Fractionally Charged Zero-Energy Single-Particle Excitations in a Driven Fermi Sea

Abstract

A voltage pulse of a Lorentzian shape carrying a half of the flux quantum excites out of a zerotemperature 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. Introduction.-Recent realization of a triggered singleelectron source [1-10] opens a new era for a coherent electronics [11][12][13][14][15][16][17][18] by allowing it to go quantum much like a quantum optics. The analogues of the famous quantum optics effects were successfully demonstrated with single electrons in solid state circuits such as partitioning of electrons [7,[19][20][21] in Hanbury-Brown and Twiss geometry and quantum-statistical repulsion of electrons [7,22] in Hong-Ou-Mandel geometry. Tomography of a singleelectron state [23] and a preparation of few-electron Fock states [20,24,25] are already reported.

Levitons for electron quantum optics

“…, the nature of half‐integer Lorentzian charge pulses has been studied and it has been shown that they can form remarkable fractionally charged zero‐energy single‐particle excitations states. Separating the half‐leviton into a charge part and its accompanying neutral electron–hole cloud, showed that half‐levitons and antihalf‐levitons mixed in a semi‐transparent electronic beam‐splitter can elastically annihilate. This property is not shared with ordinary distinguishable electron and hole excitations.…”

On-demand electron source with tunable energy distribution

“…which cannot exist without the presence of electron-hole excitation. 15 These works demonstrate the possibility of manipulating electron-hole excitation via engineering the temporal profile of the voltage pulse. In contrast, if the thermal transport is concerned, 16-23 the electron-hole excitation are favorable, since they carry a finite amount of energy, while do not affect the average charge transport.…”

Heat and charge transport measurements to access single‐electron quantum characteristics

“…This linear property of the correlation functions can be used, for example, to separate out a single-particle contribution from the multi-particle one, see, for example, Ref. [72]. F.1.2 Single-particle incoming states When the sources emit single particles in a pure state, we have G (1) γ (t 1 ; t 2 ) = Ψ * γ (t 1 )Ψ γ (t 2 ), γ = 1, 2.…”