Quasiparticle Tunneling and High Bias Breakdown in the Fractional Quantum Hall Effect
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CitationDillard, Colin. 2012. Quasiparticle Tunneling and High Bias Breakdown in the Fractional Quantum Hall Effect. Doctoral dissertation, Harvard University.
AbstractThe integer and fractional quantum Hall eﬀects arise in two-dimensional electron systems subject to low temperature and high perpendicular magnetic ﬁeld. The phenomenology of these two eﬀects is rich and provides interesting insight into quantum physics. We present two experimental studies of phenomena in the fractional quantum Hall regime. The ﬁrst examines the tunneling conductance of quasiparticles at ﬁlling factor 5/2. This state is of signiﬁcant interest because it lies outside the traditional Jain hierarchy of fractional quantum Hall states and because it may be the ﬁrst physical system found to exhibit non-abelian particle statistics. A quantum point contact is used to bring edge states on opposite sides of the system in proximity to each other, allowing quasiparticles to tunnel between the edge states. By annealing the gates forming the quantum point contact at diﬀerent voltages we control the tunneling strength for ﬁxed temperature and bias. We demonstrate a transition from strong to weak tunneling controlled in this manner. In the weak tunneling regime, the DC bias and temperature dependence of the tunneling conductance is ﬁt to a theoretical form, resulting in values for the quasiparticle charge \(e*\) and the interaction parameter \(g\). The values of these parameters are used to help distinguish between proposed candidate states for the 5/2 wave function. Quantitative and qualitative results are most consistent with the abelian 331 state. Our second main focus is the breakdown of the fractional quantum Hall states at ﬁlling factors 4/3 and 5/3. Breakdown of integer and fractional quantum Hall states is known to occur when the Hall and longitudinal resistances deviate from their ideal values at nonzero critical currents. Although multiple studies of breakdown in the integer quantum Hall regime have been reported, corresponding results for the fractional regime are scarce. We observe breakdown over a range of integer states that is consistent with previous results. However, breakdown in the fractional regime is found to exhibit markedly diﬀerent behavior. In particular, the magnitude of the critical current decreases with increased sample width. This behavior is opposite that observed for integer ﬁlling factors and does not seem to be explicable based on current theories of breakdown.
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