One-dimensional Lieb superlattices: from the discrete to the continuum limit

Area of Science:

• Condensed Matter Physics
• Materials Science
• Solid State Physics

Background:

• The Lieb lattice features unique linear Dirac-like and flat topological electronic bands.
• Periodic electrostatic superlattices (SLs) can modify lattice electronic properties.

Purpose of the Study:

• To tailor Lieb lattice electronic properties using 1D electrostatic superlattices.
• To investigate the electronic band structure evolution and transport signatures in Lieb superlattices.
• To explore the impact of discrete lattice symmetry-breaking at superlattice interfaces.

Main Methods:

• Numerical modeling of electronic structure at the tight-binding level.
• Analysis of band structure evolution from discrete to continuum regimes.
• Consideration of lattice symmetry-breaking effects at well/barrier interfaces.

Main Results:

• Discovered novel band structure features including quadratic and flat band intersections, and tilted Dirac cones.
• Identified additional anisotropic Dirac cones at energies predicted for super-Klein tunnelling (SKT).
• Demonstrated the absence of universal SKT when discrete lattice details are accounted for.

Conclusions:

• Periodic 1D superlattices significantly alter Lieb lattice electronic properties.
• Discrete lattice symmetry-breaking at interfaces leads to deviations from idealized predictions.
• Findings are relevant for experimental transport studies in artificial and material-based Lieb superlattices.