Abstract
In this chapter we use ‘soft-wall’ boundary confinement, that is, a potential profile with finite slope, to induce charge current controllability in a two-terminal transport setup. In particular, the isolation of energetically persistent scattering pathways from the resonant manifold of an elongated electron billiard in the deep quantum regime is demonstrated. This in turn enables efficient conductance switching at varying temperature and Fermi velocity , using a weak magnetic field. The effect relies on the interplay between the elongated soft-wall confinement and magnetic focusing , which together rescale the scattering pathways and decouple quasi-bound states from the attached leads. The mechanism proves robust against billiard shape variations and qualifies as a nanoelectronic current control element. Excerpts and figures from Morfonios and Schmelcher (Phys. Rev. Lett. 113(8):086802, 2014) reprinted with permission. Copyright (2014) by the American Physical Society.
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Notes
- 1.
Note that the switching here is the opposite to that of Chap. 6, where the zero-field conductance was suppressed and raised by the field: we here have the on-state of the switch in absence of the field, and the off-state for finite field strength.
- 2.
For the κ- and B-ranges plotted in Fig. 7.4, only the bundles demarcating the very lowest Landau levels are clearly discernible (e.g. l = 2, 3); they become fainter with increasing κ at fixed low B because of the participation of an increasing number of crossing or anticrossing levels which obscure the structure of the spectrum (see, e.g., l = 4, 5, 6).
- 3.
The level diagram here strongly resembles the original Darwin-Fock spectrum , since at such low energy the wave function poorly resolves the difference of the used confinement from a parabolic one. The resulting nearly exact multilevel crossings have been studied experimentally for two [22] and three [23] mixing levels which can coherently form a ‘dark’ state (complete cancellation of resonance amplitude).
- 4.
Note that for B = 0 only odd → odd or even → even mode transitions survive due to the conserved x-parity of the stationary scattering eigenstates (as evident, e.g., from Fig. 7.5a).
- 5.
This estimate gives a fairly accurate account of the transport properties relevant for switching for the billiard shape and soft-wall used so far, since the background transmission is practically constant at B = 0, B s . This holds also in the immediate vicinity of this setup in parameter space. If the shape is drastically modified, however, \(\overline{T}\) is a rough estimate and the actual background variation in T(κ) (and the corresponding conductance) for every individual case should be considered to conclude on energy-dependent switching contrast; this is done here for sample soft-wall profiles.
- 6.
In [25], a magnetoresistance resonance is caused by cascading of similar backscattered states in an array of smaller billiards (relative to lead openings) with a different kind of soft-wall potential; this resonant property occurs at very low temperature and is attributed to classical dynamics through a parabolic model potential. In [26], the same peak is attenuated for a single billiard, and another peak appears for B = 0, lowering switching efficiency. This is in contrast to the mechanism proposed here which relies on decoupling of resonances from an efficiently switchable, energetically robust scattering continuum of a single billiard.
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Morfonios, C.V., Schmelcher, P. (2017). Current Control in Soft-Wall Electron Billiards: Energy-Persistent Scattering in the Deep Quantum Regime. In: Control of Magnetotransport in Quantum Billiards. Lecture Notes in Physics, vol 927. Springer, Cham. https://doi.org/10.1007/978-3-319-39833-4_7
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