Modern nanotechnology techniques offer new opportunities for fabricating structures and devices at the micrometer and sub-micrometer level. Here, we use focused ion beam techniques to realize micrometer-sized Janus bimetallic cylinders acting as drift tube devices, which are able to impart a controlled phase shift to an electron wave. The phase shift results from the presence of contact potentials in the cylinders, in a similar manner to the electrostatic Aharonov–Bohm effect in bimetallic wires. We use electron Fraunhofer interference to demonstrate that such bimetallic structures introduce phase shifts that can be tuned to desired values by varying the dimensions of the pillars, in particular their heights. Such devices are promising for electron beam shaping and for the realization of electrostatic Zernike phase plates (i.e., devices that are able to impart a constant phase shift between an unscattered and a scattered electron wave) in electron microscopy, in particular, cryo-electron microscopy.

1.
C.
Shukla
and
A.
Das
, “Ion vortex beam,” arXiv:1711.02896 (2017).
2.
G. M.
Vanacore
,
G.
Berruto
,
I.
Madan
,
E.
Pomarico
,
P.
Biagioni
,
R. J.
Lamb
,
D.
McGrouther
,
O.
Reinhardt
,
I.
Kaminer
,
B.
Barwick
,
H.
Larocque
,
V.
Grillo
,
E.
Karimi
,
F. J.
García de Abajo
, and
F.
Carbone
, “
Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields
,”
Nat. Mater.
18
,
573
579
(
2019
).
3.
K.
Nagayama
, “
Another 60 years in electron microscopy: Development of phase-plate electron microscopy and biological applications
,”
J. Electron Microsc. (Tokyo)
60
,
S43
S62
(
2011
).
4.
R. M.
Glaeser
, “
Invited review article: Methods for imaging weak-phase objects in electron microscopy
,”
Rev. Sci. Instrum.
84
,
eid111101
(
2013
).
5.
R.
Cambie
,
K. H.
Downing
,
D.
Typke
,
R. M.
Glaeser
, and
J.
Jin
, “
Design of a microfabricated, two-electrode phase-contrast element suitable for electron microscopy
,”
Ultramicroscopy
107
,
329
339
(
2007
).
6.
J.
Perry-Houts
,
B.
Barton
,
A.
Schmid
,
N.
Andresen
, and
C.
Kisielowski
, “
Novel long-lived electrostatic work function phase plates for TEM
,”
Microsc. Microanal.
18
,
476
477
(
2012
).
7.
H.
Tamaki
,
H.
Kasai
,
K.
Harada
,
Y.
Takahashi
, and
R.
Nishi
, “
Development of a contact-potential-type phase plate
,”
Microsc. Microanal.
19
,
1148
1149
(
2013
).
8.
Y.
Aharonov
and
D.
Bohm
, “
Significance of electromagnetic potentials in the quantum theory
,”
Phys. Rev.
115
,
485
491
(
1959
).
9.
Y.
Aharonov
, “Non-local phenomena and the Aharonov-Bohm effect,” in Proceedings of the International Symposium on Foundations of Quantum Mechanics (ISQM’83), edited by S. Kamefuchi, H. Ezawa, Y. Murayama, M. Namiki, S. Nomura, Y. Ohnuki, and T. Yajima (Physical Society of Japan, Tokyo, 1984), pp. 10–19.
10.
S.
Olariu
and
I. I.
Popescu
, “
The quantum effects of electromagnetic fluxes
,”
Rev. Mod. Phys.
57
,
339
436
(
1985
).
11.
T. H.
Boyer
, “
Classical electromagnetic deflections and lag effects associated with quantum interference pattern shifts: Considerations related to the Aharonov-Bohm effect
,”
Phys. Rev. D
8
,
1679
1693
(
1973
).
12.
T. H.
Boyer
, “
Semiclassical explanation of the Matteucci-Pozzi and Aharonov-Bohm phase shifts
,”
Found. Phys.
32
,
41
49
(
2002
).
13.
G.
Matteucci
,
G. F.
Missiroli
, and
G.
Pozzi
, “
A new electrostatic phase-shifting effect
,”
Ultramicroscopy
10
,
247
251
(
1982
).
14.
G.
Matteucci
and
G.
Pozzi
, “
New diffraction experiment on the electrostatic Aharonov-Bohm effect
,”
Phys. Rev. Lett.
54
,
2469
2472
(
1985
).
15.
G.
Matteucci
,
F. F.
Medina
, and
G.
Pozzi
, “
Electron-optical analysis of the electrostatic Aharonov-Bohm effect
,”
Ultramicroscopy
41
,
255
268
(
1992
).
16.
G.
Matteucci
,
G. F.
Missiroli
, and
G.
Pozzi
, “Electron holography of long-range electrostatic fields,” in Advances in Imaging and Electron Physics, edited by P. W. Hawkes (Elsevier, 2002), Vol. 122, pp. 173–249.
17.
G.
Pozzi
, “Particles and waves in electron optics and microscopy,” in Advances in Imaging and Electron Physics, edited by P. W. Hawkes (Academic Press, New York, 2016), Vol. 194.
18.
E.
Ball
, “
Potential from a ring of charge
,”
Proc. Inst. Electrical Eng.
124
,
664
(
1977
).
19.
F. R.
Zypman
, “
Off-axis electric field of a ring of charge
,”
Am. J. Phys.
74
,
295
300
(
2006
).
20.
O.
Ciftja
,
A.
Babineaux
, and
N.
Hafeez
, “
The electrostatic potential of a uniformly charged ring
,”
Eur. J. Phys.
30
,
623
627
(
2009
).
21.
G. B.
Arfken
and
H.-J.
Weber
,
Mathematical Methods for Physicists
, 6th ed. (
Elsevier
,
Boston
,
2005
).
22.
A. H.
Tavabi
,
V.
Migunov
,
C.
Dwyer
,
R. E.
Dunin-Borkowski
, and
G.
Pozzi
, “
Tunable caustic phenomena in electron wavefields
,”
Ultramicroscopy
157
,
57
64
(
2015
).
23.
S.
Wolfram
,
The Mathematica Book
, 4th ed. (
Wolfram Media
,
Champaign, IL
,
1999
).
24.
M.
Beleggia
,
T.
Kasama
,
R. E.
Dunin-Borkowski
,
S.
Hofmann
, and
G.
Pozzi
, “
Direct measurement of the charge distribution along a biased carbon nanotube bundle using electron holography
,”
Appl. Phys. Lett.
98
,
243101
(
2011
).
25.
C.
Gatel
,
A.
Lubk
,
G.
Pozzi
,
E.
Snoeck
, and
M.
Hÿtch
, “
Counting elementary charges on nanoparticles by electron holography
,”
Phys. Rev. Lett.
111
,
025501
(
2013
).
26.
M.
Beleggia
,
L.
Gontard
, and
R.
Dunin-Borkowski
, “
Local charge measurement using off-axis electron holography
,”
J. Phys. D: Appl. Phys.
49
,
294003
(
2016
).
27.
M.
Born
and
E.
Wolf
,
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light
, 4th ed. (
Pergamon Press
,
Oxford
,
1969
).
28.
H. B.
Michaelson
, “
The work function of the elements and its periodicity
,”
J. Appl. Phys.
48
,
4729
4733
(
1977
).
29.
J. R.
Rumble
,
D. R.
Lide
, and
T. J.
Bruno
,
CRC Handbook of Chemistry and Physics : A Ready-reference Book of Chemical and Physical Data
(
CRC Press
,
2020
).
30.
H.
Kohl
and
L.
Reimer
,
Transmission Electron Microscopy: Physics of Image Formation
(
Springer
,
2008
).
31.
G.
Pozzi
,
M.
Beleggia
,
T.
Kasama
, and
R. E.
Dunin-Borkowski
, “
Interferometric methods for mapping static electric and magnetic fields
,”
C. R. Phys.
15
,
126
139
(
2014
).
32.
P.
Thakkar
,
V. A.
Guzenko
,
P.-H.
Lu
,
R. E.
Dunin-Borkowski
,
J. P.
Abrahams
, and
S.
Tsujino
, “
Fabrication of low aspect ratio three-element Boersch phase shifters for voltage-controlled three electron beam interference
,”
J. Appl. Phys.
128
,
134502
(
2020
).
33.
P.
Bevington
and
D.
Robinson
,
Data Reduction and Error Analysis for the Physical Sciences
(
McGraw-Hill Education
,
2003
).
34.
S.
Fürhapter
,
A.
Jesacher
,
C.
Maurer
,
S.
Bernet
, and
M.
Ritsch-Marte
, “Spiral phase microscopy,” in Advances in Imaging and Electron Physics, edited by P. W. Hawkes (Elsevier, 2007), Vol. 146, pp. 1–56.
35.
R.
Juchtmans
,
L.
Clark
,
A.
Lubk
, and
J.
Verbeeck
, “
Spiral phase plate contrast in optical and electron microscopy
,”
Phys. Rev. A
94
,
023838
(
2016
).
36.
R.
Juchtmans
and
J.
Verbeeck
, “
Local orbital angular momentum revealed by spiral-phase-plate imaging in transmission-electron microscopy
,”
Phys. Rev. A
93
,
023811
(
2016
).
37.
G.
Pozzi
,
P.-H.
Lu
,
A. H.
Tavabi
,
M.
Duchamp
, and
R. E.
Dunin-Borkowski
, “
Generation of electron vortex beams using line charges via the electrostatic Aharonov-Bohm effect
,”
Ultramicroscopy
181
,
191
196
(
2017
).
38.
A. H.
Tavabi
,
H.
Larocque
,
P.-H.
Lu
,
M.
Duchamp
,
V.
Grillo
,
E.
Karimi
,
R. E.
Dunin-Borkowski
, and
G.
Pozzi
, “
Generation of electron vortices using nonexact electric fields
,”
Phys. Rev. Res.
2
,
013185
(
2020
).
39.
G.
Pozzi
,
V.
Grillo
,
P.-H.
Lu
,
A. H.
Tavabi
,
E.
Karimi
, and
R. E.
Dunin-Borkowski
, “
Design of electrostatic phase elements for sorting the orbital angular momentum of electrons
,”
Ultramicroscopy
208
,
112861
(
2020
).
40.
A. H.
Tavabi
,
P.
Rosi
,
E.
Rotunno
,
A.
Roncaglia
,
L.
Belsito
,
S.
Frabboni
,
G.
Pozzi
,
G. C.
Gazzadi
,
P.-H.
Lu
,
R.
Nijland
et al., “
Experimental demonstration of an electrostatic orbital angular momentum sorter for electron beams
,”
Phys. Rev. Lett.
126
,
094802
(
2021
).
41.
G.
Ruffato
,
E.
Rotunno
,
L. M. C.
Giberti
, and
V.
Grillo
, “
Arbitrary conformal transformations of wave functions
,”
Phys. Rev. Appl.
10
,
1
11
(
2021
).
42.
J.
Verbeeck
,
A.
Béché
,
K.
Müller-Caspary
,
G.
Guzzinati
,
M. A.
Luong
, and
M.
Den Hertog
, “
Demonstration of a 2×2 programmable phase plate for electrons
,”
Ultramicroscopy
190
,
58
65
(
2018
).
43.
M.
Malac
,
S.
Hettler
,
M.
Hayashida
,
E.
Kano
,
R. F.
Egerton
, and
M.
Beleggia
, “
Phase plates in the transmission electron microscope: Operating principles and applications
,”
Microscopy
70
,
75
115
(
2021
).
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