Distribution of persistent currents in a multi-arm mesoscopic ring

Maiti, Santanu K.; Saha, Srilekha; Karmakar, S. N.

doi:10.1140/epjb/e2010-10737-0

Cited by 11 publications

(8 citation statements)

References 19 publications

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“…Persistent current being one such exotic quantum mechanical phenomenon observed in normal metal mesoscopic rings and nanotubes pierced by Aharonov-Bohm (AB) flux φ. Prior to its experimental evidence, the possibility of a non-decaying current in normal metal rings was first predicted by Büttiker, Imry and Landauer 3 in a pioneering work, and, in the sub-sequent years theoretical attempts were made [4][5][6][7][8][9][10][11][12][13][14][15][16][17] to understand the actual mechanism behind it. The experimental realization of this phenomenon of non-decaying current in metallic rings/cylinders has been established quite in late.…”

Section: Introductionmentioning

confidence: 99%

Magneto-transport in a quantum network: evidence of a mesoscopic switch

2012

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We investigate magneto-transport properties of a θ shaped three-arm mesoscopic ring where the upper and lower sub-rings are threaded by Aharonov-Bohm fluxes φ1 and φ2, respectively, within a non-interacting electron picture. A discrete lattice model is used to describe the quantum network in which two outer arms are subjected to binary alloy lattices while the middle arm contains identical atomic sites. It is observed that the presence of the middle arm provides localized states within the band of extended regions and lead to the possibility of switching action from a high conducting state to a low conducting one and vice versa. This behavior is justified by studying persistent current in the network. Both the total current and individual currents in three separate branches are computed by using second-quantized formalism and our idea can be utilized to study magnetic response in any complicated quantum network. The nature of localized eigenstates are also investigated from probability amplitudes at different sites of the quantum device. PACS numbers: 73.23.-b, 73.23.Ra.

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Section: Introductionmentioning

confidence: 99%

Magneto-transport in a quantum network: evidence of a mesoscopic switch

2012

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“…We note that a related multiring or multiarm setup has recently been studied within the non-interacting tight-binding formalism. 45 We take the hopping amplitude between the sites within the ring and within the lead as a constant, t 0 = −t, and measure all energies in the units of t. For the ring part of the system, we consider rings with the next-nearest neighbour coupling (2NN) that is given by the hopping amplitude t ′ .…”

Section: Model and Methodsmentioning

confidence: 99%

Fractional periodicity of persistent current in coupled quantum rings

Ijäs

Harju

2012

Phys. Rev. B

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We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as asymmetry. In the weakly coupled case, we find fractional periodicity at all electron fillings at sufficiently high Hubbard U, similar to isolated rings. For strongly coupled rings, on the contrary, fractional periodicity is only observed at sufficiently large negative gate voltages and high interaction strengths. This is explained by the formation of a bound correlated state in the ring that is effectively weakly coupled to the lead

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“…Through a Fourier transformation and the implementation of the fluctuation‐dissipation theorem, we can write the total current as

I = \int d ω f (ω) [j_{p} ((), ω) + j_{J} ((), ω)]

with

j_{p} false(ω false)

being the current density for the persistent current contribution given by [ 60 ]

j_{p} (ω) = \frac{e}{ℏ π} \sum_{k} 2 \sin (\frac{2 π}{N} normalΦ + k) Im {⟨ false⟨ c_{k}^{†}; c_{k} false⟩ ⟩}_{ω}^{r}

which is completely equivalent to expression (13). Hence,

j_{J} false(ω false)

is the Josephson density current, given by

\begin{matrix} true \\ right j ((), ω) & = & left - \frac{4 e}{h} \sum_{k} Im [λ_{(-)}^{' *} e^{i k j} Im {false⟨ ⟨ a^{†}; c_{k}^{†} ⟩ false⟩}_{ω}^{r} + λ_{(+)}^{'} e^{i k j} Im {false⟨ ⟨ a; c_{k}^{†} ⟩ false⟩}_{ω}^{r} \\ left + λ_{(-)} Im {false⟨ ⟨ f^{†}; c_{k}^{†} ⟩ false⟩}_{ω}^{r} + λ_{(+)} Im false⟨ ⟨ f; c_{k}^{†} \end{matrix}

…”

Section: Persistent and DC Josephson Currentsmentioning

confidence: 99%

Josephson and Persistent Currents in a Quantum Ring between Topological Superconductors

et al. 2021

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In this work, the spectra in an Aharonov–Bohm quantum‐ring interferometer forming a Josephson junction between two topological superconductor (TSC) nanowires are investigated. The TSCs host Majorana bound states at their edges, and both the magnetic flux and the superconducting phase difference between the TSCs are used as control parameters. A tight‐binding approach is used to model the quantum ring coupled to both TSCs, described by the Kitaev effective Hamiltonian. The problem is solved by means of exact numerical diagonalization of the Bogoliubov‐de Gennes Hamiltonian and obtain the spectra for two sizes of the quantum ring as a function of the magnetic flux and the phase difference between the TSCs. Depending on the size of the quantum ring and the coupling, the spectra display several patterns. Those are denoted as line, point, and undulated nodes, together with flat bands, which are topologically protected. The first three patterns can be possibly detected by means of persistent and Josephson currents. Hence, the results could be useful to understand the spectra and their relation with the behavior of the current signals.

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Distribution of persistent currents in a multi-arm mesoscopic ring

Cited by 11 publications

References 19 publications

Magneto-transport in a quantum network: evidence of a mesoscopic switch

Magneto-transport in a quantum network: evidence of a mesoscopic switch

Fractional periodicity of persistent current in coupled quantum rings

Josephson and Persistent Currents in a Quantum Ring between Topological Superconductors

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