Related papers: A general approach to quantum Hall hierarchies
Nature of the fractional quantum Hall state at Landau level filling factor 5/2 remains elusive despite intensive experimental and theoretical work. While the leading theoretical candidates are Moore-Read Pfaffian (Pf) and its particle-hole…
Quantum geometry is a fundamental concept to characterize the local properties of quantum states. It is recently demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features…
Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works…
The Jain theory of hierarchical Hall states is reconsidered in the light of recent analyses that have found exact relations between projected Jain wavefunctions and conformal field theory correlators. We show that the underlying conformal…
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured…
Analyzing the effective conformal field theory for the parafermionic Hall states, corresponding to filling fractions nu_k=2+k/(kM+2), k=2,3,..., M odd, we show that the even k plateaux are expected to be more stable than their odd k…
We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers.…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free…
Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological orders. However, the topological order of these states remains hotly debated.…
Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and…
The recent measurement of a half-integer thermal conductance for the $\nu=5/2$ fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the…
We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved…
The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this…
Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
We identify some hidden symmetries of Chern-Simons theories, such as appear in the effective theory for quantized Hall states. This allows us to determine which filling fractions admit spin-singlet quantum Hall states. Our results shed some…
In this thesis, I will present studies on the collective modes of the fractional quantum Hall states, which are bulk neutral excitations reflecting the incompressibility that defines the topological nature of these states. It was first…
We formulate a field theory for a class of spin-singlet quantum Hall states (the Haldane-Rezayi state and its variants) which have been proposed for the quantized Hall plateaus observed at the second lowest Landau level. A new essential…
Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…
Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula $\rho_{xy} = h/e^2\nu$ from first principles has remained elusive. In this work, we revisit the Landau and…