Valleytronics in a nutshell

Both classical and quantum computing face significant challenges. On the classical side, silicon field effect transistor technology is reaching the fundamental limits of scaling and there is no replacement technology which has yet demonstrated even comparable performance to the current generation of commercially available silicon CMOS. On the quantum side, scaling the number of entangled superconducting or trapped ion qubits to that required to solve useful problems is an enormous challenge with current device technology. Both fields stand to benefit from transformational devices based on new physical phenomena. Two-dimensional transition metal dichalcogenides (TMDs) possess a number of intriguing electronic, photonic, and excitonic properties.

A lack of inversion symmetry coupled with the presence of time-reversal symmetry endows 2D TMDs with individually addressable valleys in momentum space at the K and K’ points in the first Brillouin zone. This valley addressability opens the possibility of using the momentum state of electrons, holes, or excitons as a completely new paradigm in information processing.

Periodic semiconductor crystal lattices often have degenerate minima in the conduction band at certain points in momentum space. We refer to these minima as valleys, and devices which exploit the fact that carriers are present in one valley versus another are referred to as valleytronic devices. Though degenerate valleys are present in many periodic solids, in most cases it is impossible to address or manipulate carriers in one valley independently from another as the valley state of a carrier is not coupled to any external force we can apply. Thus it is not possible to construct valleytronic devices out of most materials. This is in contrast to spintronics, for example, where the electron spin is readily manipulated by magnetic fields through the electron spin magnetic moment or (less easily) by electric fields through spin-orbit coupling.

In some cases, carrier mass anisotropy along different crystal orientations can result in valley polarization; preferential scattering occurs from one valley into another. This has been shown in diamond, aluminum arsenide, silicon, and bismuth at cryogenic temperatures. However, these materials still lack a strong coupling between the valley index (sometimes called the valley pseudospin) and any external quantity such as an applied field.  It is not clear that there is a way to use mass anisotropy to produce a useful device such as a switch. So we do not consider this class of materials in our discussion of valleytronics.

The recent emergence of 2D materials has provided a more encouraging space in which to explore manipulation and control of the valley index. 2D materials with hexagonal lattices such as graphene or transition metal dichalcogenides (TMDs) can have valleys at the K and K’ points in the Brillouin zone. But to detect or manipulate carriers selectively in one valley we need some measureable physical quantity which distinguishes the two.

The 2H phases of 2D transition metal dichalcogenides lack inversion symmetry and as a result exhibit contrasting Berry curvatures and orbital magnetic moment between the K and K’ valleys. if the Berry curvature has different values at the K and K’ points one can expect different electron, hole, or exciton behavior in each valley as a function of an applied electric field. If the orbital magnetic moment has different values at the K and K’ points one can expect different behavior in each valley as a function of an applied magnetic field. Contrasting values of Berry curvature and orbital magnetic moment at the K and K’ points give rise to optical circular dichroism between the two valleys which allows selective excitation through photons of right or left helicity. Monolayer 2D transition metal dichalcogenides meet this requirement and are the most promising candidates for valleytronic applications.

 

valleytronics
Sketch denoting the circular optical dichroism of the K and -K valley in TMDC monolayers

 

By Riccardo Pisoni, PhD student at the Ensslin Nanophysics group at ETH Zurich, Zurich, Switzerland

 

References:

The Valleytronics Materials, Architectures, and Devices Workshop, sponsored by the MIT Linclon Laboratory Technology Office and co-sponsored by NSF, MIT Samberg Center on August 22-23, 2017.

Wu, W. Yao, D. Xiao, T.F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides”, Nature Physics, 10:343 (2014)

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