Anomalous tunneling in a strong magnetic field and a smooth potential

Hajdu, János; Me, Raikh; Tv, Shahbazyan

doi:10.1103/physrevb.50.17625

Cited by 9 publications

(8 citation statements)

References 4 publications

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“…16,17. First experiments [28][29][30] indicated that there is a jump in non-diagonal component, σ xy , of the conductivity at ferromagnetic transition confirming the theoretical prediction. Very recently 11,12 , upon improving the quality of the samples, a very accurate quantization of σ xy was demonstrated.…”

Section: Introductionsupporting

confidence: 58%

“…This suggests that chiral edge modes can "communicate" with each other using nonchiral modes, which are less localized, as virtual intermediate states. [28][29][30][31] This is how the extended confinement may cause the smearing of the QAH transition.…”

Section: Discussionmentioning

confidence: 99%

“…[4][5][6][7][8][9][10][11][12][13][14][15][28][29][30] This doping gives rise to a spontaneous magnetization caused by exchange between the impurities. The most exciting consequence of this magnetization is that the associated spin splitting re- .…”

Section: Introductionmentioning

confidence: 99%

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Effect of extended confinement on the structure of edge channels in the quantum anomalous Hall effect

Yue¹,

Raǐkh²

2016

Phys. Rev. B

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Quantum anomalous Hall (QAH) effect in the films with nontrivial band structure accompanies the ferromagnetic transition in the system of magnetic dopants. Experimentally, the QAH transition manifests itself as a jump in the dependence of longitudinal resistivity on a weak external magnetic field. Microscopically, this jump originates from the emergence of a chiral edge mode on one side of the ferromagnetic transition. We study analytically the effect of an extended confinement on the structure of the edge modes. We employ the simplest model of the extended confinement in the form of potential step next to the hard wall. It is shown that, unlike the conventional quantum Hall effect, where all edge channels are chiral, in QAH effect, a complex structure of the boundary leads to nonchiral edge modes which are present on both sides of the ferromagnetic transition. Wave functions of nonchiral modes are different above and below the transition: on the "topological" side, where the chiral edge mode is supported, nonchiral modes are "repelled" from the boundary, i.e. they are much less localized than on the "trivial" side. Thus, the disorder-induced scattering into these modes will boost the extension of the chiral edge mode. The prime experimental manifestation of nonchiral modes is that, by contributing to longitudinal resistance, they smear the QAH transition.

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Section: Introductionsupporting

confidence: 58%

Section: Discussionmentioning

confidence: 99%

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Effect of extended confinement on the structure of edge channels in the quantum anomalous Hall effect

Yue¹,

Raǐkh²

2016

Phys. Rev. B

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“…The references [1,2,3,4,5,6,7,8,9] say that it is impossible. Indeed, when an electron enters under the barrier its velocity deviates, due to the cyclotron effect, from a tunneling path with no magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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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“…The major motivation, however, comes from the fact that tunneling in a magnetic field is an interesting and in many respects unusual theoretical problem, even in the single-particle formulation. Existing results, although often highly nontrivial, are limited to the cases where the potential has either a special form [13][14][15][16] (e.g., linear 13 or parabolic 15 ), or a part of the potential or the magnetic field are in some sense weak [17][18][19][20][21][22] . The problem of tunneling has two parts.…”

mentioning

confidence: 99%

Tunneling decay in a magnetic field

Sharpee

Dykman

Platzman³

2002

Phys. Rev. A

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We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the set of the particle Hamiltonian trajectories in complex phase space and time. In a magnetic field, the tunneling particle comes out from the barrier with a finite velocity and behind the boundary of the classically allowed region. The exit location is obtained by matching the decaying and outgoing WKB waves at a caustic in complex configuration space. Different branches of the WKB wave function match on the switching surface in real space, where the slope of the wave function sharply changes. The theory is not limited to tunneling from potential wells which are parabolic near the minimum. For parabolic wells, we provide a bounce-type formulation in a magnetic field. The theory is applied to specific models which are relevant to tunneling from correlated two-dimensional electron systems in a magnetic field parallel to the electron layer.

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Anomalous tunneling in a strong magnetic field and a smooth potential

Cited by 9 publications

References 4 publications

Effect of extended confinement on the structure of edge channels in the quantum anomalous Hall effect

Effect of extended confinement on the structure of edge channels in the quantum anomalous Hall effect

Cyclotron enhancement of tunneling

Tunneling decay in a magnetic field

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