NRL researchers take a step toward valleytronics – a competitor to spintronics

The band structure of graphene with its two valleys is shown in blue and red.

Valley-based electronics, also known as valleytronics, is one step closer to reality. Two researchers at the Naval Research Laboratory (NRL) have shown that the valley degree of freedom in graphene can be polarized through scattering off a line defect. Unlike previously proposed valley filters in graphene, which rely on confined structures that have proven hard to achieve experimentally, the present work is based on a naturally occurring line defect that has already been observed.

Physical Review Letters – Graphene Valley Filter Using a Line Defect

Can valleytronics ever compete against spintronics? We remain a bit skeptical. Although scattering from K to K′ calls for a large momentum transfer, it may still happen in realistic graphene devices. The reason is that the edges of the graphene flake or adatoms that stick to the surface can provide sharp enough scattering potentials to mix K and K′. Once K and K′ are mixed, the performance of the valley filter will be altered. A big advantage of the proposal by Gunlycke and White based on the line defect observed is that it should suffer much less from this type of disorder compared to previous proposals based, for instance, on edged graphene nanoribbons

With its two degenerate valleys at the Fermi level, the band structure of graphene provides the opportunity to develop unconventional electronic applications. Herein, we show that electron and hole quasiparticles in graphene can be filtered according to which valley they occupy without the need to introduce confinement. The proposed valley filter is based on scattering off a recently observed line defect in graphene. Quantum transport calculations show that the line defect is semitransparent and that quasiparticles arriving at the line defect with a high angle of incidence are transmitted with a valley polarization near 100%.

Physics viewpoint – A defect controls transport in graphene

The field of spintronics, which uses the spin of an electron besides its charge as a carrier of information in electronics, has seen much theoretical and experimental progress over the last decades. The spin degree of freedom interacts less with its environment than does the charge degree of freedom. Hence spin-based electronics may have some advantages—less dissipation of power, for example—over charge-based ones. Since spin is the intrinsic angular momentum of an electron, found in each and every electronic system, the efficacy of a specific material for spintronics depends on how well it can control and store spin.

Can we find additional degrees of freedom—similar to the electron spin—as alternative carriers of information? The answer is yes. For instance, graphene, in which carbon atoms are arranged in a two-dimensional honeycomb lattice, has two pseudospin degrees of freedom in addition to the electron spin. These pseudospin degrees of freedom behave in a mathematically similar way to the electron spin, i.e., they act like additional intrinsic angular momenta of the electron. The pseudospins are both related to the peculiar band structure of graphene, shown

Electronic dispersion of graphene. The conduction band and the valence band touch each other at six discrete points. These points are called K points. The six points can be divided into two in-equivalent sets of three points each. The points within each set are all equivalent because they can reach each other by reciprocal lattice vectors. The two in-equivalent points are called K and K′ and form the valley isospin degree of freedom in graphene. The name valley isospin stems from the similarity of the vicinity of these points with a valley. The zoom shows that the dispersion relation close to the K points looks like the energy spectrum of massless Dirac particles.

One is called sublattice pseudospin and the other valley isospin. The former occurs due to the bipartite honeycomb lattice, which has two distinct sublattices. Whenever the direction of motion of the electron changes, the sublattice pseudospin also has to change and realign to the new direction of motion. Therefore it is vulnerable to disorder and apparently not useful as a carrier of information. In this it differs from the valley isospin, which distinguishes between the two independent valleys in the band structure of graphene, commonly called K and K′, see above. The valley isospin is more robust against disorder than the sublattice pseudospin as it needs a large momentum transfer (on the order of the inverse lattice spacing of graphene) to scatter from K to K′. This offers the possibility of developing valleytronics devices that are similar in concept to spintronics devices.

A schematic of the proposed valley filter. An incoming electron (with angle of incidence α) approaching a line defect in graphene having components in both valleys K and K′ transmits the defect, for instance, preferentially in valley K for a large angle of incidence, whereas the component in K′ will be reflected in a specular way. This effect could be used to produce a valley-polarized current out of an unpolarized stream of electrons.

Information in solid-state, either classical or quantum, is generally carried by electrons and holes. The information can be encoded in various degrees of freedom such as charge or spin. Charge representations, for example the absence or presence of an electron in a quantum dot, are attractive as they are easily manipulated and interrogated through electric fields. The advantage of spin representations, used in the field of spintronics, is their superior shielding from undesired electric fluctuations in the environment, making the information in these latter representations more robust. In the future, there might be a third middle-ground alternative in the valley degree of freedom that exists in certain crystals, including graphene.

The valley degree of freedom in graphene gained attention in 2007 when it was proposed that electrons and holes could be filtered according to which valley they occupy. Unfortunately, the structures required for this and subsequent valley filters are difficult to fabricate, and as a result a valley filter has yet to be demonstrated experimentally. The present study from NRL shows that an extended line defect in graphene acts as a natural valley filter. “As the structure is already available, we are hopeful that valley-polarized currents could be generated in the near future” said Dr. Daniel Gunlycke who made the discovery together with Dr. Carter White. Both work in NRL’s Chemistry Division.

Valley refers to energy depressions in the band structure, which describes the energies of electron waves allowed by the symmetry of the crystal. For graphene, these regions form two pairs of cones that determine its low-bias response. As a large crystal momentum separates the two valleys, the valley degree of freedom is robust against slowly varying potentials, including scattering caused by low-energy acoustic phonons that often require low-bias electronic devices to operate at low temperatures typically only accessible in laboratories.

Valley polarization is achieved when electrons and holes in one valley are separated spatially from those in the other valley, but this is difficult to do as the two valleys have the same energies. It was found, however, that this spatial separation can be obtained in connected graphene structures that possess reflection symmetry along a particular crystallographic direction with no bonds crossing the reflection plane. This property turns out to be present in a recently observed line defect in graphene. The reflection symmetry only permits electron waves that are symmetric to pass through the line defect. Anti-symmetric waves are reflected. By projecting an arbitrary low-energy wave in graphene onto its symmetric component, one gets the transmission amplitude through this defect, which is strongly dependent on the valley. Electron and hole waves approaching the line defect at a high angle of incidence results in a polarization near 100%.

There is a long way to go before valleytronics can become a viable technology, explains Gunlycke. The recent advance, however, provides a realistic way to reach a crucial milestone in its development

Helical scattering and valleytronics in bilayer graphene

We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60° over a large energetic range in one of the valleys, and down to −60° in the other. In a Y-junction geometry, this can be used to create and detect valley polarization.

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