scholarly journals Impurities and Landau level mixing in a fractional quantum Hall state in a flat-band lattice model

2014 ◽  
Vol 90 (16) ◽  
Author(s):  
Topi Siro ◽  
Mikko Ervasti ◽  
Ari Harju
Keyword(s):  
Landau Level ◽  
Lattice Model ◽  
Quantum Hall ◽  
Flat Band ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Landau Level Mixing ◽  
Quantum Hall State

scholarly journals Pfaffian paired states for half-integer fractional quantum Hall effect

2020 ◽  
Vol 34 (21) ◽  
pp. 2030004
Author(s):  
M. V. Milovanović ◽  
S. Djurdjević ◽  
J. Vučičević ◽  
L. Antonić
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Perturbative Approach ◽  
Fractional Quantum Hall ◽  
Half Integer ◽  
Landau Level Mixing

In this review, the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ([Formula: see text]-wave) Cooper pairing and are characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian and anti-Pfaffian are selected when Landau level mixing is not strong, and can be taken into account perturbatively, the particle–hole (PH) Pfaffian state requires non-perturbative inclusion of at least two Landau levels. Our findings, for small Landau level mixing, are in accordance with numerical investigations in the literature, and call for a non-perturbative approach in the search for PH Pfaffian correlations. We demonstrated that a method based on the Chern–Simons field-theoretical approach can be used to generate characteristic interaction pseudo-potentials for Pfaffian paired states.

scholarly journals Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
K. A. Villegas Rosales ◽  
S. K. Singh ◽  
Meng K. Ma ◽  
Md. Shafayat Hossain ◽  
Y. J. Chung ◽  
...  
Keyword(s):  
Layer Thickness ◽  
Landau Level ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Wigner Solid ◽  
Landau Level Mixing
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