capacitance measurement techniques to ascertain the energy gaps at various filling factors, yielding consistent results that emphasize many-body interactions, akin to fractional quantum Hall effects observed in other systems.

The research implications are multifaceted. The findings enhance our understanding of many-body physics specific to graphene, broadening the theoretical approaches that tackle problems within quantum field theory and condensed matter physics. The identification of negative compressibility and fractional quantum Hall effects indicates promising future exploration directions, potentially informing novel electronic and quantum computing applications. Understanding how interaction effects modify electron behavior in graphene could pave the way for advanced materials engineering, particularly in systems reliant on low-dimensional physics. Future studies may explore the role of other materials in modifying these unique attributes, or explore higher-dimensional adaptative structures derived from the properties illustrated within this work on graphene.