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Register a new userOrbital Kondo effect in fractional quantum Hall systems
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We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $ u=1$ or fractional $ u=1/3$ quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $ u=1/3$ fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $ u=1$ and $ u=1/3$.
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We investigate the non-universal part of the orbital entanglement spectrum (OES) of the nu = 1/3 fractional quantum Hall effect (FQH) ground-state with Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the Laughlin model state OES whose level counting is completely determined by its topological order. We find that the OES levels of the Coulomb interaction ground-state are organized in a hierarchical structure that mimic the excitation-energy structure of the model pseudopotential Hamiltonian which has a Laughlin ground state. These structures can be accurately modeled using Jains composite fermion quasihole-quasiparticle excitation wavefunctions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also consider the thermodynamical OES of the model pseudopotential Hamiltonian at finite temperature. The observed good match between the thermodynamical OES and the Coulomb OES suggests a relation between the entanglement gap and the true energy gap.
We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd(1-x)Mn(x)Te. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around filling factor v = 3/2 as a function of an in-plane magnetic field, i.e. of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor 5/3 can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a novel means to manipulate fractional states.
A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors v = N/M = 1(2m+1). Within this model the complimentary wavefunction for v = 1-1/(2m + 1) is found explicitly and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.
The entanglement entropy of the $ u = 1/3$ and $ u = 5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a clear signature of a transition as a function of the disorder strength for the $ u = 5/2$ state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.
Local excitations in fractional quantum Hall systems are amongst the most intriguing objects in condensed matter, as they behave like particles of fractional charge and fractional statistics. In order to experimentally reveal these exotic properties and further to use such excitations for quantum computations, microscopic control over the excitations is necessary. Here we discuss different optical strategies to achieve such control. First, we propose that the application of a light field with non-zero orbital angular momentum can pump orbital angular momenta to electrons in a quantum Hall droplet. In analogy to Laughlins argument, we show that this field can generate a quasihole or a quasielectron in such systems. Second, we consider an optical potential that can trap a quasihole, by repelling electrons from the region of the light beam. We simulate a moving optical field, which is able to control the position of the quasihole. This allows for imprinting the characteristic Berry phase which reflects the fractional charge of the quasihole.
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