Our current electronic technologies are based on the control of the motion of electrons in semiconducting materials. Although the motion of electrons is ultimately described by the equations of quantum mechanics, effectively, the motion of electrons in semiconductors can be described using classical equations of motion. However, electrons have other degrees of freedom, such as spin, which are intrinsically quantum mechanical. Attempts to control it have led to the field of Spintronics. Nevertheless, in certain materials like Graphene, electrons are endowed with an additional degree of freedom called “valley pseudo spin”.
In recent years, much effort has been recently devoted to the control of the valley degree of freedom in graphene and other two dimensional materials, a emerging field nowadays known as “Valleytronics”. Thus, a research group in Manchester, UK, led by the Nobel Prize Winners Prof. Andre Geim and Prof. Kostya Novoselov recently observed the generation of valley polarized currents in a device made of graphene deposited on Boron nitrate. The effect responsible for the generation of valley currents is termed “valley Hall effect” (VHE) because the valley currents (like the Hall currents in the classical Hall effect) are perpendicular to applied electric field.
Recently, the group led by Prof. Miguel Cazalilla (DCS of NCTS and professor in NTHU Physics) has proposed an alternative route to the generation of such spin currents . Their work has been published in journal “2D Materials” of the UK Institute of Physics (Impact factor for 2016: 9.611) . According to their proposal, with modest levels of strain, graphene can also sustain a classical VHE. The latter can be detected in nonlocal transport measurements. Zhang, Huang and Cazalilla provided a comprehensive theory of the strain-induced VHE starting from a microscopic quantum Boltzmann equation. This allowed them to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only parameters characterizing the transport theory. Using their new theory, they computed the nonlocal resistance of a Hall bar device in the diffusive regime. The theory developed by Zhang, Huang, and Cazalilla is also relevant for the study of moderate strain effects in the (nonlocal) transport properties of other two-dimensional materials and van der Walls heterostructures.
 “Valley Hall effect and nonlocal transport in strained graphene”, X.P. Zhang, C. Huang, and M. A. Cazalilla, 2D Materials, 4, 024007 (2017).
Figure Caption: (a) The valley Hall angle is plotted against chemical potential μ for different temperatures T = 0, 100, 300 K. (b) Limit of applicability of semiclassical theory in the plane of absolute temperature, T, and chemical potential μ.