Observation of Aharonov-Bohm effect by electron holography

Tonomura, Akira; Matsuda, Tsuyoshi; Suzuki, Ryō; Fukuhara, A.; Osakabe, Nobuyuki; Umezaki, H.; Shinagawa, K.; Sugita, Y.; Fujiwara, Hideo

doi:10.1007/3-540-11994-9_23

Cited by 6 publications

(13 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that due to its non trivial topology a torus can contain inside a magnetic field without any leak. This was done experimentally in [6], [29]- [32] and theoretically in [3]- [5].…”

Section: Physical Considerationsmentioning

confidence: 99%

High-velocity estimates for Schrödinger operators in two dimensions: Long-range magnetic potentials and time-dependent inverse scattering

Ballesteros

Weder

2015

Rev. Math. Phys.

View full text Add to dashboard Cite

We introduce a general class of long-range magnetic potentials and derive high velocity limits for the corresponding scattering operators in quantum mechanics, in the case of two dimensions. We analyze the high velocity limits that we obtain in the presence of an obstacle and we uniquely reconstruct from them the electric potential and the magnetic field outside the obstacle, that are accessible to the particles. We additionally reconstruct the inaccessible fluxes (magnetic fluxes produced by fields inside the obstacle) modulo 2π, which give a proof of the Aharonov-Bohm effect. For every magnetic potential A in our class, we prove that its behavior at infinity (A∞(v),v ∈ S 1 ) can be characterized in a natural way; we call it the long-range part of the magnetic potential. Under very general assumptions, we prove that A∞(v)+ A∞(−v) can be uniquely reconstructed for everyv ∈ S 1 . We characterize properties of the support of the magnetic field outside the obstacle that permit us to uniquely reconstruct A∞(v) either for allv ∈ S 1 or forv in a subset of S 1 . We also give a wide class of magnetic fields outside the obstacle allowing us to uniquely reconstruct the total magnetic flux (and A∞(v) for allv ∈ S 1 ). This is relevant because, as it is well-known, in general the scattering operator (even if it is known for all velocities or energies) does not define uniquely the total magnetic flux (and A∞(v)). We analyze additionally injectivity (i.e. uniqueness without giving a method for reconstruction) of the high velocity limits of the scattering operator with respect to A∞(v). Assuming that the magnetic field outside the obstacle is not identically zero, we provide a class of magnetic potentials for which injectivity is valid.

show abstract

“…Note that due to its non trivial topology a torus can contain inside a magnetic field without any leak. This was done experimentally in [6], [29]- [32] and theoretically in [3]- [5].…”

Section: Physical Considerationsmentioning

confidence: 99%

High-velocity estimates for Schrödinger operators in two dimensions: Long-range magnetic potentials and time-dependent inverse scattering

Ballesteros

Weder

2015

Rev. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…Indeed two different electron paths are phase shifted with respect to each other by ∆φ = A · ds = Σ B · dS. The Aharonov-Bohm phase shift is commonly exploited through electron holography to measure the in-plane component of the magnetization [58]. The fabrication of magnetic phase plates for contrast enhancement through the Aharonov-Bohm phase is also currently under study [59].…”

Section: ) and Electronmentioning

confidence: 99%

Shaping electron beams for the generation of innovative measurements in the (S)TEM

Verbeeck

Guzzinati

Clark

et al. 2014

Comptes Rendus. Physique

View full text Add to dashboard Cite

In TEM, a typical goal consists of making a small electron probe in the sample plane in order to obtain high spatial resolution in scanning transmission electron microscopy. In order to do so, the phase of the electron wave is corrected to resemble a spherical wave compensating for aberrations in the magnetic lenses. In this contribution we discuss the advantage of changing the phase of an electron wave in a specific way in order to obtain fundamentally different electron probes opening up new application in the (S)TEM. We focus on electron vortex states as a specific family of waves with an azimuthal phase signature and discuss their properties, production and applications. The concepts presented here are rather general and also different classes of probes can be obtained in a similar fashion showing that electron probes can be tuned to optimise a specific measurement or interaction.

show abstract

“…From the interference pattern, known as an electron hologram, a phase image and an amplitude image of the specimen can be reconstructed. In the absence of magnetic fields and diffraction contrast, the phase change of an electron as it passes through a specimen of thickness, t is given by; where C E is a constant dependent on the energy of the electron wave, V is the electrostatic potential and z , the electron beam direction (Tomomura, 1982).…”

Section: Introductionmentioning

confidence: 99%

Quantitative off‐axis electron holography of GaAs p‐n junctions prepared by focused ion beam milling

Cooper

Truche

Twitchett-Harrison

et al. 2009

Journal of Microscopy

View full text Add to dashboard Cite

SummaryFocused Ion beam (FIB) prepared GaAs p-n junctions have been examined using off-axis electron holography. Initial analysis of the holograms reveals an experimentally determined builtin potential in the junctions that is significantly smaller than predicted from theory. In this paper we show that through combinations of in situ annealing and in situ biasing of the specimens, by varying the intensity of the incident electron beam, and by modifying the FIB operating parameters, we can develop an improved understanding of phenomena such as the electrically 'inactive' thickness and subsequently recover the predicted value of the built-in potential of the junctions.

show abstract

Observation of Aharonov-Bohm effect by electron holography

Cited by 6 publications

References 8 publications

High-velocity estimates for Schrödinger operators in two dimensions: Long-range magnetic potentials and time-dependent inverse scattering

High-velocity estimates for Schrödinger operators in two dimensions: Long-range magnetic potentials and time-dependent inverse scattering

Shaping electron beams for the generation of innovative measurements in the (S)TEM

Quantitative off‐axis electron holography of GaAs p‐n junctions prepared by focused ion beam milling

Contact Info

Product

Resources

About