Manipulation of electron flow using near-zero index semiconductor metamaterials

We study the possibility of controlling the propagation of ballistic electrons using an electronic metamaterial with zero quantum index of refraction. This is obtained by tailoring the band structure of a semiconductor superlattice to exhibit a Dirac cone at the center of the Brillouin zone, creating an artificial quantum medium with zero refractive index for electrons. We demonstrate attractive functionalities, such as anomalous tunneling, ideal matching, electronic routing, cloaking, and focusing. We envision applications in nanoelectronics and sensing.

Figure 1

Bloch energy eigenvalues and eigenmodes of the considered square semiconductor superlattice, at the center of the Brillouin zone, for varying values of the filling ratio $r/a$. Accidental triple degeneracy is obtained for $r/a=0.115$ and $E=2.36$ eV between the first doubly degenerate dipolar eigenstate and the second monopolar eigenstate.

Figure 2

(a) Band diagram of the superlattice for $r/a=0.115$ for which a Dirac cone is induced at the center of the Brillouin zone (b).

Figure 3

Demonstration of zero index quantum metamaterial. Electrons propagating in the AlAs background are scattered by a prism made of the proposed quantum metamaterial (incidence from the left). At the second interface, the refracted angle is identically zero, unlike the incidence angle, demonstrating that the effective index of the superlattice vanishes at the Dirac cone energy.

Figure 4

Routing electrons and cloaking obstacles. Electronic flow, incident from the bottom 2D AlAs quantum wire, is significantly disturbed and poorly transmitted to the upper channel when confronted to a 180° turn made out of the same material (a). When connected via the zero index metamaterial (b), electrons teleport through the superlattice with total transmission and no phase shift, as if the space in between were absent. In the presence of a large GaAs obstacle, this exotic tunneling phenomenon remains unaffected, and no collision with the obstacle occurs, demonstrating the cloaking capabilities of the zero effective index semiconductor.

Figure 5

Focusing and defocusing. In panel (a), a plane electronic matter wave is focused by a lens made of our zero-index quantum metamaterial, creating a hot spot with concentrated probability current and interaction capability. On the contrary, panel (b) demonstrates the inverse transformation, from a tightly focused Gaussian beam into a plane wave. In both cases, the beams are incident from the left.