Khatua, Bansal, and Shahar Reply:

Khatua, Pradip; Bansal, Bhavtosh; Shahar, D.

doi:10.1103/physrevlett.113.158902

Cited by 8 publications

(18 citation statements)

References 4 publications

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“…Endoh et al [31] have considered numerical simulations of the passage of such electrons through narrow constrictions. Recent experiments observed controlled electron diffraction for both single-and double-slit configurations [32,33].…”

Section: Example 3: Free Wave Packetmentioning

confidence: 99%

Numerical solutions of the time-dependent Schrödinger equation in two dimensions

2017

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The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrödinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference scheme in space. Extra care has to be taken for the needed precision of the time development. The method permits a systematic study of the accuracy and efficiency in terms of powers of the spatial and temporal step sizes. To illustrate its utility the method is applied to several two-dimensional systems.

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Section: Example 3: Free Wave Packetmentioning

confidence: 99%

Numerical solutions of the time-dependent Schrödinger equation in two dimensions

2017

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“…A recent experiment using time of flight measurement of electrons in the AB setup [11] seems to rule out classical and semiclassical explanations of AB effect. In contrast, single slit diffraction experiment using ballistic electrons in quantum point contacts [12] claims the equivalence of quantum formalism a la Aharonov-Bohm phase to the classical picture of electrons under the Lorentz force. We have pointed out that the claim could be misleading [13].…”

Section: Introductionmentioning

confidence: 96%

“…We have pointed out that the claim could be misleading [13]. The classical correspondence discussed in [12] is based on the so called Feynman's thought experiment [14].…”

Section: Introductionmentioning

confidence: 99%

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Physical reality of electromagnetic potentials and the classical limit of the Aharonov–Bohm effect

Tiwari

2017

Quantum Stud.: Math. Found.

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Recent literature on the Aharonov-Bohm effect has raised fundamental questions on the classical correspondence of this effect and the physical reality of the electromagnetic potentials in quantum mechanics. Reappraisal on Feynman's approach to the classical limit of AB effect is presented. The critique throws light on the significance of quantum interference and quantum phase shifts in any such classical correspondence. Detailed analysis shows that Feynman arguments are untenable on physical grounds and the claim made in the original AB paper that this effect had no classical analog seems valid. The importance of nonintegrable phase factor distinct from the AB phase factor, here termed as Fock-London-Weyl phase factor for the historical reasons, is underlined in connection with the classical aspects/limits. A topological approach incorporating the physical significance of the interaction field momentum is proposed. A new idea emerges from this approach that attributes the origin of the AB effect to the exchange of modular angular momentum.

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“…In the topological phase this spindle-shaped connection separates the opposite spin currents to the two channels [ Fig. 1(a at 32 nm to the right of the slit opening a zigzag ribbon of width 6.5 nm is connected as a detector [26]. In order to gain additional control in the interference device we introduce local gates (yellow gates in Fig.…”

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confidence: 99%

Electron interferometry and quantum spin Hall phase in silicene

2019

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We discuss devices for detection of the topological insulator phase based on the two-path electron interference. For that purpose we consider buckled silicene for which a local energy gap can be opened by vertical electric field to close one of the paths and for which the quantum spin Hall insulator conditions are controlled by the Fermi energy. In quantum spin Hall phase the interference is absent due to the separation of the spin currents and the conductance of the devices include sharp features related to localized resonances. In the normal transport conditions the two-path interference produces a regular Aharonov-Bohm oscillations in the external magnetic field.Quantum spin Hall (QSH) insulators [1-3] form a class of two-dimensional topological insulators with bulk energy gap and topologically protected currents of a fixed spin-orbital helicity. The QSH phase [4] is discussed for bulk nanostructures including HgTe quantum wells [5][6][7][8] and InAs/GaSb interfaces [9,10] as well as graphenelike monolayer Xenes materials [11,12], including silicene [13][14][15][16][17]. The QSH conditions in silicene occur for the Fermi energy near the charge neutrality point [13][14][15][16][17]. The Fermi energy in 2D monolayer materials can be controlled by external gating. In the QSH phase the spin currents are confined by opposite edges of the sample, which was used for proposals of spin sources and spin filters in silicene [18][19][20][21][22][23]. In this paper we propose electron interferometer devices that can be used for detection of the QSH transport conditions. The devices are based on the idea of two-path interference and the spin separation by the split silicene ribbon [18]. We consider a double slit interference device as well as a quantum ring and find that in the normal phase one observes smooth Aharonov-Bohm conductance oscillations while in the QSH regime only sharp conductance features due to the localized resonances with circular current loops are observed. In silicene both the localized resonances and the Aharonov-Bohm oscillations can be intentionally switched off by applying a local electric field to one of the arms of the split channels, due to the buckling of the crystal lattice that translates the electric field into a local energy gap [24,25] that stops the current flow.The schematics of the double slit interferometer depicted in [Fig. 1(a)]. The electrons are fed from the left by the silicene ribbon of a zigzag edge of 6.5 nm width. The zigzag ribbon supports the spin-polarized edge transport at the Fermi energy E F ∈ (−3, 3) meV with respect to the charge neutrality point [see the dispersion relation in Fig. 1(b)]. In the quantum spin Hall insulator phase the opposite spin currents flow at the opposite edges of the ribbon [see Fig. 1(a)]. The input lead splits into two channels of the same width. In the topological phase this spindle-shaped connection separates the opposite spin currents to the two channels [ Fig. 1(a)]. The split channels are connected to semi-infinite open plane of silicene [ F...

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Khatua, Bansal, and Shahar Reply:

Cited by 8 publications

References 4 publications

Numerical solutions of the time-dependent Schrödinger equation in two dimensions

Numerical solutions of the time-dependent Schrödinger equation in two dimensions

Physical reality of electromagnetic potentials and the classical limit of the Aharonov–Bohm effect

Electron interferometry and quantum spin Hall phase in silicene

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