Composite fermion nonlinear sigma models

Abstract

We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ = π and a corresponding violation of particle-hole symmetric electrical transport σ xy = 1 2 e 2 h . When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.

Coulomb effects in electronic transport

“…[114,115] Optical conductivity has the Drude form for clean systems, which can be traced to the exact cancellation between the self-energy and vertex diagrams. [116,117] Non-zero resistance can be introduced by taking into account Umklapp scattering, [114,118] potential disorder, [116,119,120] or random fluctuations of the fermion-boson coupling [115] inspired by the Sachdev-Ye-Kitaev (SYK) model. [9,121] The absence of quasiparticle excitations is supported be several types of experiments.…”

Emergent QED$_3$ from half-filled flat Chern bands

“…In the N f = 3 theory, PHsymmetric disorder (a random magnetic field component for the electrons) is exactly marginal, leading to a line of fixed points with varying dynamical critical exponent, z > 1. For generic disorder breaking PH, the theory runs to strong disorder and gives way to diffusion (z = 2), leading to a quantum critical point governed by a gauged non-linear sigma model (NLSM) [76,77] which at mean field level resembles Pruisken's theory of the IQH transition [78,79]. Determining the universal properties of NLSMs of this type remains an important open problem.…”

Enhanced magnetism and persistent insulating state in Mn doped Sr2IrO4

“…Besides the Sr site doping, the Ir site doping is also informative to learn the basic properties of Sr 2 IrO 4 . Previously, several transition-metal elements such as Ru, Rh, Sn, Fe, and Co have been utilized for partial substitution at the Ir site of Sr 2 IrO 4 [26][27][28][29]. The impacts on the transport behaviors upon Ir-site doping diverge into two distinct results: the first one is a metallic like behavior in Sr 2 Ir 1−x Ru x O 4 .…”