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تسجيل مستخدم جديدTowards identification of a non-abelian state: observation of a quarter of electron charge at $ u=5/2$ quantum Hall state
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The fractional quantum Hall effect, where plateaus in the Hall resistance at values of coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows along the edges carried by charged excitations (quasi particles) whose charge is a fraction of the electron charge. While earlier research concentrated on odd denominator fractional values of $ u$, the observation of the even denominator $ u=5/2$ state sparked a vast interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics is non-abelian. In other words, interchanging of two quasi particles may modify the state of the system to an orthogonal one, and does not just add a phase as in for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data of shot noise generated by partitioning edge currents in the $ u=5/2$ state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other potentially possible values, such as e/2 and e. While not proving the non-abelian nature of the $ u=5/2$ state, this observation is the first step toward a full understanding of these new fractional charges.
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We analyze charge-$e/4$ quasiparticle tunneling between the edges of a point contact in a non-Abelian model of the $ u=5/2$ quantum Hall state. We map this problem to resonant tunneling between attractive Luttinger liquids and use the time-dependent
density-matrix renormalization group (DMRG) method to compute the current through the point contact in the presence of a {it finite voltage difference} between the two edges. We confirm that, as the voltage is decreases, the system is broken into two pieces coupled by electron hopping. In the limits of small and large voltage, we recover the results expected from perturbation theory about the infrared and ultraviolet fixed points. We test our methods by finding the analogous non-equilibrium current through a point contact in a $ u=1/3$ quantum Hall state, confirming the Bethe ansatz solution of the problem.
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We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $ u=5/2$. Our studies are performed using both exact diagonalization a
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