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Half-levitons -- zero-energy excitations of a driven Fermi sea

A voltage pulse of a Lorentzian shape carrying a half of the flux quantum excites out of a zero-temperature Fermi sea an electron in a mixed state, which looks like a quasi-particle with an effectively fractional charge $e/2$. A prominent feature of such an excitation is a narrow peak in the energy distribution function laying exactly at the Fermi energy $ μ$. Another spectacular feature is that the distribution function has symmetric tails as above as below $ μ$, which results in a zero energy of an excitation. This sounds improbable since at zero temperature all available states below $ μ$ are fully occupied. The resolution is lying in the fact that such a voltage pulse excites also electron-hole pairs which free some space below $ μ$ and thus allow a zero-energy quasi-particle to exist. I discuss also how to address separately electron-hole pairs and a fractionally charged zero-energy excitation in experiment.