Graphene has been touted as the new wonder material for electronics. As we have observed earlier, the excitement is due to the extraordinarily high carrier mobilities, among other interesting properties [1]. Unfortunately, graphene has no band gap, so it must be chemically or physically modified to become a useful semiconductor.

Chemical doping is developing apace, with electron donors (like alkali metals) [3] and hole donors (like bismuth and gold) [2] now experimentally established. Equally interesting is hydrogen “doping” (see references in [1]), realized by reacting graphene with hydrogen. This reaction has generally been carried out globally, but it occurs to me that one might use beam technology to drive localized reactions: proton beam, atomic hydrogen beam, or e-beam induction à la Zeiss MeRiT. All these procedures result in simultaneously splitting the valence and conduction bands and moving the fermi level.

Very recently, Chen’s group at Purdue reports a solid-state reaction under 30 kV e-beam bombardment of graphene on a substrate [4]. This reaction likewise modifies the band structure. (The authors claim that the dose, ~1800 μC / cm^2, is “typical” SEM exposure.)

Physically restructuring graphene also results in changes to its electrical properties, due to edge states (akin to surface states in 3-dimensional materials). Extremely high e-beam doses (~30 C / cm^2 at 200 kV) result in material removal from the beam impact point. Drndić’s group reports [5] creating holes and lines in suspended graphene by this method. The review by Krasheninnikov and Nordlund [6] is a highly valuable resource in regard to such physical restructuring of materials. The shorter review [7], also by Krasheninnikov, focuses on carbon materials.

References:

[1] Berashevich, Chakraborty, “Graphene and graphane: New stars of nanoscale electronics”, arXiv:1003.0044.
[2] Gierz, et al., “Atomic Hole Doping of Graphene”, arXiv:0808.0621.
[3] Ohta, et al., “Controlling the Electronic Structure of Bilayer Graphene”, Science 313, 951 (2006).
[4] Childres, et al., “Effect of electron-beam irradiation on graphene field effect devices”, arXiv:1008.4561.
[5] Fischbein, Drndić, “Electron Beam Nanosculpting of Suspended Graphene Sheets”, arXiv:0808.2974.
[6] Krasheninnikov, Nordlund, “Ion and electron irradiation-induced effects in nanostructured materials”, J Appl Phys 107, 071301 (2010).
[7] Krasheninnikov, Banhart, “Engineering of nanostructured carbon materials with electron or ion beams”, Nature Materials, 6 (2007) 723-33.

Geometric phase (or Pancharatnam-Berry phase) has many surprising effects. What is this variously named “phase”? To quote Wikipedia, “The Berry phase occurs when [two] parameters are changed simultaneously but very slowly (adiabatically), and eventually brought back to the initial configuration.” [1] A light-hearted and easily understood introduction can be found in section 1 of ref. [2]. In what follows, I give a few examples of geometric phase effects that are relevant to nano-technology. (A lengthy review of the Berry phase in electronics can be found in [3].)

• A group at TU Denmark have shown in [4] that the Berry phase effects associated with electrical current flowing through a conductive molecular bridge may induce mechanical vibration sufficiently strong to rupture the bridge. This phenomenon is unrelated to electromigration, Joule heating, or other well-known effects. It is purely a result of the quantum mechanical phase of the electric waves.

• In an interesting experiment [5], Kohmura-san and colleagues at RIKEN demonstrate millimeter distance translation of X-rays by bent silicon crystals. The crystal was bent only 80 nm or so to achieve a beam displacement of 1.5 mm. See [6] for a brief summary.

• The Hasman group at the Technion have constructed optical structures showing technologically applicable geometric phase behavior. In [7] and [8] they display nano-lithographically defined gratings and apertures which can act as optical switches, among other things.

Try the little demonstration in [2]. It will serve as a reminder to keep your eyes open to the geometric phase.

References:

[1] Wikipedia article,  http://en.wikipedia.org/wiki/Berry’s_phase
[2] Robert W. Batterman, “Falling Cats, Parallel Parking, and Polarized Light”, http://philsci-archive.pitt.edu/archive/00000794/00/falling-cats.pdf
[3] Di Xiao, et al., “Berry Phase Effects on Electronic Properties”, Rev. Mod. Phys. 82 (2010) 1959-2007, http://rmp.aps.org/abstract/RMP/v82/i3/p1959_1
[4] Jing-Tao Lu, et al., “Blowing the Fuse: Berry’s Phase and Runaway Vibrations in Molecular Conductors”, Nano Letters 10 (2010) 1657-63, http://pubs.acs.org/doi/abs/10.1021/nl904233u
[5] Yoshiki Kohmura, et al., “Berry-Phase Translation of X Rays by a Deformed Crystal”, Phys. Rev. Lett. 104 (2010) 244801, http://prl.aps.org/abstract/PRL/v104/i24/e244801
[6] Adams, “Geometric phase kicks x rays down a new path”, http://physics.aps.org/articles/v3/50
[7] Erez Hasman, et al., “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures”, Optics Communications 209 (2002) 45-54, DOI: 10.1016/S0030-4018(02)01598-5, http://www.sciencedirect.com/science/article/B6TVF-4645DRF-1/2/6f0b7ca5cf17b751e48bbf1cf1e77d03
[8] Yuri Gorodetski, “Observation of Optical Spin Symmetry Breaking in Nanoapertures”, Nano Lett., Vol. 9, No. 8, 2009, http://pubs.acs.org/doi/abs/10.1021/nl901437d