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Register a new userElectronic wave-packets in integer quantum Hall edge channels: relaxation and dissipative effects
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We theoretically investigate the evolution of the peak height of an energy resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor $ u=2$. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energy. We investigate this quantity assuming a short range capacitive coupling between the edges. Moreover, we also take into account phenomenologically the possibility of energy dissipation towards additional degrees of freedom both linear and quadratic in the injection energy. Comparing with recent experimental data, we rule out the non-dissipative case as well a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate to describe the behavior of the quasi-particle peak at short enough propagation lengths.
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A theoretical study of the single electron coherence properties of Lorentzian and rectangular pulses is presented. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose charge and shape reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.
Charge equilibration between quantum-Hall edge states can be studied to reveal geometric structure of edge channels not only in the integer quantum Hall (IQH) regime but also in the fractional quantum Hall (FQH) regime particularly for hole-conjugate states. Here we report on a systematic study of charge equilibration in both IQH and FQH regimes by using a generalized Hall bar, in which a quantum Hall state is nested in another quantum Hall state with different Landau filling factors. This provides a feasible way to evaluate equilibration in various conditions even in the presence of scattering in the bulk region. The validity of the analysis is tested in the IQH regime by confirming consistency with previous works. In the FQH regime, we find that the equilibration length for counter-propagating $delta u $ = 1 and $delta u $ = -1/3 channels along a hole-conjugate state at Landau filling factor $ u $ = 2/3 is much shorter than that for co-propagating $delta u $ = 1 and $delta u $ = 1/3 channels along a particle state at $ u $ = 4/3. The difference can be associated to the distinct geometric structures of the edge channels. Our analysis with generalized Hall bar devices would be useful in studying edge equilibration and edge structures.
Since the charged mode is much faster than the neutral modes on quantum Hall edges at large filling factors, the edge may remain out of equilibrium in thermal conductance experiments. This sheds light on the observed imperfect quantization of the thermal Hall conductance at $ u=8/3$ and can increase the observed thermal conductance by two quanta at $ u=8/5$. Under certain unlikely but not impossible assumptions, this might also reconcile the observed thermal conductance at $ u=5/2$ with not only the PH-Pfaffian order but also the anti-Pfaffian order.
A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor u=2, with results that account well for the observations.
We report time-of-flight measurements on electrons travelling in quantum-Hall edge states. Hot-electron wave packets are emitted one per cycle into edge states formed along a depleted sample boundary. The electron arrival time is detected by driving a detector barrier with a square wave that acts as a shutter. By adding an extra path using a deflection barrier, we measure a delay in the arrival time, from which the edge-state velocity $v$ is deduced. We find that $v$ follows $1/B$ dependence, in good agreement with the $vec{E} times vec{B}$ drift. The edge potential is estimated from the energy-dependence of $v$ using a harmonic approximation.
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