Unraveling Electron Chirality in Graphene

Carbon atoms in graphene sit on a honeycomb lattice, a seemingly simple structure that nonetheless underlies the electronic and optical properties that have made graphene a world-famous material in recent years [1]. In this lattice, a property of the electrons with the smallest binding energy (i.e., those near the Fermi level) is that they follow a linear dispersion relation confined to two dimensions. The direction along which an electron propagates and the amplitude of its wave function are not independent, so the electrons are said to possess the property of chirality, or handedness. Pinning down fundamental details about these exotic electron states is important for developing graphene-based devices, but measuring this property directly has, however, remained elusive. Now, in a paper appearing in Physical Review Letters, Yang Liu and colleagues at the University of Illinois at Urbana-Champaign have used photoemission with circularly polarized light to detect the chirality, as well as the so-called phase factor, of the wave functions describing electrons in doped singleand bilayer graphene [2]. In addition to establishing a “fingerprint” of graphene electron chirality in photoemission measurements, Liu et al. demonstrate a technique with wide applicability to other two-dimensional materials. Graphene was discovered in 2004. Since then, experimentalists have found, in this one material, evidence for an unconventional room-temperature quantum Hall effect (QHE), a fractional QHE, ambipolar transport, and exceptionally high charge mobility—the latter an important property for engineering ultrafast devices. Such phenomena, among others, make graphene a promising platform for all-carbon nanoelectronics [1, 3]. These properties of singleand bilayer graphene, which are both semiconductors with a vanishing band gap if they don’t interact with the environment, depend crucially on the quasiparticle band structure and the unusual chiral phase relations of the wave functions describing the valence and conduction electrons [4]. Close to the Fermi level, the energy of a graphene electron moving in the honeycomb lattice varies linearly with its momentum—this is why the electrons are said to behave as massless Dirac particles. In addition to possessing a physical (magnetic) spin, the charge carriers in graphene also possess a pseudospin, which is a quantum labeling associated with the fact that the unit cell of the honeycomb lattice consists of two different sublattices. In addition to spin and pseudospin, a third quantum label for graphene electrons is the two-component isospin degree of freedom, also called the valley index. Graphene’s conduction and valence bands are defined by two inequivalent sets of “Dirac cones,” which sit at the points K and K ′ in the Brillouin zone. The isospin degree of freedom arises from the degeneracy of the electronic states associated with these inequivalent zone corners. It is the property of isospin that gives electrons in graphene a chirality: their energy spectrum is isotropic, but the relative phases of the two components of the spinor eigenstates (up or down) rotate with the propagation direction of the electron, which tends to align the pseudospins (parallel or antiparallel, respectively) to this direction. In monolayer graphene, the direction of this pseudospin vector tracks the rotation of the electron momentum, resulting in a Berry’s phase of π [5, 6], but in bilayer graphene, the pseudospin rotates twice as fast, resulting in a Berry’s phase of 2π [3]. The ability to unravel these electronic properties is a crucial ingredient for the design and optimization of novel graphene-based devices. Therefore, angle-resolved photoemission spectroscopy (ARPES), which in its simplest form measures the energy and momentum of electrons kicked out from the surface by an incident photon, has been employed extensively to directly probe the quasiparticle band structure of graphene systems. ARPES has allowed experimentalists to determine the conical band