Corresponding author: Vitaly A. Tkachenko (vtkach@isp.nsc.ru)

Magnetotransport in two submicron-sized devices formed on the basis of GaAs/AlGaAs structures has been simulated using nonequilibrium Green functions. The effect of a perpendicular magnetic field on quantum transport in a quasi-one-dimensional quantum dot and in an Aharonov–Bohm interferometer has been analyzed in a single-particle approximation. Magnetic field oscillations of two-terminal conductance of the devices, equilibrium (persistent) current distributions and magnetic moment generated in the devices by persistent currents have been determined using numerical methods. Correlations between the magnetic moment, magnetic field oscillations of conductance and energy resonance in a specific magnetic field have been traced. Sufficiently regular conductance oscillations similar to Aharonov–Bohm ones have been revealed for a quasi-one-dimensional quantum dot at small magnetic fields (0.05–0.4 T). For a ring interferometer the contribution to the total equilibrium current and magnetic moment at a specific energy may change abruptly both in magnitude and in sign as a result of changing magnetic field within one Aharonov–Bohm oscillation. We show that the conductance of an interferometer is determined not by the number of modes propagating in the ring but rather by the effect of triangular quantum dots at the ring entrance that produce a strong reflection. The period of the calculated Aharonov–Bohm oscillations is in agreement with the measurement results for these devices.

Flexibly controlled submicron devices formed on the basis of high-mobility 2D electron gas and GaAs/AlGaAs heterostructures have been the main object of experimental quantum nanophysics. For example, one-particle interference phenomena in the conductance

Measurement of Aharonov–Bohm oscillations in the conductance _{0}/Δ_{0} =

Two examples are quite illustrative in this respect. One of them is the Aharonov–Bohm interferometer with an effective ring diameter of 0.7 µm created at the Institute for Semiconductor Physics of the Siberian Branch of the Russian Academy of Sciences by electron lithography and reactive ion etching [^{6} and 2.5 × 10^{6} cm^{2}/(V × s), respectively. In these cases the researchers had a basis for realistic simulation in the form of detailed information on the main specific features of solid state device technologies (materials composition, layer thicknesses and 3D geometry). Comparatively large dimensions of these devices (0.7 µm) combined with the high quality of the 2D electron gas and nanolithography allowed ignoring the disorder in the first approximation. The self-consistent solution of the 3D electrostatics problem provided for close-to-real simple forms of effective 2D potential

However the magnetotransport properties have not yet been calculated for these two devices. These properties include the magnetic field oscillations of two-terminal conductance

The aim of this work is to complement realistic simulations for the examples of the ring and the quantum dot not only with a calculation of magnetic field conductance oscillations but also with a calculation of persistent currents and magnetic moment. The calculated conductance oscillations can be compared with earlier measured ones and the calculation of equilibrium currents and the respective magnetic moment is necessary for understanding quantum phenomena and evaluating the prospects for new experiments.

The total equilibrium current for the preset Fermi energies _{F} and _{F}. To calculate d_{i}_{F} and bias voltage

Figures _{F} = 0.1 meV that sufficiently regular oscillations cover the range from 0.05 to 0.4 T. Note that experiments with this quantum dot detected Aharonov–Bohm oscillations with the period Δ_{0}/Δ_{smooth}(

The peaks in the

The calculated equilibrium current pattern in the quasi-one-dimensional quantum dot for a resonance peak in a moderate magnetic field with _{0}/Δ

The ~200×400 nm^{2} region in the center of the dot is almost free from currents. On the contrary for the resonance _{F} concentrates near the quantum dot center (Fig.

Note that the equilibrium current in the quantum dot in Figs

The equilibrium current _{F} = 0.1 meV but the determinant contribution to the total magnetic moment is made by some resonance states located near the Fermi level and corresponding to

One can see three of these states for _{F} = 0.1 meV which corresponds to the counterclockwise direction of the total equilibrium current _{F} = 0.1 meV (Fig.

Note the regularity of the positions of the main and additional (narrow) peaks in the conductance

The calculated magnetic field characteristics of the quasi-one-dimensional quantum dot at _{F} = 0.1 meV: the dependences of the conductance and the derivative of the magnetic moment d

Distribution of total equilibrium current

The total equilibrium current

Dependences of the electron transmission coefficient

Figure _{smooth}(_{F} = 0). However the calculated conductance of the device is only slightly more than unity, just like in the earlier measurements [

The backscattering of electrons incident from the supplying quantum wires produces complex vortices inside the triangular quantum dots as can be seen from the d_{i} inside the ring yields that the resultant persistent currents _{up}, _{down} flowing in the top and bottom ring branches only depend on

Figure

Note that the total equilibrium current and magnetic moment calculations are complicated by the presence of narrow quasi-level states which may make a significant contribution and therefore the calculations should be conducted at a small step, this making them quite time-consuming, but easily parallelizable [

The calculated magnetic field characteristics of the ring interferometer at the Fermi level (

The contribution of d

Magnetic field oscillations of conductance in nanosized systems, distributions of equilibrium (persistent) currents and magnetic moment induced by this current were calculated based on calculations results for 3D electrostatic potential in devices with ballistic quantum dots and ring interferometers. There is a correlation between the behavior of conductance and magnetic moment. Magnetic field oscillations of conductance of a quantum dot are similar to Aharonov–Bohm oscillations. The calculated period of the Aharonov–Bohm oscillations agrees with the experimental one for these devices. Since the results reported herein were obtained on the basis of experimental data on the technology and operation of mesoscopic nanosized devices [

The work was supported by Grant No. 19-72-30023 of the Russian Research Foundation. Calculations involving computer resources of the Joint Supercomputer Center of the Russian Academy of Sciences were fulfilled under State Assignment No. 0306-2019-0011.