Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem

Abstract: Motivated by recent experiments on Kondo insulators, we theoretically study quantum oscillations from disorder-induced in-gap states in small-gap insulators. By solving a non-Hermitian Landau level problem that incorporates the imaginary part of electron's self-energy, we show that the oscillation period is determined by the Fermi surface area in the absence of the hybridization gap, and derive an analytical formula for the oscillation amplitude as a function of the indirect band gap, scattering rates, and temperature. Over a wide parameter range, we find that the effective mass is controlled by scattering rates, while the Dingle factor is controlled by the indirect band gap. We also show the important effect of scattering rates in reshaping the quasiparticle dispersion in connection with angle-resolved photoemission measurements on heavy fermion materials.

Quantum Oscillation from In-Gap States and Non-Hermitian Landau Level Problem

This paper investigates the phenomenon of quantum oscillations in disordered small-gap insulators, with particular interest in Kondo insulators such as SmB$_6$ and YbB$_{12}$. The authors approach this by examining disorder-induced in-gap states and employing a non-Hermitian framework to integrate the imaginary component of the electron's self-energy within the Landau level problem. Their analytical results have significant implications for understanding the oscillation period and amplitude in terms of Fermi surface areas, scattering rates, and the indirect band gap.

The study introduces a comprehensive framework for interpreting quantum oscillations in small-gap systems, deviating from the conventional behavior observed in metals. The oscillation period derived in this model is indicative of the underlying Fermi surface geometry, found to be determined by the Fermi surface area in scenarios where the hybridization gap is absent. Furthermore, this work delineates an analytical expression for oscillation amplitude, correlating it with key variables such as scattering rates and temperature. The authors highlight that within a wide spectrum of parameters, the effective mass that influences temperature-dependent oscillation amplitudes is controlled predominantly by these scattering rates, contrary to the more traditional Dingle factor relationships seen in metals.

One of the significant results posited by the authors is the role of scattering rates in modifying quasiparticle dispersion. The imaginary part of electron self-energy contributes to this modification, leading to partial filling of the hybridization gap, thereby generating significant low-energy states inside the gap. This has been corroborated by the paper's theoretical calculations and aligns with experimental findings observed through angle-resolved photoemission spectroscopy (ARPES) in materials such as SmB$_6$.

The application of a non-Hermitian Landau level framework represents an innovative aspect of this study. By integrating the role of imaginary self-energy terms, the research provides a more generalized insight into understanding the damping and broadening effects on quasiparticle levels influenced by disorder. The result showcases how this framework successfully describes Lifshitz-Kosevich (LK) behavior in insulators under certain conditions, lending a quantified approach to predict the quantum oscillation characteristics even in the absence of a conventional Fermi surface due to hybridization effects.

The implications of this research are manifold. Practically, this work offers a quantitative tool to test the effects of disorders in small-gap insulators, with predictions that can assist in refining and comparing experimental photoemission data to better understand quasiparticle lifetimes and associated conduction phenomena in these materials.

Theoretically, this paradigm shift towards embracing non-Hermitian physics within condensed matter challenges traditional views on quantum oscillations, enabling a cohesive understanding across materials with significant impurity scattering and hybridization. Future developments in artificial quantum systems, particularly in tailored disordered environments, can draw upon these findings to examine complex oscillatory behaviors beyond conventional settings.

In considering future research directions, exploring the disorder-induced semimetallic phase detailed by the authors may provide even deeper insights into the crossover behavior between insulating and metallic states in complex, multi-band systems. Furthermore, extending this treatment to three-dimensional models and other topological phases could reveal additional universalities within the non-Hermitian context.

This paper provides a robust analytical treatment that adds a significant dimension to our comprehension of quantum dynamics in disordered small-gap insulators, setting a path for continued exploration in both experimental validations and theoretical advances.