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

Abstract

By exploring the four-terminal transmission of a semi-elliptic open quantum billiard in dependence of its geometry and an applied magnetic field, it is shown that a controllable switching of currents between the four terminals can be obtained. Depending on the eccentricity of the semiellipse and the width and placement of the leads, high transmittivity at zero magnetic field is reached either through states guided along the curved boundary or focused onto the straight boundary of the billiard. For small eccentricity, attachment of leads at the ellipse foci can yield optimized corresponding transmission, while departures from this behavior demonstrate the inapplicability of solely classical considerations in the deep quantum regime. The geometrically determined transmission is altered by the phase-modulating and deflecting effect of the magnetic field, which switches the pairs of leads connected by high transmittivity. It is shown that the elliptic boundary is responsible for these very special transport properties. At higher field strengths edge states form and the multiterminal transmission coefficients are determined by the topology of the billiard. The combination of magnetotransport with geometrically optimized transmission behavior leads to an efficient control of the current through the multiterminal structure.

Conductance microscopy of quantum dots weakly or strongly coupled to the conducting channel

“…In this work we discuss the interpretation of the G mapping for the quantum dot side-attached to a conducting channel. We develop the results of our previous study [35] for a cavity strongly coupled to the channel and a single mode transport which indicated that the LDOS and G maps are clearly correlated only at Fano resonances [36,37,38,39,40]. Here, we study a quantum dot with variable opening (coupling) to the channel.…”

Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

“…Moreover, S‐matrices are unitary in each iteration of the assembly process, which makes calculations numerically stable. The present method may be used to overcome memory limitations of KWANT package that takes advantage of the sparsity of Hamiltonian matrix, which can be employed to explore transport in quantum billiards with external magnetic fields …”

“…Hamiltonian has successfully explained transport properties of multiple nanostructured materials . Planar quantum billiards with different shapes under magnetic fields have been also modeled by using a tight‐binding discretization, with interesting magnetically‐mediated current switching effects …”

Current Control by Resonance Decoupling and Magnetic Focusing in Soft-Wall Billiards

“…Their transport properties are drastically altered by an externally applied magnetic field [18][19][20][21][22][23][24][25][26], and they therefore dominate the intense investigation of coherent magnetotransport in the mesoscopic regime, where quantum interference meets and overlaps with the notion of oriented paths. Specifically, generalized Aharonov-Bohm (AB) oscillations [27] from phase modulation of interfering states [19,23,28] combine with the Lorentz deflection [24,29,30] of electrons up to the formation of edge states [19,24,31]. An intriguing question is how to controllably separate path-mediated magnetotransport dynamics from (resonant) interference effects in a regime where the two strongly overlap, that is, at wavelengths comparable to the system size.…”

“…As a result, the setup enables efficient finite-temperature current switching via a weak magnetic field, for varying Fermi energy. represented on a tight-binding lattice, and the transmission function T (E) is computed via an extended recursive Green function scheme [24,33,34]. This allows for efficient and accurate transport calculations in a highly resolved parameter space for the considered low-energy regime.…”