Spin Circuit Model for 2D Channels with Spin-Orbit Coupling

In this paper we present a general theory for an arbitrary 2D channel with “spin momentum locking” due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, −). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U−, and D−. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green’s function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling

INQUIRY-BASED APPROACH AND NUMERICAL SIMULATIONS: A POWERFUL INTEGRATION IN CONDENSED MATTER PHYSICS EDUCATION

In this chapter, we present and discuss two inquiry-based learning paths on condensed matter physics topics in which numerical simulations play a relevant role. The first one addresses the study of the electron transport dynamics via simulative explorations in 3D semiconductors. His emphasis is not on student modelling skills, but rather on a chain of reasoned investigations performed within a learning environment aimed at supporting a valuable understanding of the physics concepts underlying the complex world of semiconductor electronics. The second learning path is a 5E-cycle-based workshop of advanced physics targeted to strengthen student’s understanding of the various aspects of the Hall Effect. In this latter, the instructors stimulate a discussion about the classical, integer and fractional quantum Hall effects. Both learning paths represent a powerful instrument for educators introducing young undergraduates to the effectiveness of numerical simulations to investigate a physical system where the theoretical processes are well known, but analytical methods of examination still provide only approximate results. Our findings show that the stimulated activation of the inquiry process, also by means of numerical simulations, can represent an effective teaching/learning method. This approach successfully engages students into active learning and, at the same time, supports the clarifying of important experimental and technological aspects of material science, representing a feasible example of combination of a traditional lecture-based teaching method with efficacious teaching/learning strategies