Coherent electron transport in bent cylindrical surfaces

Marchi, A.; Reggiani, Susanna; Rudan, Massimo; Bertoni, Alberto

doi:10.1103/physrevb.72.035403

Cited by 58 publications

(73 citation statements)

References 17 publications

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“…With these techniques we built a numerical code which we validated by reproducing the result for the electron transmittance in an axially symmetric cylindrical junction studied in [10].…”

Section: Quantum Particle In a Curved Surface With Azimuthal Symmetrymentioning

confidence: 99%

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Geometric effects in the electronic transport of deformed nanotubes

et al. 2016

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Abstract. Quasi-two-dimensional systems may exibit curvature, which adds three-dimensional influence to their internal properties. As shown by da Costa [1], charged particles moving on a curved surface experience a curvature-dependent potential which greatly influence their dynamics. In this paper, we study the electronic ballistic transport in deformed nanotubes. The one-electron Schrödinger equation with open boundary conditions is solved numerically with a flexible MAPLE code made available as Supplementary Data. We find that the curvature of the deformations have indeed strong effects on the electron dynamics suggesting its use in the design of nanotube-based electronic devices.

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“…With these techniques we built a numerical code which we validated by reproducing the result for the electron transmittance in an axially symmetric cylindrical junction studied in [10].…”

Section: Quantum Particle In a Curved Surface With Azimuthal Symmetrymentioning

confidence: 99%

“…Ballistic electron transport in nanotubes is known to be drastically affected by variations of the tube geometry [10,11] and therefore, of the local curvature. This effect is the main concern of the present article.…”

Section: Introductionmentioning

confidence: 99%

Geometric effects in the electronic transport of deformed nanotubes

et al. 2016

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“…On the basis of this, one then deduces an effective dimensionally reduced Schrödinger equation. The thin-wall quantization procedure has been widely employed since [7][8][9][10][11][12][13][14] . From the experimental point of view, the realization of an optical analogue of the curvature-induced geometric potential can be taken as empirical evidence for the validity of Da Costa's squeezing procedure 15 .…”

Section: Pacs Numbersmentioning

confidence: 99%

Curvature-induced geometric potential in strain-driven nanostructures

et al. 2011

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The experimental progress in synthesizing low dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. The current theoretical paradigm relies on a thin wall quantization method introduced by Da Costa [2]. In Ref.[3] Jensen and Dandoloff find that when employing the thin wall quantization in presence of externally applied electric and magnetic fields, an unphysical orbital magnetic moment appears. This anomalous result is taken as evidence for the breakdown of the thin wall quantization. We show, however, that in a proper treatment within the Da Costa framework: (i) this anomalous contribution is absent and (ii) there is no coupling between external electromagnetic field and surface curvature [1]. PACS numbers:To derive the thin wall quantization in presence of external electromagnetic field we start with the Schrödinger equation that is minimally coupled with the four component vector potential in a generic curved threedimensional space. Adopting Einstein summation convention and tensor covariant and contravariant components, we havewhere Q is the particle charge, G ij are the contravariant components of the metric tensor and A i are the covariant components of the vector potential A with the scalar potential defined by V = −A 0 . The covariant derivative D i is as usual defined bywhere v j are the covariant components of a vector field v and Γ k ij are the Christoffel symbolsFrom Eq. (1) one obtainswhere for convenience we introduced the time gauge covariant derivative D 0 = ∂ t − iQA 0 / . To proceed further, it is useful to define a coordinate system. As in Ref.[2-4] we consider a surface S with parametric equations r = r(q 1 , q 2 ). The portion of the 3D space in the immediate neighborhood of S can be then parametrized as R(q 1 , q 2 ) = r(q 1 , q 2 ) + q 3N (q 1 , q 2 ) withN (q 1 , q 2 ) the unit vector normal to S. We then find, in agreement with previous studies [2][3][4], the relations among G ij and the covariant components of the 2D surface metric tensor g ij to bewith α indicating the Weingarten curvature tensor of the surface S [2, 4]. We recall that the mean curvature M and the Gaussian curvature K of the surface S are related to the Weingarten curvature tensor byNow we can apply the thin-layer procedure introduced by Da Costa [2] and take into account the effect of a confining potential V λ (q 3 ), where λ is a squeezing parameter that controls the strength of the confining potential. When λ is large, the total wavefunction will be localized in a narrow range close to q 3 = 0. This allows one to take the q 3 → 0 limit in the Schrödinger equation. For the sake of clarity, it is better to introduce the indices a, b which can assume the values 1, 2 alone. From the structure of the metric tensor, one finds the following limiting relations:With this, the Schrödinger equation Eq. (2) can be then recast aswhere H S is an effective 2D Hamiltonian that depends on the surface S alone and readsTh...

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“…With the hard wall boundary condition in z direction, the Neumann function in Eq. (20) should be omitted because of its singularity at z = 0. With finite ρ, when λ goes to zero Eq.…”

Section: Bound States and Energy Shifts On A Truncated Conementioning

confidence: 99%

“…It clearly shows that T is functional dependent on R 1 with oscillation and the oscillating amplitude gradually enlarges as R 1 /R 2 increases. Furthermore, the resonant peaks of T are less pronounced for a larger a. Alex Marchi and his/her coworkers have modeled the cylindrical junction that joins two cylinders with different radii as a revolution surface with a five degree polynomial generatrix for guaranteeing a C 2 regularity of the junction structure and a corresponding continuity of the geometric potential [20]. By contrast, the geometric potential (14) is discontinuous because that the generatrix of the second order derivative ρ ′′ (z) is discontinuous at points with z = −a, −a + ε, a − ε, a.…”

Section: Coherent Electron Transport In a Truncated Cone-like Junmentioning

confidence: 99%

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

Wang

Liang

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

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We study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.

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Coherent electron transport in bent cylindrical surfaces

Cited by 58 publications

References 17 publications

Geometric effects in the electronic transport of deformed nanotubes

Geometric effects in the electronic transport of deformed nanotubes

Curvature-induced geometric potential in strain-driven nanostructures

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

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