Injection of spinning electrons from quantum wires into 2D electron reservoirs

Significance 

In mesoscopic physics, ballistic conduction is defined as the transport of electrons in a medium, having negligible electrical resistivity caused by scattering. Specifically, mesoscopic systems based on GaAs/AlGaAs heterostructures have been reported to allow the rich physics of ballistic electron transport. A favorite system for studying ballistic electrons is the high mobility two-dimensional electron gas (2DEG) which resides at the interface between GaAs and AlGaAs layered semiconductors. By proper gating on top of the heterostructure, one can create confined low-dimensional systems like quantum wires (QWs) and quantum point contacts (QPCs). It is possible to control the flow of electrons by applying electric and magnetic fields.

At low temperature and small electric bias, only the electrons near the Fermi energy contribute to the current. It has been shown that, under certain conditions, the propagation of ballistic electrons in semiconductor quantum wires, of electromagnetic waves in wave guides, of sound waves in pipes with different geometry, light propagation in optical fibers for photonic applications are all described by the same type of Helmholtz equation. All the same, the precise control of spin states and spin dependent electron transport is required for applications in spintronics and quantum information processing.

Presently, the technique of transverse electron focusing has been proposed to study electron transmission through a QPC by means of investigation of the position, the shape and the height of the focusing peaks. Nonetheless, further research on the spin-splitting effect when a transverse magnetic field is applied in the 2D region is necessitated. To this end, a team of researchers from the Department of Physics, Chemistry and Biology at Linköping University in Sweden: Ivan Yakimenko, Irina Yakimenko and Karl-Fredrik Berggren designed a model illustrated in the figure for electron flow from a quantum wire into a 2D region through an opening having different geometries. Their work is currently published in Journal of Physics: Condensed Matter.

To begin with, the researchers studied the transport of electrons into the 2D reservoir from a quantum wire having a rectangular opening without a magnetic field using the proposed mode-matching on a grid method. They then studied the conic and rounded openings which are more typical in real semiconductor structures. Lastly, the spin-splitting effect in an applied transverse magnetic field in the 2D region was investigated.

For the examined cases, the team reported that the geometry of the opening did not play a crucial role for the electron propagation. In fact, it was seen that when a perpendicular magnetic field was applied, the electron paths in the 2D reservoir were curved. These observations were further analyzed both classically and quantum-mechanically. Consequently, it was established that the effect was clearly present for realistic choices of device parameters and consistent with observations.

In summary, the study presented the numerical cross-examination of electron transport from the injector wire into the open two-dimensional reservoir with and without magnetic field. Remarkably, the study demonstrated the development of the novel mode-matching technique and further studied electron flow through the coupled wire with rectangular, conic and rounded openings. In an interview with Advances in Engineering, Professor Karl-Fredrik Berggren further affirmed that the results of their study may be applied in designing magnetic focusing devices and spin separation.

Injection of spinning electrons from quantum wires into two-dimensional electron reservoirs - Advances in Engineering
Probability current density of an electron propagating through the wire with conic opening into two-dimensional electron reservoir with the energy of incoming electron of 4 meV.

About the author

Irina Yakimenko is a professor in Theoretical Physics at the Department of Physics, Chemistry and Biology (IFM), Linköping University (LiU) in Linköping (Sweden). In 1982 she graduated from Kiev State University; subsequently in 1991, she completed her PhD in Physical and Mathematical Sciences at the Bogolyubov Institute for Theoretical Physics, in Kiev, Ukraine. Since 1997, she has been working at Linköping University, and in 2010 she became, as mentioned, professor in Theoretical Physics at IFM in Linköping, Sweden.

Presently, her research interests fall within the field of quantum physics, in particular, studies of electron transport in low-dimensional semiconductor structures, effects of magnetic field and electron correlation on electron transport, quantum information processing and quantum computing. Her teaching covers theoretical physics within the programme of applied physics and electrical engineering.

About the author

Ivan Yakimenko graduated with M.Sc.Eng. (Master of Science degree in Engineering) in 2018 from Linköping University (LiU) in Linköping (Sweden). In 2010, he graduated from Katedralskolan in Linköping after following a program in natural science with a profile in mathematics and computer science.

During his time at LiU, he was enrolled in the Applied Physics and Electrical Engineering programme and later, he elected the master’s profile in Theory, Modelling and Visualization at the Department of Physics, Chemistry and Biology (IFM), LiU in Linköping (Sweden). His master’s degree concerns modelling ballistic electron transport through differently shaped geometries in low-dimensional quantum wires under supervision of Prof. Karl-Fredrik Berggren, LiU. Currently, his main research interests involve quantum physics, particularly quantum information and quantum computers.

About the author

Karl-Fredrik Berggren, Professor em. in theoretical Physics within Dept. Phys., Chem. and Biol. (IFM), Linköping University (LiU), Sweden. Current research: Condensed matter, quantum phenomena in low-dimensional structures; non-Hermitian quantum mechanics including exceptional points in quantum and classical situations; wave physics including wave chaos, formation of vortices and vortex lattices.

In brief, he has served in periods on a national level as member of the Swedish National Research Council, the Council for Engineering Science and the Council for High Performance Computing. He has also participated in a number national and international evaluations of educational and research programs, for example in engineering physics, and research infrastructures in different fields as well as managed the National .Supercomputer Center (NSC) in Swden and the European Spallation Source Scandinavia (ESS-S) initiative. At LiU he has chaired the board of the educational program in Applied Physics and Electrical Engineering, most importantly during its renewal and implementation of the focused CDIO curriculum  (Concieve, Design, Implement, Operate) integrating academic and industrial practice.

Reference

Ivan P Yakimenko, Irina I Yakimenko, Karl-Fredrik Berggren. Basic modelling of effects of geometry and magnetic field for quantum wires injecting electrons into a two-dimensional electron reservoir. Journal of Physics: Condensed Matter, volume 31 (2019) 345302 (12pp)

Go To Journal of Physics: Condensed Matter

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