Quantum Hall Fabry–Pérot interferometer: Logic gate responses

Abstract

Scanning Fabry-Pérot interferometer with largely tuneable free spectral range for high resolution spectroscopy of single quantum dots Rev. Sci. Instrum. 82, 073103 (2011); 10.1063/1.3601016 Quantum nanojunctions as spintronic logic operators: Gate response in a two input ballistic interferometer Fabry-Pérot interferometer utilized for displacement measurement in a large measuring range Rev. Sci. Instrum. 81, 093102 (2010); 10.1063/1.3480551 Broadband precision wavelength meter based on a stepping Fabry-Pérot interferometer Rev. Sci. Instrum. 75, 3318 (2004);We discuss the electron transport through a quantum Hall Fabry-Pérot interferometer ͑QHFPI͒ obtained with two quantum point contacts ͑QPCs͒ in series along a ballistic quantum wire by focusing on the effects due to quantum interference and to quantum Hall effect. We calculate the conductance-energy and conductance-magnetic field characteristics as functions of the geometrical parameters and gate voltages. QHFPI may be utilized in designing electronic logic gates: XOR and OR ͑NOR and XNOR͒ gates responses are investigated. The width of each QPC is modulated by metallic electrodes where two gate voltages, namely, V a and V b , are applied. Those external voltages are treated as the two inputs of the gates. After fixing appropriately the working Fermi energy, the magnetic field strength, and the distance between the barriers, a low output Hall current ͑0͒ ͑in the logical sense͒ appears just if both inputs are low ͑0͒, while a high output Hall current ͑1͒ results otherwise. It clearly demonstrates the OR gate behavior. By changing the parameters, a XOR gate can be produced, where a high output current ͑1͒ appears, when just one of the two inputs is low ͑0͒, while a low output current ͑0͒ results if both inputs are low ͑0͒ or high ͑1͒.

Ballistic 3-port interferometric logic gates in the quantum Hall regime

“…it extends in the (x,y) plane, and a uniform magnetic field B is applied along z, such that the vector potential can be chosen as ) 0 , , 0 ( Bx A  . Then, as discussed in [13], the single-…”

“…. Then, as discussed in [13], the singleparticle Hamiltonian describing the propagation of an electron with effective mass m and wavevector components along the x and y directions…”

“…To correlate the outputs with the operation of logic gates, we must first specify the manner of encoding the logic values of both inputs and outputs. As in [13], we encode the input logic values in the potential applied on each of the three QPCs, which can be either  0 V 0, corresponding to the logic value 0, or  1 V 0.5 eV, associated to the logic value 1. The input logic states are then ) , , ( it follows that the transmission coefficients T at all ports have a smooth variation with energy except for the input logic state (111), for which rapid variations of the transmission occur for specific resonant energies denoted as r E (a similar behavior was reported in [13]).…”

“…A different route for implementing logic operations in solid-state systems involves configurations in materials with long mean-free-paths of charge carriers, such as graphene [9][10][11] or 2DEGs [12] based on interference between quantum wavefunctions traversing different paths. This last category includes also logic gates based on quantum interference between edge states in electron interferometers defined by quantum point contacts (QPCs) [13,14]. Such few-or single-channel electron interferometers working in the quantum Hall effect regime have the advantage of high sensitivity and visibility [15], as well as of a well-establish, even analytical [13,16,17], modeling of propagating single-particle wavefunctions or wavepackets.…”

“…This last category includes also logic gates based on quantum interference between edge states in electron interferometers defined by quantum point contacts (QPCs) [13,14]. Such few-or single-channel electron interferometers working in the quantum Hall effect regime have the advantage of high sensitivity and visibility [15], as well as of a well-establish, even analytical [13,16,17], modeling of propagating single-particle wavefunctions or wavepackets. Moreover, conditional operations involving logic gates implemented by electronic interferometers based on edge states could be envisaged taking into account the Coulomb interaction of different interferometers [14,18,19] or the coupling of different cavities by edge states [20].…”