Skip to main content
    • Aa
    • Aa

On-Column 2p Bound State with Topological Charge ±1 Excited by an Atomic-Size Vortex Beam in an Aberration-Corrected Scanning Transmission Electron Microscope

  • Huolin L. Xin (a1) and Haimei Zheng (a1)

Atomic-size vortex beams have great potential in probing the magnetic moment of materials at atomic scales. However, the limited depth of field of vortex beams constrains the probing depth in which the helical phase front is preserved. On the other hand, electron channeling in crystals can counteract beam divergence and extend the vortex beam without disrupting its topological charge. Specifically, in this article, we report that atomic vortex beams with topological charge ±1 can be coupled to the 2p columnar bound states and propagate for more than 50 nm without being dispersed and losing its helical phase front. We give numerical solutions to the 2p columnar orbitals and tabulate the characteristic size of the 2p states of two typical elements, Co and Dy, for various incident beam energies and various atomic densities. The tabulated numbers allow estimates of the optimal convergence angle for maximal coupling to 2p columnar orbital. We have also developed analytic formulae for beam energy, convergence angle, and hologram-dependent scaling for various characteristic sizes. These length scales are useful for the design of pitch-fork apertures and operations of microscopes in the vortex-beam imaging mode.

Corresponding author
Corresponding author. E-mail:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

L. Allen , M. Beijersbergen , R. Spreeuw & J. Woerdman (1992). Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 45, 81858189.

L.J. Allen , S.D. Findlay , M.P. Oxley & C.J. Rossouw (2003). Lattice-resolution contrast from a focused coherent electron probe. Part I. Ultramicroscopy 96, 4763.

G.R. Anstis , D.Q. Cai & D.J.H. Cockayne (2003). Limitations on the s-state approach to the interpretation of sub-angstrom resolution electron microscope images and microanalysis. Ultramicroscopy 94, 309327.

I.V. Basistiy , M.S. Soskin & M.V. Vasnetsov (1995). Optical wavefront dislocations and their properties. Opt Comm 119, 604612.

M.W. Beirjersbergen , R.P.C. Coerwinkel , M. Kristensen & J.P. Woerdman (1994). Helical-wavefront laser beams produced with a spiral phaseplate. Opt Comm 112, 321327.

K. Bliokh , Y. Bliokh , S. Savel'ev & F. Nori (2007). Semiclassical dynamics of electron wave packet states with phase vortices. Phys Rev Lett 99, 190404.

K.Y. Bliokh , M.R. Dennis & F. Nori (2011). Relativistic electron vortex beams: Angular momentum and spin-orbit interaction. Phys Rev Lett 107, 174802.

G.F. Brand (1999). Phase singularities in beams. Am J Phys 67, 55.

J.H. Chen & D. Van Dyck (1997). Accurate multislice theory for elastic electron scattering in transmission electron microscopy. Ultramicroscopy 70, 2944.

J.M. Cowley & A. Moodie (1957). The scattering of electrons by atoms and crystals. I. A new theoretical approach. Acta Crystallogr 10, 609619.

J.E. Curtis , B.A. Koss & D.G. Grier (2002). Dynamic holographic optical tweezers. Opt Comm 207, 169175.

K. Fujiwara (1961). Relativistic dynamical theory of electron diffraction. J Phys Soc Jpn 16, 22262238.

P. Geuens & D. Van Dyck (2002). The S-state model: A work horse for HRTEM. Ultramicroscopy 93, 179198.

D. Gratias & R. Portier (1983). Time-like perturbation method in high-energy electron diffraction. Acta Crystallogr A 39, 576584.

D.G. Grier (2003). A revolution in optical manipulation. Nature 424, 910.

H. Hashimoto (1964). Energy dependence of extinction distance and transmissive power for electron waves in crystals. J Appl Phys 35, 277.

H. He , M.E.J. Friese , N.R. Heckenberg & H. Rubinsztein-Dunlop (1995). Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys Rev Lett 75, 826829.

N.R. Heckenberg , R. McDuff , C.P. Smith & A.G. White (1992). Generation of optical phase singularities by computer-generated holograms. Opt Lett 17, 221223.

R. Henderson (1995). The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Q Rev Biophys 28, 171193.

R.A. Herring (2011). A new twist for electron beams. Science 331, 155.

S. Hillyard , R.F. Loane & J. Silcox (1993). Annular dark-field imaging: Resolution and thickness effects. Ultramicroscopy 49, 1425.

S. Hillyard & J. Silcox (1993). Thickness effects in ADF STEM zone-axis images. Ultramicroscopy 52, 325334.

R. Hovden , H.L. Xin & D.A. Muller (2010). Determining resolution in an abberration-corrected era: Why your probe is larger than you thought. Microsc Microanal 16, 152153.

C. Humphreys (1979). The scattering of fast electrons by crystals. Rep Prog Phys 42, 18251887.

V. Intaraprasonk , H.L. Xin & D.A. Muller (2008). Analytic derivation of optimal imaging conditions for incoherent imaging in aberration-corrected electron microscopes. Ultramicroscopy 108, 14541466.

K.T. Kapale & J.P. Dowling (2005). Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in bose-einstein condensates via optical angular momentum beams. Phys Rev Lett 95, 173601.

E.J. Kirkland (2010). Advanced Computing in Electron Microscopy. New York: Springer Verlag.

E.J. Kirkland , R.F. Loane & J. Silcox (1987). Simulation of annular dark field stem images using a modified multislice method. Ultramicroscopy 23, 7796.

B.J. McMorran , A. Agrawal , I.M. Anderson , A.A. Herzing , H.J. Lezec , J.J. McClelland & J. Unguris (2011b). Electron vortex beams with high quanta of orbital angular momentum. Science 331, 192195.

P.D. Nellist & S.J. Pennycook (1999). Incoherent imaging using dynamically scattered coherent electrons. Ultramicroscopy 78, 111124.

J.F. Nye & M.V. Berry (1974). Dislocations in wave trains. P Roy Soc A-Math Phy 336, 165190.

A. O'Neil , I. MacVicar , L. Allen & M. Padgett (2002). Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys Rev Lett 88, 053601.

M. Padgett , J. Courtial & L. Allen (2004). Light's orbital angular momentum. Phys Today 57(5), 3540.

S.J. Pennycook & D.E. Jesson (1990). High-resolution incoherent imaging of crystals. Phys Rev Lett 64, 938941.

A. Rother & K. Scheerschmidt (2009). Relativistic effects in elastic scattering of electrons in TEM. Ultramicroscopy 109, 154160.

P. Schattschneider (2008). Exchange of angular momentum in EMCD experiments. Ultramicroscopy 109, 9195.

P. Schattschneider , M. Stöger-Pollach , S. Löffler , A. Steiger-Thirsfeld , J. Hell & J. Verbeeck (2012). Sub-nanometer free electrons with topological charge. Ultramicroscopy 115, 2125.

P. Schattschneider & J. Verbeeck (2011). Theory of free electron vortices. Ultramicroscopy 111, 14611468.

M. Uchida & A. Tonomura (2010). Generation of electron beams carrying orbital angular momentum. Nature 464, 737739.

S. Van Aert , P. Geuens , D. Van Dyck , C. Kisielowski & J. Jinschek (2007). Electron channelling based crystallography. Ultramicroscopy 107, 551558.

D. Van Dyck & W. Coene (1984). The real space method for dynamical electron diffraction calculations in high resolution electron microscopy: I. Principles of the method. Ultramicroscopy 15, 2940.

D. Van Dyck & M.O. deBeeck (1996). A simple intuitive theory for electron diffraction. Ultramicroscopy 64, 99107.

J. Verbeeck , P. Schattschneider , S. Lazar , M. Stoger-Pollach , S. Loffler , A. Steiger-Thirsfeld & G. Van Tendeloo (2011a). Atomic scale electron vortices for nanoresearch. Appl Phys Lett 99, 203109203111.

J. Verbeeck , H. Tian & A. Béché (2011b). A new way of producing electron vortex probes for STEM. Ultramicroscopy 113, 8387.

J. Verbeeck , H. Tian & P. Schattschneider (2010). Production and application of electron vortex beams. Nature 467, 301304.

H.L. Xin & D.A. Muller (2009). Aberration-corrected ADF-STEM depth sectioning and prospects for reliable 3D imaging in S/TEM. J Elec Microsc 58, 157165.

H.L. Xin & D.A. Muller (2010a). Electron microscopy: A new spin on electron beams. Nature Nanotechnol 5, 764765.

H.L. Xin & D.A. Muller (2010b). Three-dimensional imaging in aberration-corrected electron microscopes. Microsc Microanal 16, 445455.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Microscopy and Microanalysis
  • ISSN: 1431-9276
  • EISSN: 1435-8115
  • URL: /core/journals/microscopy-and-microanalysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 1
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 101 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st July 2017. This data will be updated every 24 hours.