Effect of a velocity barrier on the ballistic transport of Dirac fermions

Concha, Andres; Tešanović, Zlatko

doi:10.1103/physrevb.82.033413

Cited by 77 publications

(55 citation statements)

References 30 publications

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“…Unlike optics, for normal incidence ( ¼ 0), the perfect transmission (T ¼ 1, R ¼ 0) occurs, which reflects the prohibited backscattering on the surface of the TI. This is similar to graphene [6,12,13] but the transmittance in our case monotonically decreases with the incidence angle.…”

supporting

confidence: 76%

“…The current conservation in the z direction is written as R þ T ¼ 1, where R jrj 2 and T v 2 cos 0 v 1 cos jtj 2 are the reflectance and the transmittance, respectively. We note that the wave function should eventually be discontinuous at the junction when the velocities are different, as has been studied in the context of graphene [12,13]. The reason is the following.…”

mentioning

confidence: 81%

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Gapless Interface States between Topological Insulators with Opposite Dirac Velocities

2011

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The Dirac cone on a surface of a topological insulator shows linear dispersion analogous to optics and its velocity depends on materials. We consider a junction of two topological insulators with different velocities, and calculate the reflectance and transmittance. We find that they reflect the backscattering-free nature of the helical surface states. When the two velocities have opposite signs, both transmission and reflection are prohibited for normal incidence, when a mirror symmetry normal to the junction is preserved. In this case we show that there necessarily exist gapless states at the interface between the two topological insulators. Their existence is protected by mirror symmetry, and they have characteristic dispersions depending on the symmetry of the system.

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supporting

confidence: 76%

mentioning

confidence: 81%

Gapless Interface States between Topological Insulators with Opposite Dirac Velocities

2011

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“…In defining our model, we have made the conceptually simple assumption that the region of the line junction is distinct from the tunneling region so that the tunneling does not modify the boundary condition introduced in Eq. (30). (We note that the system described in Eq.…”

Section: Junction Between Surface Velocities With Opposite Signsmentioning

confidence: 99%

Junction between surfaces of two topological insulators

Sen

Deb

2012

Phys. Rev. B

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We study the properties of a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time reversal invariant system, we show that the line junction is characterized by an arbitrary parameter \alpha which determines the scattering from the junction. If the surface velocities have the same sign, we show that there can be edge states which propagate along the line junction with a velocity and orientation of the spin which depend on \alpha and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle \phi with respect to each other. We study the scattering and differential conductance through the line junction as functions of \phi and \alpha. We also find that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on \phi. Finally, if the surface velocities have opposite signs, we find that the electrons must transmit into the two-dimensional interface separating the two topological insulators.Comment: 11 pages, 6 figures; corrected Eqs. 20 and 21 and Figs. 4 and 5; conclusions remain unchange

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“…In analogous with optics, the total internal reflection (TIR) emerges when a Dirac fermion wave hits from a denser medium (region I) on a rarer medium (the barrier region II). This behavior is interpreted as ξ > 1 in our studied system 9,18,[20][21][22] . To demonstrate such a critical angle in BLG, we plot transmission probability T (θ 1 ) as a function of the incidence angle in Fig.6 for several values of velocity.…”

Section: Transport Across a Single Velocity Barriermentioning

confidence: 99%

Control over band structure and tunneling in bilayer graphene induced by velocity engineering

Cheraghchi

Adinehvand

2013

J. Phys.: Condens. Matter

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The band structure and transport properties of massive Dirac fermions in bilayer graphene with velocity modulation in space are investigated in the presence of a previously created band gap. It is pointed out that velocity engineering may be considered as a factor to control the band gap of symmetry-broken bilayer graphene. The band gap is direct and independent of velocity value if the velocity modulated in two layers is set up equally. Otherwise, in the case of interlayer asymmetric velocity, not only is the band gap indirect, but also the electron-hole symmetry fails. This band gap is controllable by the ratio of the velocity modulated in the upper layer to the velocity modulated in the lower layer. In more detail, the shift of momentum from the conduction band edge to the valence band edge can be engineered by the gate bias and velocity ratio. A transfer matrix method is also elaborated to calculate the four-band coherent conductance through a velocity barrier possibly subjected to a gate bias. Electronic transport depends on the ratio of velocity modulated inside the barrier to that for surrounding regions. As a result, a quantum version of total internal reflection is observed for thick enough velocity barriers. Moreover, a transport gap originating from the applied gate bias is engineered by modulating the velocities of the carriers in the upper and lower layers.

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Effect of a velocity barrier on the ballistic transport of Dirac fermions

Cited by 77 publications

References 30 publications

Gapless Interface States between Topological Insulators with Opposite Dirac Velocities

Gapless Interface States between Topological Insulators with Opposite Dirac Velocities

Junction between surfaces of two topological insulators

Control over band structure and tunneling in bilayer graphene induced by velocity engineering

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