Diffractive paths for weak localization in quantum billiards

Abstract

We study the weak-localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity ͑when approaching the lead mouths from the cavity interior͒ to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding antipeak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.

Transport through open quantum dots: Making semiclassics quantitative

“…The information on paths governing quantum transport can be reliably extracted from the two-dimensional Fourier transforms of the quantum mechanical S-matrix elements, 16 S nm (k, B). The S-matrix elements display a strongly fluctuating pattern as a function of k and B (see Fig.…”

“…Refs. 1,2,8,16,17,18,19,20,28,45,46,47,48,49 and references therein) where the later corresponds to the restriction to terms q = q ′ in the double sum over paths when calculating |t SCA nm | 2 from Eq. (7).…”

“…III we introduce the GTD-UTD diffraction approximation which is a key to the quantitative agreement between the PSCA and quantum mechanics for transport properties. The important role of pseudo-paths and a proper diffraction theory is demonstrated on the level of quantum mechanical length-area spectra 16 in Sec. IV.…”

Magnetic field-induced control of transport in multiterminal focusing quantum billiards

“…Their quantum version models nanoscale transport devices, usually realized by controllably confining a 2D electron gas at a semiconductor interface, and sets the grounds for the theoretical description and experimental investigation of coherent transport in the mesoscopic regime. The transport properties of such billiards are extensively examined in the context of various interesting phenomena, including the quantization of conductance in mesoscopic systems, 1,2 the appearance of Fano resonances in transmission, [3][4][5][6] resonance trapping, 7,8 shot noise in quantum dots, 9,10 Andreev tunneling and reflection, 11,12 as well as conductance fluctuations, 13,14 localization effects, [15][16][17] decoherence 5,18,19 and dephasing 3,20 in ballistic nanostructures. Billiards also serve as ideal systems for the study of the relation of quantum transport to its classical counterpart and the crossover between them.…”

Weak localization inAlxGa1−xAs/GaAs/AlxMinkov1, Шерстобитов2, Германенко3 et al. 2008Phys. Rev. B3040View full textAdd to dashboardCite

“…The transport properties of two-dimensional ͑2D͒ semiconductor structures with antidots array were intensively studied both experimentally [1][2][3][4][5][6][7][8][9][10][11] and theoretically [12][13][14][15][16] in the last 10-15 years. The main concern was with the investigations of the ballistic systems, in which l Ͼ d , D, where l is the mean free path, d and D are the size of antidots and the period of antidots array, respectively.…”