Related papers: Novel method distinguishing between competing topo…
We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for…
The existence of edge states and zero energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed matter systems such as the fractional quantum Hall states, p+ip superconductors, and Z_2…
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 ($p$-wave) Cooper pairing and are…
Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…
In this paper we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to…
The $\nu = 2/3$ fractional quantum Hall state is the hole-conjugate state to the primary Laughlin $\nu = 1/3$ state. We investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure…
It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate…
Topological insulators can be generally defined by a topological field theory with an axion angle theta of 0 or pi. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that…
We consider a non-Abelian candidate state at filling factor $\nu=3/7$ state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e. at filling factor $\nu=2+3/7$), this state is energetically superior to the…
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…
We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the…
Recent theoretical insights into the possibility of non-Abelian phases in $\nu=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body…
We perform numerical studies to determine if the fractional quantum Hall state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space approach we…
We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall…
While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to…
The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the…
Strongly interacting electrons in a topologically non trivial band may form exotic phases of matter. An especially intriguing example of which is the fractional quantum anomalous Hall phase, recently discovered in twisted transition metal…
We compute the backscattered current in a double point-contact geometry of a Quantum Hall system at filling fraction $\nu=5/2$ as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality…
The edge of spin unpolarized or spin polarized $\nu=2/3$ fractional quantum Hall states is predicted by the effective theory to support a backward moving neutral mode in addition to a forward moving charge mode. We study this issue from a…
The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is…