Tunneling in a magnetic field

Ivlev, B.

doi:10.1103/physreva.73.052106

Cited by 11 publications

(16 citation statements)

References 21 publications

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“…[3], where it was taken u(y) = u 0 y 2 /a 2 + y 4 /a 4 . The decaying wave function is illustrated in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…1, where we do not know a detailed form of the wave function. The vortex structure of the wave function is a consequence of a specific analytical form of the potential u(y) [3] and does not depend on the magnetic field. For example, for a quadratic u(y) topological vortices under the barrier are absent and there are smooth current curves only.…”

Section: Electric Current Under the Barriermentioning

confidence: 99%

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Euclidean resonance in a magnetic field

Ivlev

2007

Phys. Rev. A

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An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed region, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.

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“…[3], where it was taken u(y) = u 0 y 2 /a 2 + y 4 /a 4 . The decaying wave function is illustrated in Fig.…”

Section: Discussionmentioning

confidence: 99%

Section: Electric Current Under the Barriermentioning

confidence: 99%

Euclidean resonance in a magnetic field

Ivlev

2007

Phys. Rev. A

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“…One can find the action (31) by a direct solution of the HamiltonJacobi equation (10). Since the condition (11) holds at all y, it follows from (10) that ∂σ(0, y) ∂y…”

Section: A Total Actionmentioning

confidence: 99%

“…See, for example, [10,11]. The expression in the square brackets is the Lagrangian in terms of imaginary time.…”

Section: Classical Trajectoriesmentioning

confidence: 99%

“…Nevertheless, to calculate a tunneling rate with the exponential accuracy it is not necessary to solve the Hamilton-Jacobi equation (10) in the full {x, y} plane. It is sufficient to track σ(x, y) along a classical trajectory {x(τ ), y(τ )}, where τ = −it is imaginary time since an underbarrier classical motion is impossible.…”

Section: Classical Trajectoriesmentioning

confidence: 99%

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Cyclotron enhancement of tunneling

Medvedeva

Larkin²,

Ujevic³

et al. 2008

Phys. Rev. B

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A state of an electron in a quantum wire or a thin film becomes metastable, when a static electric field is applied perpendicular to the wire direction or the film surface. The state decays via tunneling through the created potential barrier. An additionally applied magnetic field, perpendicular to the electric field, can increase the tunneling decay rate for many orders of magnitude. This happens, when the state in the wire or the film has a velocity perpendicular to the magnetic field. According to the cyclotron effect, the velocity rotates under the barrier and becomes more aligned with the direction of tunneling. This mechanism can be called cyclotron enhancement of tunneling.

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