Transmission gaps, trapped modes and Fano resonances in Aharonov–Bohm connected mesoscopic loops

Mrabti, T.; Labdouti, Z.; Abouti, O. El; Boudouti, El Houssaine El; Fethi, Fouad; Djafari‐Rouhani, Bahram

doi:10.1016/j.physleta.2018.01.003

Cited by 12 publications

(12 citation statements)

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“…We shall avoid the details of calculation where an analysis of the Shr€ odinger equation in presence of a magnetic flux gives rise to the bulk Green's function of an infinite wire. These calculations are presented elsewhere [65].…”

Section: Green's Functions Approachmentioning

confidence: 99%

“…The inverse of the Green's function g À1 1 ðM 1 M 1 Þ in the space of interface M 1 ¼ f0; 1g of a finite wire of length d 1 (Fig. 2(a)) can be written as a (2 � 2) matrix [65]:…”

Section: Green's Functions Approachmentioning

confidence: 99%

“…The inverse of the Green's function g À1 r ðM 2 M 2 Þ in the space of interface M 2 ¼ f1; 2g of the ring made of two wires of length d and in presence of a magnetic flux Φ (Fig. 2(b)) can be written as a (2 � 2) matrix, namely [65].…”

Section: Green's Functions Approachmentioning

confidence: 99%

“…and ii) the Green's function of the two semi-infinite leads in the space of interface M 3 ¼ f0g, which is given by Ref. [65].…”

Section: Transmission and Reflection Coefficientsmentioning

confidence: 99%

“…These latter resonances are characterized by a peak followed by a dip in the transmission spectra as a consequence of a destructive interference of the waves, giving rise to an asymmetric line shape. These resonances have been the subject of intensive study from the theoretical and experimental point of view in single [47][48][49][50][51][52][53][54][55][56][57] and double [58][59][60][61][62][63][64][65] rings placed between two leads. In addition to Fano resonances, persistent currents are also studied in detail in A-B structures made of one or double rings [47,53,58] in presence of the magnetic flux and impurity or quantum dots in the arms of the ring.…”

Section: Introductionmentioning

confidence: 99%

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Aharonov-Bohm-effect induced transparency and reflection in mesoscopic rings side coupled to a quantum wire

Mrabti

Labdouti

Mouadili

et al. 2020

Physica E: Low-dimensional Systems and Nanostructures

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We demonstrate analytically and numerically the possibility of existence of the analogues of electromagnetic induced transparency (EIT) and electromagnetic induced reflection (EIR) in a simple mesoscopic structure. The latter consists of a ring of length 2d attached vertically to two semi-infinite leads (waveguide) by a wire of length d 1 . The ring is threaded by a magnetic flux Φ, the so-called Aharonov-Bohm effect. The number of dangling wire-ring resonators attached at the same point can be increased to N. First, we demonstrate analytically that in the absence of the magnetic flux (Φ ¼ 0) and for particular values of d 1 , the structure may present some states that are confined in the ring and do not interact with the waveguide states. These trapped states fall in the continuum states of the two leads and therefore represent bound in continuum (BIC) states. These states are characterized by a zero width resonance (i.e., infinite life-time) in the transmission and reflection spectra. In presence of a weak magnetic flux (Φ 6 ¼ 0), the BIC states transform to EIT or EIR resonances for specific values of the lengths d 1 and d of the wire and the ring respectively. In addition to the numerical results, we have developed Taylor expansion calculations of the transmission and reflection coefficients around EIT and EIR resonances to show that the latter can be written following a Fano shape. In particular, we have deduced the Fano parameter q and the quality factor Q of these resonances as function of N and the flux Φ. We have found that Q decreases as function of Φ for both EIT and EIR resonances, whereas it increases (decreases) as function of N for EIT (EIR) resonances. These results show the possibility of tuning EIT and EIR resonances by means of the magnetic flux Φ and the number of dangling resonators N. The effect of temperature on EIT and EIR resonances is also considered through an analysis of the Landauer-Buttiker conductance formula obtained from transmission. The theoretical results are obtained within the framework of the Green's function method which enables us to deduce analytically the dispersion relation, transmission and reflection coefficients. These results may have important applications for electronic transport in mesoscopic systems such as filters and demultiplexers.

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Section: Green's Functions Approachmentioning

confidence: 99%

“…The inverse of the Green's function g À1 1 ðM 1 M 1 Þ in the space of interface M 1 ¼ f0; 1g of a finite wire of length d 1 (Fig. 2(a)) can be written as a (2 � 2) matrix [65]:…”

Section: Green's Functions Approachmentioning

confidence: 99%

Section: Green's Functions Approachmentioning

confidence: 99%

“…and ii) the Green's function of the two semi-infinite leads in the space of interface M 3 ¼ f0g, which is given by Ref. [65].…”

Section: Transmission and Reflection Coefficientsmentioning

confidence: 99%