Related papers: Response Function of the Fractional Quantized Hall…
Opposite spin Landau levels in a quantum well can be brought into coincidence by tilting the magnetic field away from normal orientation. We demonstrate that the magnetotransport anomaly at integer filling factors that was recently…
In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct…
It is shown, with the help of exact diagonalization studies on systems with up to sixteen electrons, in the presence of up to two delta function impurities, that the Pfaffian model is inadequate for the actual quasiholes and quasiparticles…
The robustness of fractional quantum Hall states is measured as the energy gap separating the Laughlin ground-state from excitations. Using thermodynamic approximations for the correlation functions of the Laughlin state and the quasihole…
We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb…
The true nature of the lowest-energy, long-wavelength neutral excitation of the fractional quantum Hall effect has been a long outstanding problem. In this Letter, we establish that it is a two-roton bound state.
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 present scanning optical stroboscopic confocal microscopy and spectroscopy measurements wherein three degrees of freedom, namely energy, real-space, and real-time, are resolvable. The edge-state propagation is detected as a temporal…
Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall…
The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this…
In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the…
In the fractional quantum Hall effect regime we measure diagonal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions,…
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb…
Recently, it was discussed that the $\nu=1/3$ fractional quantum Hall state can be expressed by a one-dimensional lattice model with an exact matrix-prduct ground state, when toroidal boundary conditions are assumed for a narrow strip…
Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling factor range in the second Landau level where the states significantly differ from those in the lowest…
Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples [Villegas Rosales {\it et al.}, Phys. Rev. Lett. {\bf 127}, 056801 (2021)] open the…
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence…
It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed…