FIG 4 - uploaded by Guido Goldoni
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DOS as a function of the energy and the coupling parameter α c (colour code given in the legend). For reference, we show three energy levels corresponding to k 2 r = 8, which evolve from the n = 0, ±1 levels at α c = 0, as indicated. The vertical line at α c = 1.3 shows the position of the DOS reported in Fig. 5.
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We compute the single-particle states of a two-dimensional electron gas confined to the surface of a cylinder immersed in a magnetic field. The envelope-function equation has been solved exactly for both an homogeneous and a periodically modulated magnetic field perpendicular to the cylinder axis. The nature and energy dispersion of the quantum sta...
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Context 1
... DOS, as a function of the energy and α c , is shown in Fig. 4. We can recognise different regimes: i) at small α c (low field), the orbital Zeeman splitting lifts the double degeneracy of the zero-field bands, ii) at intermediate fields, the energy of the states is lowered by the interaction with the field, and iii) at large fields, different subbands merge into highly degenerate levels, ...
Context 2
... i) at small α c (low field), the orbital Zeeman splitting lifts the double degeneracy of the zero-field bands, ii) at intermediate fields, the energy of the states is lowered by the interaction with the field, and iii) at large fields, different subbands merge into highly degenerate levels, reminiscent of the corresponding 2D Landau level. In Fig. 4, the energy splitting due to the orbital Zeeman effect is shown for the two states n = 1 (dash-dotted line) and n = −1 (solid line) 34 , for a specific k 2 value. As the field is switched on, the degenerate levels split, then the energy decreases and reaches a minimum for a value of α c that is larger for larger n and k 2 . The locus ...
Context 3
... high values of α c , the energy levels gather into Landau levels, whose energy grows linearly with B. The first Landau level is formed, independently of k 2 , by the states n = 0 and n = 1, the second one by the states n = −1 and n = 2 and so on. The Landau levels are well recognisable in the density of states of Fig. 4 where they appear as dark lines. In the top panel of Fig. 5, the most prominent feature is peak C which corresponds to the formation of the first Landau level. Due to the finite curvature the energy levels acquire a finite dispersion, which gives rise to the 1D-like tail of the DOS on the low energy side, unlike the standard 2D Landau ...
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Citations
... The investigation of two-dimensional electron gases with cylindrical symmetry (C2DEGs) also attracted great deal of attention [21][22][23][24][25][26]. For instance, one of the first theoretical calculations of the quantum Hall effect in two-dimentional electron gases (2DEGs) considered a system with cylindrical symmetry [27]. ...
The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons.
... The investigation of two-dimensional electron gases with cylindrical symmetry (C2DEGs) also attracted great deal of attention [21][22][23][24][25][26]. For instance, one of the first theoretical calculations of the quantum Hall effect in two-dimentional electron gases (2DEGs) considered a system with cylindrical symmetry [27]. ...
The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons.
... However, it is quite surprising that the quantum Hall effect has been more difficult to observe in ultra-clean suspended graphene [88,89] rather than for graphene over a SiO 2 substrate. A possible explanation is that suspended graphene tends to form scrolls at the edges, where the layer is no longer orthogonal to the magnetic field, whose effective value changes according to the curvature [90]. This motivated our theoretical study of magnetotransport in large graphene ribbons with scrolled edges [91], which shows that the effective magnetic field, i.e. its component orthogonal to the layer, oscillates and changes its sign across the scrolls, thus inducing extra nonchiral channels. ...
... However, it is quite surprising that the quantum Hall effect has been more difficult to observe in ultra-clean suspended graphene [88,89] rather than for graphene over a SiO 2 substrate. A possible explanation is that suspended graphene tends to form scrolls at the edges, where the layer is no longer orthogonal to the magnetic field, whose effective value changes according to the curvature [90]. This motivated our theoretical study of magnetotransport in large graphene ribbons with scrolled edges [91], which shows that the effective magnetic field, i.e. its component orthogonal to the layer, oscillates and changes its sign across the scrolls, thus inducing extra nonchiral channels. ...
... Over the years, electronic transport properties in electromagnetic field have been a subject of active studies both theoretically and experimentally [20][21][22][23][24][25][26][27], because of its great application potential and the demand on understanding the physics involved. With the advent and development of nanoelectronics, theoretical physicists have tried to study the effects of the geometrical deformation in electromagnetic field by conductance [28][29][30], density of states [31], magnetic moment [32], magnetoresistance [33], resistance [34], energy level structure [35,36], persistent currents [37], spin current [38] and spin precession [39]. However, the polarization effect of the electronic transport on the basis of the geometrical deformation has been researched seldom. ...
Noninteracting electrons confined to a corrugated surface are considered in the presence of magnetic field, the corresponding effective Pauli equation is given in the thin-layer quantization formalism. We find that a curvature-induced spin and magnetic field coupling except the well-known geometric potential appears in the effective dynamics. By numerical calculation, we discuss the spin-dependent transport properties of confined electrons in magnetic field, and we find that the transmission probability and spin polarization are modified by the curvature of surface.
... The electronic properties of two-dimensional electron gas (2DEG) subjected to a spatially varying local gradient magnetic field have been studied extensively in the past several decades. [1][2][3][4][5][6][7] Such structure can be easily obtained by depositing ferromagnetic stripes on the top of GaAs/AlGaAs heterostructure, 8,9 as clearly shown schematically in Fig. 1(a). After the stripe be magnetized, the stray magnetic field surrounding the system would be produced. ...
Based on the tight-binding method, we investigate the energy spectrum and localization of electronic states in 2DEG subjected to a spatially local gradient magnetic field. Generally, such structure can be obtained easily by placing ferromagnetic stripes on the surface of semiconductor heterojunction. Considering the numerical accuracy, the actual calculated profiles of magnetic field are used in this work. By adjusting the width of stripe d and the amplitude of magnetic field, the energy spectra and the square root of probability density are obtained. The former is convergent when the width d is zero or becomes very large and the latter shows that the ground states are localized at the center of 2DEG. For large B and small width d, the energy level crossing between the ground and the first excited states would cause the pattern of probability density splitting into two parts. We also study the case of four stripes on the top of 2DEG. For emphasizing the effect of magnetic field, the harmonic potential is removed. The low energy levels tend to bundle themselves into groups because there exists three similar magnetic potential wells in this situation. All these findings will help us to further understand the electronic properties of 2DEG in varying magnetic field.
... Nanotubes and nanowires have attracted a fair amount of attention since the early propositions of carbon nanotubes as primary constituents of future nanoelectronic devices [1][2][3][4][5][6][7][8][9][10]. In line with this, extensive investigations have been performed to study the quantum mechanics of a particle on twodimensional curved surfaces, most notably on curved surfaces with cylindrical symmetry [11][12][13][14][15][16][17][18][19]. These prior investigations were directed to the study of the physical effects of surface-constrained particle that depend both on the curvature and the involved electromagnetic fields. ...
... These prior investigations were directed to the study of the physical effects of surface-constrained particle that depend both on the curvature and the involved electromagnetic fields. These effects include the confinement of carriers over bent surfaces [20], the formation of Landau levels [20,11], and the quantum Hall effect. For a prismatic core multishell nanowire, it has been observed that the edges provide one-dimensional quantum channels for localization of carriers and that a strong magnetic field perpendicular to the nanowire axis leads to the formation of Landau levels [20]. ...
We calculate the energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in uniform electric and magnetic fields. Using separation of variables method and a change of independent variable, we show that the problem can be reduced to a one-dimensional Schödinger equation for a periodic potential. The effect of varying the shape of the cross-section while keeping the same perimeter and the strengths of the electric and magnetic fields are investigated for elliptical, corrugated, and nearly-rectangular tubes with radial dimensions of the order of a nanometer. The geometric potential has minima at the angular positions where there is a significant amount of curvature. For the elliptical and corrugated tubes, it is shown that as the tube departs from the circular shape of cross-section the double-degeneracy between the energy levels is lifted. For the nearly-rectangular tube, it is shown that energy level crossings occur as the horizontal dimension of the tube is varied while keeping the same perimeter and radius of circular corners. The interplay between the curvature and the strength of the electric and magnetic fields determines the overall behavior of the energy levels. As the strength of the electric field increases, the overall potential gets skewed creating a potential well on the side corresponding to the more negative electric potential. The energy levels of the first few excited states approach more positive values while the ground state energy level approaches a more negative value. For large electric fields, all bound state energy levels tend to more negative values. The contribution of weak magnetic fields to the overall potential behaves in the same way as the electric field contribution but with its sign depending on the direction of the component of the momentum parallel to the cylindrical axis. Large magnetic fields lead to pairing of energy levels reminiscent of 2D Landau levels for the elliptical and nearly-rectangular tubes.
... Carriers on * manoles@ru.is both sides of the lines are deflected towards opposite directions and thus confined into so called snaking states [19][20][21][22]. Higher energy electrons start to occupy Landau states and form cyclotron orbits localized in the areas where the radial component of the field takes maximal values. ...
We analyze theoretically electronic transport through a core-shell nanowire in the presence of a transversal magnetic field. We calculate the conductance for a variable coupling between the nanowire and the attached leads and show how the snaking states, which are low-energy states localized along the lines of vanishing radial component of the magnetic field, manifest their existence. In the strong coupling regime they induce Aharonov-Bohm-like conductance oscillations, which, by decreasing the coupling to the leads, evolve into well resolved peaks. These results show that the formation of snaking states in the
nanowire affects magnetoconductance measurements irrespective of the strength of the contacts with the leads. We analyze theoretically electronic transport through a core-shell nanowire in the presence of a transversal magnetic field. We calculate the conductance for a variable coupling between the nanowire and the attached leads and show how the snaking states, which are low-energy states localized along the lines of vanishing radial component of the magnetic field, manifest their existence. In the strong coupling regime they induce Aharonov-Bohm-like conductance oscillations, which, by decreasing the coupling
to the leads, evolve into well resolved peaks. These results show that the formation of snaking states in the nanowire affects magnetoconductance measurements irrespective of the strength of the contacts with the leads.
... It is well-known that quantum confinement may modulate the behavior of itinerant electrons and significantly alter the physical properties of various nanoscale systems, such as core-shell nanowires [1] and nanoscale two-dimensional bent electron gases [2]. In addition, quantum-size effects modify the electronic structure of the organic-metal interfaces when a bulk metal crystal is replaced by a uniform thin film, [3,4] change the surface reactivity of thin films, [5] shift the energy gap between the conduction and valence band in TiO 2 nanoparticles [6] etc. ...
Since the 1960's it has been well known that the basic superconductive quantities can exhibit oscillations as functions of the thickness (diameter) in superconducting nanofilms (nanowires) due to the size quantization of the electronic spectrum. However, very little is known about the effects of quantum confinement on the microscopic properties of vortices. Based on a numerical solution to the Bogoliubov-de Gennes equations, we study the quantum-size oscillations of the vortex core resulting from the sequential interchange of the Kramer-Pesch and anti-Kramer-Pesch regimes with changing nanocylinder radius. The physics behind the anti-Kramer-Pesch anomaly is displayed by utilizing a semi-analytical Anderson approximate solution. We also demonstrate that the anti-Kramer-Pesch vortex core is robust against thermal smearing and results in a distinctive two-maxima structure in the local density of states, which can be used to identify the existence of the anti-Kramer-Pesch vortex.
... In Ref. 14, transport measurements were performed on segments of cylinders, and a notable asymmetry in the magnetoresistance was observed with respect to field orientation. Furthermore, simulations of a cylindrical electron gas immersed in a perpendicular field predicted the formation of states with distinct characteristics, localized in different regions around the circumference [15,16]. Propagating states tend to be localized in narrow channels, where the magnetic field is parallel to the surface, laterally confined by a Lorentz force. ...
... The relevant states are localized in the cyclotron regions, as the example in Fig. 2(c) illustrates. Accordingly, these are cyclotron states condensed into a Landau level [15,16,18]. Observe that the Landau level is split into spin up and down branches by the Zeeman term. ...
We model a core-shell nanowire (CSN) by a cylindrical surface of finite
length. A uniform magnetic field perpendicular to the axis of the cylinder
forms electron states along the lines of zero radial field projection, which
can classically be described as snaking states. In a strong field, these states
converge pairwise to quasidegenerate levels, which are situated at the bottom
of the energy spectrum. We calculate the conductance of the CSN by coupling it
to leads, and predict that the snaking states govern transport at low chemical
potential, forming isolated peaks, each of which may be split in two by
applying a transverse electric field. If the contacts with the leads do not
completely surround the CSN, as is usually the case in experiments, the
amplitude of the snaking peaks changes when the magnetic field is rotated,
determined by the overlap of the contacts with the snaking states.
