Coherent electron focusing with quantum point contacts in a two-dimensional electron gas

Abstract

Transverse electron focusing in a two-dimensional electron gas is mvestigated expenmentally and theoretically for the flrst time. A split Schottky gate on top of a GaAs-Al x Ga,_^As heterostructure defines two point contacts of variable width, which are used äs mjector and collector of ballistic electrons As evidenced by their quantized conductance, these are quantum point contacts with a width comparable to the Fermi wavelength At low magnetic flelds, skipping orbits at the electrongas boundary are directly observed, thereby establishing that boundary scattenng is highly specular Large additional oscillatory structure in the focusing spectra is observed at low temperatures and for small pomt-contact size This new phenomenon is mterpreted in terms of mterference of coherently excited magnetic edge states m a two-dimensional electron gas A theory for this effect is given, and the relation with nonlocal resistance measurements in quantum ballistic transport is discussed It is pomted out, and expenmentally demonstrated, that four-termmal transport measurements m the electron-focusmg geometry constitute a determmation of either a generalized longitudmal resistance or a Hall resistance At high magnetic fields the electron-focusmg peaks are suppressed, and a transition is observed to the quantum Hall regime The anomalous quantum Hall effect m this geometry is discussed m light of a four-termmal resistance formula

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

“…Naturally, the energy of the LLs depends on the cyclotron orbit alone, and thus it is independent of the size and shape of the dot. But also, this size-and-shape independence is shared to a large degree 61 by the Halperin-type edge states between LLs, 38 whose energy can be derived (to the lowest order) from a semiclassical or WKB quantization of a single arc of the skipping orbits, both for nonrelativistic [41][42][43] and Dirac electrons. 53 Of interest for the present study are the AharonovBohm-type refinements concerning the Halperin-type edge states investigated [44][45][46][47] for the case of SQDs.…”

“…[35][36][37] Nevertheless important theoretical studies concerning topological aspects of nonrelativistic electrons in finite systems under strong magnetic fields have been performed by assuming hard-wall boundaries. Well known among such studies are the investigations [38][39][40][41][42][43] (initiated by Halperin 38 ) regarding the edge states related to the integer-quantum-Hall-effect (IQHE) and those [44][45][46][47] (initiated by Sivan and Imry 44 ) on the Aharonov-Bohm (AB) oscillations which are superimposed on the de Haas -van Alphen (dHvA) oscillations. Halperin introduced a hard boundary through an infinite-box-type confining potential, while Sivan and Imry used a 10 × 10 square-lattice tight-binding (TB) model.…”

Interference Effects in a Tunable Quantum Point Contact Integrated with an Electronic Cavity

“…Soon after the first observation of quantized conductance in a quasi-one-dimensional (1D) quantum wire [19,20], a number of interesting observations have been made such as the "0.7 structure" [21], incipient Wigner lattice [22,23], coherent electron focusing [24][25][26], etc. Experiments of coupling between a QPC, which provides a stream of collimated 1D electrons, and a waveguide [15] and that between a quantum dot and cavity [16] have been performed, where a pronounced modulation of conductance of the system and changing of Coulomb peaks were observed.…”

Quantum Point Contacts and Coherent Electron Focusing

“…Point contacts can also be used to inject a divergent beam of ballistic electrons in the 2DEG. The focusing of such a beam by a transverse magnetic field, acting äs a lens, has been demonstrated in an electron focusing experiment [8,9]. *A 2DEG is a degenerate electron gas which is strongly confined in one direction by an electrostatic potential well at the Interface between two semiconductors, such that only the lowest quantum level in the well is occupied.…”

“…[From Ref. 6] The boundary of the 2DEG, also defined by means of a gate, acts äs a high quality mirror, causing specular boundary scattering [8,9]. For sufficiently large gate voltages the point contact width is smaller than the Fermi wavelength of the electrons.…”