REVIEW Valleytronics www.small-journal.com Valleytronics: Opportunities, Challenges, and Paths Forward Steven A. Vitale,* Daniel Nezich, Joseph O. Varghese, Philip Kim, Nuh Gedik, Pablo Jarillo-Herrero, Di Xiao, and Mordechai Rothschild The workshop gathered the leading A lack of inversion symmetry coupled with the presence of time-reversal researchers in the field to present their symmetry endows 2D transition metal dichalcogenides with individually latest work and to participate in honest and addressable valleys in momentum space at the K and K′ points in the first open discussion about the opportunities Brillouin zone. This valley addressability opens up the possibility of using the and challenges of developing applications of valleytronic technology. Three interactive momentum state of electrons, holes, or excitons as a completely new para- working sessions were held, which tackled digm in information processing. The opportunities and challenges associated difficult topics ranging from potential with manipulation of the valley degree of freedom for practical quantum and applications in information processing and classical information processing applications were analyzed during the 2017 optoelectronic devices to identifying the Workshop on Valleytronic Materials, Architectures, and Devices; this Review most important unresolved physics ques- presents the major findings of the workshop. tions. The primary product of the work- shop is this article that aims to inform the reader on potential benefits of valleytronic 1. Background devices, on the state-of-the-art in valleytronics research, and on the challenges to be overcome. We are hopeful this document The Valleytronics Materials, Architectures, and Devices Work- will also serve to focus future government-sponsored research shop, sponsored by the MIT Lincoln Laboratory Technology programs in fruitful directions. Though we provide some intro- Office and co-sponsored by NSF, was held in Cambridge, MA, duction to valley physics and to the state of existing knowledge, USA on August 22–23, 2017. Valleytronics is an emerging field this article is not intended to be a comprehensive review of the that promises transformational advances in information pro- literature. For that the reader is referred to several excellent cessing through the use of a particle’s momentum index, pos- review articles related to 2D materials and valleytronics.[6–13] sibly in conjunction with its charge and/or spin. Isolation of 2D materials such as graphene[1–3] and transition metal dichalcoge- [4,5] nides (TMDs) has allowed realization of experiments, which 2. Introduction confirm our understanding of valley physics. However, develop- ment of useful devices for valleytronic computing or other tech- When atoms brought together in close proximity form a crystal, nologies requires significant advancements in material quality, the electrons of the constituent atoms interact with each other device designs, and circuit architectures. and with the atoms themselves, giving rise to distinct bands of energy that determine the electronic properties of the crystal- line material. In semiconducting crystals, the bonding electrons Dr. S. A. Vitale, Dr. D. Nezich, Dr. J. O. Varghese, Dr. M. Rothschild populate a filled band of allowed states known as the valence MIT Lincoln Laboratory 244 Wood Street, Lexington, MA 02421, USA band, and are separated from an unfilled band of higher energy E-mail: [email protected] known as the conduction band by an energy gap that contains Prof. P. Kim no allowed states (the band gap). For some semiconductors, Department of Physics regions of minimum energy can appear in the conduction band Harvard University that are indistinguishable from one another except for the direc- 11 Oxford Street, Cambridge, MA 02138, USA tion of the crystal axes along which the energy band is oriented. Prof. N. Gedik, Prof. P. Jarillo-Herrero Department of Physics Thus when carriers are excited across the band gap from the Massachusetts Institute of Technology valence band into these minima in the conduction band, they 77 Massachusetts Avenue, Cambridge, MA 02139, USA will possess the same energy (be energy-degenerate), but will Prof. D. Xiao have differing crystal momenta depending on the orientations Department of Physics of the axes. These minima we refer to as valleys, and devices Carnegie Mellon University exploiting the fact that electrons, holes, or excitons (hereafter, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA particles) are present in one valley versus another we refer to The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/smll.201801483. as valleytronic devices. Selectively populating one momentum- distinguishable valley versus another—creating a valley polari- DOI: 10.1002/smll.201801483 zation—is the key enabling feature of valleytronics. Small 2018, 1801483 1801483 (1 of 15) © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.small-journal.com The localization of a particle to a region of momentum space yields a new index by which to characterize it, namely, the valley Steven A. Vitale is a Senior pseudospin. This is in addition to the discrete spin index nor- Member of the Technical Staff mally associated with a particle. Though energy-degenerate val- at MIT Lincoln Laboratory. leys are present in many periodic solids, it is usually impossible His research interests include to address or manipulate particles in one valley independently novel devices for information from another as the valley state of a particle does not strongly processing, diamond transis- couple to an applied external force. Thus it is impractical to con- tors, ultra-low power compu- struct useful valleytronic devices out of most materials. This is tation, and plasma processing in contrast to spintronics, for example, where the electron spin of advanced materials. is readily manipulated by magnetic fields through the electron Prior to Lincoln Laboratory, spin magnetic moment or (less easily) by electric fields through he developed front-end spin–orbit coupling. For valleytronics to be useful, it is also of plasma processes at Texas paramount importance that the particles populating a valley Instruments for the 90–45 nm CMOS silicon technology reside there for long enough to perform a desired function. nodes. He holds a Ph.D. in chemical engineering from In some materials anisotropy of the particle mass along MIT, an M.S. in nuclear engineering from MIT, and a B.S. different crystal orientations can result in valley polarization in chemical engineering from Johns Hopkins University. under an applied field; preferential scattering occurs from one valley to another. This has been shown in diamond, aluminum Daniel Nezich is a technical arsenide, silicon, and bismuth at cryogenic temperatures. How- staff member at MIT Lincoln ever, these materials still lack a strong coupling between the Laboratory. He received valley index and an external field. It is not possible to selectively his B.S. in physics (2003) initialize, manipulate, and readout particles in a specific valley. at Michigan Technological So we do not consider these materials in our discussion of University and Ph.D. in valleytronics. physics (2010) at the Fortunately, a class of materials does exist in which the valley Massachusetts Institute of pseudospin can be more readily addressed. In stark contrast to Technology. He specializes all other materials, 2D materials such as graphene and mono- in low-dimensional mate- layer molybdenum disulfide possess valleys at the inequivalent rial growth, processing, and K and K′ points in the Brillouin zone (Figure 1), which exhibit characterization in systems strong valley-selective interactions with applied electric and including carbon nanotubes, graphene, and transition magnetic fields. The isolation and investigation of these mate- metal dichalcogenides. rials were seminal events in the field of valleytronics. As one can see in the histogram of publications in the field in Figure 2, the isolation of graphene in 2004 catalyzed new research in Joseph O. Varghese received valley physics, but investigations into the optical properties of his B.E. degree in chemical TMD monolayers in 2010 caused an explosion in the number engineering from Cooper of valleytronic publications. Union, and his Ph.D. degree The following discussion explains why some fundamental in chemical engineering symmetries of monolayer materials are critical to valley address- from the California Institute ability; it is largely based on published work.[13–15] We first of Technology. His previous elaborate on these symmetries and some valley-related concepts work includes the design and to clarify them for the reader. fabrication of thermoelectric In order to selectively couple to distinct valley states, it is nanostructures, and scanning necessary that there exist physical quantities that can distin- probe and opto-electronic guish between them. One such quantity is the Berry curvature, investigations of nanoscale Ω. The Berry curvature describes the geometric properties of materials. He is presently a member of the Technical Staff the electronic bands, and is central to the understanding of at MIT Lincoln Laboratory where his research interests band topology-related effects. When describing the motion include 2D valleytronic materials and the development of of electrons in crystal lattices, the semiclassical equations of diamond transistor devices. motion