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Register a new userNoncommutative Quantum Hall Effect and Aharonov-Bohm Effect
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We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a transformation from the noncommutative coordinates to a set of commuting coordinates and then we write the Hamiltonian for this system. The energy spectrum and the expectation value of the current can then be calculated and the Hall conductivity can be extracted. We use the same method to calculate the phase shift for the Aharonov-Bohm effect. Precession measurements could allow strong upper limits to be imposed on the noncommutativity coordinate and momentum parameters $Theta$ and $Xi$.
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We discuss the quantum Hall effect on a single-layer graphene in the framework of noncommutative (NC) phase space. We find it induces a shift in the Hall resistivity. Furthermore, comparison with experimental data reveals an upper bound on the magnitude of the momentum NC parameter $eta$ in about $sqrt{eta}leq 2.5 , mathrm{eV}/c$.
We study the theory of Jackiw-Teitelboim gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the two-dimensional manifold. We show that this theory can be written as the ordinary quantum mechanics of a charged particle on a hyperbolic disk in the presence of a constant background magnetic field plus a pure gauge Aharonov-Bohm field. This picture allows us to exactly calculate the wavefunctions and propagators of the corresponding gravitational dynamics. With this method we are able to reproduce the gravitational density of states as well as compute the Reyni and entanglement entropies for the Hartle-Hawking state. While we reproduce the classical entropy at high temperature, we also find an extra topological contribution that becomes dominant at low temperatures. We then show how the presence of defects modify correlation functions, including the out-of-time-ordered correlation, and decrease the Lyapunov exponent. This is achieved two ways: by directly quantizing the boundary Schwarzian theory and by dimensionally reducing $SL(2,mathbb{Z})$ black holes.
Quantum interferometers are powerful tools for probing the wave-nature and exchange statistics of indistinguishable particles. Of particular interest are interferometers formed by the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) that guide electrons without dissipation. Using quantum point contacts (QPCs) as beamsplitters, these 1D channels can be split and recombined, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can be used for studying exchange statistics of anyonic quasiparticles. In this study we develop a robust QHI fabrication technique in van der Waals (vdW) materials and realize a graphene-based Fabry-Perot (FP) QHI. By careful heterostructure design, we are able to measure pure Aharonov-Bohm (AB) interference effect in the integer QHE, a major technical challenge in finite size FP interferometers. We find that integer edge modes exhibit high visibility interference due to relatively large velocities and long phase coherence lengths. Our QHI with tunable QPCs presents a versatile platform for interferometer studies in vdW materials and enables future experiments in the fractional QHE.
We have investigated experimentally resonant tunnelling through single-particle states formed around an antidot by a magnetic field, in the fractional quantum Hall regime. For 1/3 filling factor around the antidot, Aharonov-Bohm oscillations are observed with the same magnetic field period as in the integer quantum Hall regime. All our measurements are consistent with quasiparticles of fractional charge e*. However, the results are also consistent with particles of any charge (>= e*) as the system must rearrange every time the flux enclosed increases by h/e.
The phase of the wave function of charged matter is sensitive to the value of the electric potential, even when the matter never enters any region with non-vanishing electromagnetic fields. Despite its fundamental character, this archetypal electric Aharonov-Bohm effect has evidently never been observed. We propose an experiment to detect the electric potential through its coupling to the superconducting order parameter. A potential difference between two superconductors will induce a relative phase shift that is observable via the DC Josephson effect even when no electromagnetic fields ever act on the superconductors, and even if the potential difference is later reduced to zero. This is a type of electromagnetic memory effect, and would directly demonstrate the physical significance of the electric potential.
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