Magnetoconductance of a quantum wire with several antidots: A transfer-matrix study

Abstract

We report on an extended transfer-matrix technique that allows us to solve full quantum-mechanical scattering problems for mesoscopic conductors in the presence of magnetic fields. This method may be applied to two-and three-dimensional systems, and gives a scattering wave function in addition to a scattering matrix. We apply this technique to investigate the magnetoconductance of a quantum wire with a few antidots confined inside and make quantitative comparisons to experimental data on this system.

A dynamical formulation of one-dimensional scattering theory and its applications in optics

“…This relation plays a particularly useful role in modeling and the numerical investigation of various physical phenomena in optics [9], condensed matter physics [10], and acoustics [11]. The composition property of the transfer matrix is shared by another quantum mechanical quantity of central importance, namely the evolution operator U(t, t 0 ) of any Hamiltonian operator; if we denote U(t, t 0 ), U(t 1 , t 0 ), and U(t, t 1 ) respectively by U, U 1 , and U 2 , with t 1 ∈ [t, t 0 ], we have U 2 U 1 = U.…”

“…Let M 1 and M 2 be respectively the transfer matrix for v a and v − v a . Then, M 2 M 1 = M. This relation plays a particularly useful role in modeling and the numerical investigation of various physical phenomena in optics [9], condensed matter physics [10], and acoustics [11].…”

Improved transfer matrix method without numerical instability

“…The transfer matrix method (TMM) has been a useful approach for studying the physical properties. There have been many publications on the application of the TMM, such as studies of the Ising model [1][2][3][4], quantum spin [5], electronic transport [6,7], and electronic state in quasiperiodic and aperiodic chains [8,9]. The TMM is also widely applied in studying the propagation of electricmagnetic waves [10], elastic waves [11] and light waves [12] in multi-layer systems.…”

“…This has been a major limitation to the application of the OTMM. Some approaches have been developed to calculate the transport through a longer scattering area such as the scattering matrix method (SMM) [13][14][15], the extended transfer matrix technique (ETMT) [7] and the Green's function approach (GFA) [16]. In the SMM, the middle scattering region is cut into some smaller sections, then the scattering matrices of these sections are found by means of the TMM and combined together to get the total scattering matrix (SM) recursively.…”

“…Furthermore, the computing time grows linearly for adding every block by a recursive algorithm in the SMM. In the ETMT [7], the magnetoconductance of a quantum wire with several antidots was studied. The numerical technique used there could avoid numerical instability occurred in the original transfer matrix method, and was applied to a variety of 3d systems involving complicated atomic and many-body potentials.…”