Nonlinear Quantum Hall effects in Rarita-Schwinger gas

TL;DR

This paper investigates the unique quantum Hall effects in a (2+1)-dimensional Rarita-Schwinger gas, revealing non-plateau quantized conductance, nonlinear Landau level dependence, and magnetic field-induced instabilities due to higher spin relativistic fermions.

Contribution

It introduces the anomalous Hall effects in Rarita-Schwinger gases, highlighting their deviation from traditional quantum Hall paradigms and analyzing the effects of non-hermitian Hamiltonians.

Findings

Hall conductance is step-like but not quantized

Hall plateaus depend nonlinearly on Landau levels

Higher Landau levels become unstable beyond a critical magnetic field

Abstract

Emergence of higher spin relativistic fermionic materials becomes a new favorite in the study of condensed matter physics. Massive Rarita-Schwinger 3/2-spinor was known owning very exotic properties, such as the superluminal fermionic modes and even being unstable in an external magnetic field. Due to the superluminal modes and the non-trivial constraints on the Rarita-Schwinger gas, we exposit anomalous properties of the Hall effects in (2+1)-dimensions which subvert the well-known quantum Hall paradigms. First, the Hall conductance of a pure Rarita-Schwinger gas is step-like but not plateau-quantized, instead of the linear dependence on the filling factor for a pure spin-1/2 Dirac gas. In reality, the Hall conductance of the Dirac gas is of quantized integer plateaus with the unit $\frac{e^2}h$ due to the localization away from the Landau level centers. If the general localization rule is applicable to the disordered Rarita-Schwinger gas, the Hall plateaus are also expected to appear but they are nonlinearly dependent on the Landau level index. Furthermore, there is a critical magnetic field beyond which higher Landau levels become unstable. This confines the filling factor of the system. We also show that the non-hermitness of the effective Hamiltonian is not crucial to the nonlinearity of the quantum Hall conductance.