Semiconductor Meta-Graphene and Valleytronics

TL;DR

The work addresses the challenge of realizing robust valleytronic edge channels in semiconductor-based metamaterials by engineering artificial graphene (AG) and artificial hBN (AhBN) in a 2D electron gas. It combines a continuum AG model with a secondary antidot lattice to open a Dirac gap and induce nontrivial valley Chern numbers, creating topological domain-wall states at interfaces of opposite gaps. Through density-of-states analysis, spectral localizer topology, and transport simulations under realistic disorder (charge puddles and geometric imperfections), the study shows that domain-wall states persist with localization lengths of several microns, and that high aspect-ratio ribbons can enhance domain-wall–mediated transport. The results establish AhBN as a promising platform for low-dissipation valleytronics and programmable topological metamaterials in engineered 2D semiconductors.

Abstract

Nano-patterned semiconductor interfaces offer a versatile platform for creating quantum metamaterials and exploring novel electronic phenomena. In this study, we illustrate this concept using artificial graphene--a metamaterial featuring distinctive properties including Dirac and saddle points. We demonstrate that introducing additional nano-patterning can open a Dirac band gap, giving rise to what we term artificial hexagonal boron nitride (AhBN). The calculated valley Chern number of AhBN indicates the presence of topological valley Hall states confined to Dirac-gap domain walls. A key question is whether these one-dimensional edge states are topologically protected against disorder, given their vulnerability to Anderson localization. To this end, we perform band structure and electronic transport simulations under experimentally relevant disorder, including charge puddles and geometric imperfections. Our results reveal the resilience of the domain wall states against typical experimental disorder, particularly while the AhBN band gap remains open. The localization length along the domain wall can reach several microns--several times longer than the bulk electron mean free path--even though the number of bulk transport channels is greater. To enhance the effectiveness of the low-dissipation domain wall channel, we propose ribbon geometries with a large length-to-width ratio. These findings underscore both the potential and challenges of AhBN for low-energy, power-efficient microelectronic applications.

Figures (9)

• Figure 1: (a) SEM image of the experimentally produced AG with a lattice constant of $L=100$ nm. (b) Potential profile of AG. The red holes (antidots) indicate potential barriers of strength $V_1$ that low-energy electrons cannot penetrate, resulting in the graphene-like band structure in (c). (d) Addition of holes of strength $V_2$ at the A sites of the lattice breaks inversion symmetry (and sublattice symmetry) and opens the band gap at the K/K' points, as indicated in the band structure in (e). (f) Potential profile of AhBN with a domain wall. The white line indicates the domain wall, which acts as a mirror line and contains an inversion center of the entire system. (g) The band structure projected along the domain wall direction that has a translational symmetry of AG. Each red band indicates a pair of domain wall states counter-propagating at the K/K' valleys; there are two parallel domain walls in our setup to ensure the periodic boundary condition.
• Figure 2: Plot of valley Chern number $C_v$ versus energy band gap $E_g$. Insets: momentum-space distribution of the Berry curvature at indicated values of $E_g$. The regions exhibiting nonzero curvature correspond to the K/K' points. For $V_1=10\frac{h^2}{2mL^2}$, $V_2 = 0.8\frac{h^2}{2mL^2}$, $D_1=\frac{L}{2}$, $D_2=\frac{L}{4}$, and $L=100$ nm, we obtain $E_g = 0.76$ meV and $C_v =\frac{1}{4}$.
• Figure 3: (a) Potential profile of AhBN with charge puddle disorder. (b) Calculated DOS for (a) at different disorder strengths. The bulk band gap closes at a critical disorder strength. (c) The same as (a) but with a domain wall. (d) Calculated DOS for (c) at different disorder strengths. The DOS within the bulk gap remains constant, indicating that the domain wall states survive on average until the disorder is sufficient to close the bulk gap. (e,f) Local DOS of the domain wall states at the midgap energy ($1.5$ meV) for two charge-puddle configurations.
• Figure 4: (a) SEM image of an AG sample exhibiting geometric disorder with a strength of approximately $9\%$. (b) Potential profile of AhBN with geometric disorder. (c) Calculated DOS for (b) at different disorder strengths, given in maximum percentage deviation of the antidot radius from the perfect case. (d) The same as (b) but with a domain wall. (e) Calculated DOS for (d) at different disorder strengths. (f,g) Local DOS of the domain wall states at the midgap energy ($1.5$ meV) for two geometric disorder configurations.
• Figure 5: (a) Geometry of a reflection symmetric AhBN ribbon with a domain wall. (b)-(c) Energy-resolved marker $\zeta_E^{\mathcal{R}}$ (b) and local gap $\mu_{E}$ (c) as a function of energy $E$ and wavevector $k_y$ along the domain wall direction. (d)-(f) Wavefunctions $\textrm{Re}[\psi_{(k_y,E)}(x)]$ of the topological domain wall-localized states at $E = 1.37$ meV (d), $E = 2.21$ meV (e), and $E = 0.32$ meV (f), which are marked by the green, orange, and purple dots in (b)-(c), respectively.