Quantum Hall antidot

A depleted potential hill inside a two-dimensional electron gas. In a strong perpendicular magnetic field, closed quantum Hall edge states circulate around it. Coupling these states to propagating edge channels can produce resonant backscattering; Coulomb blockade can substantially alter the single-particle resonance pattern.

A quantum dot is an electron-confining potential well, whereas an antidot is a depleted potential hill. At the same magnetic field, their closed guiding-centre drift has opposite circulation. A series dot needs transmission through two barriers; a side-coupled antidot can connect already propagating quantum Hall edge states and induce backscattering. Both can have discrete energies and charging effects, but a electrical conductance peak or dip depends on lead connectivity rather than solely on the existence of a closed orbit.

A closed antidot edge orbit can tunnel-couple extended channels on opposite edges. When its electrochemical energy aligns with the reservoirs, resonant backscattering reduces conductance from an otherwise transmitting integer plateau. Different connectivity can instead add a transmission path and produce peaks. Gate voltage changes both the orbit and tunnel couplings; charging and spin alter the simplest fixed-area Aharonov-Bohm resonance sequence.

A spin-resolved resonant path adds at most $e^2/h$ to the electrical conductance of directly transmitted spectator channels. Conversely, resonant transfer into a returning edge removes at most $e^2/h$ from an otherwise open channel. For an isolated level, $T(E)={\Gamma }_L{\Gamma }_R/[(E-{ϵ}_d{)}^2+({\Gamma }_L+{\Gamma }_R{)}^2/4]$ reaches one only for equal couplings. Integer offsets follow the channel connectivity and do not follow from a local filling factor alone. temperature, asymmetry, coherent background paths and inelastic processes can change the apparent resonance height and shape.

In an integer-filling charging model, $f$ occupied spin-resolved branches can drive approximately $f$ charge rearrangements per added $h/e$ flux. Two coupled spin branches can therefore yield near-$h/(2e)$ oscillations. This does not change the elementary single-electron flux quantum and is not guaranteed by counting two independent noninteracting spin spectra alone.

For a fixed effective enclosed area $S$, changing the magnetic flux by $h/e$ changes the single-electron Aharonov-Bohm phase by $2\pi$. Gate-dependent orbit area, spin branches and charging can modify the observed conductance-resonance pattern; the lithographic depleted area need not equal the exact enclosed edge-orbit area.