Moiré band structures of twisted phosphorene bilayers

Abstract

We report on the theoretical electronic spectra of twisted phosphorene bilayers exhibiting moiré patterns, as computed by means of a continuous approximation to the moiré superlattice Hamiltonian. Our model is constructed by interpolating between effective $\Gamma$-point conduction- and valence-band Hamiltonians for the different stacking configurations approximately realized across the moiré supercell, formulated on symmetry grounds. We predict the realization of three distinct regimes for $\Gamma$-point electrons and holes at different twist angle ranges: a Hubbard regime for small twist angles $\theta <2^{\circ }$, where the electronic states form arrays of quantum-dot-like states, one per moiré supercell; a Tomonaga-Luttinger regime at intermediate twist angles $2^{\circ }<\theta \lesssim 10^{\circ }$, characterized by the appearance of arrays of quasi-1D states; and finally, a ballistic regime at large twist angles $\theta \gtrsim 10^{\circ }$, where the band-edge states are delocalized, with dispersion anisotropies modulated by the twist angle. Our method correctly reproduces recent results based on large-scale ab initio calculations at a much lower computational cost, and with fewer restrictions on the twist angles considered.

arXiv commentJournal accepted version. 20 pages, including 11 figures and 5 appendices

References in corpus (36)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Phosphorene: A New 2D Material with High Carrier Mobility
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Isolation and characterization of few-layer black phosphorus
• Moiré Excitons in Van der Waals Heterostructures
• Signatures of moiré-trapped valley excitons in MoSe${}_2$/WSe${}_2$ heterobilayers
• Observation of Moiré Excitons in WSe2/WS2 Heterostructure Superlattices
• Magic continuum in twisted bilayer WSe2
• Strain engineered direct-indirect band gap transition and its mechanism in 2D phosphorene
• Resonantly hybridised excitons in moiré superlattices in van der Waals heterostructures
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Hubbard model physics in transition metal dichalcogenide moiré bands
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene
• Tunable Moiré Bands and Strong Correlations in Small-Twist-Angle Bilayer Graphene
• Atomic reconstruction in twisted bilayers of transition metal dichalcogenides
• Interfacial ferroelectricity in marginally twisted 2D semiconductors
• Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers
• Atomic reconstruction and moiré patterns in transition metal dichalcogenide van der Waals heterostructures
• Anomalous light cones and valley optical selection rules of interlayer excitons in twisted heterobilayers
• Interlayer coupling in commensurate and incommensurate bilayer structures of transition metal dichalcogenides
• Electrons and holes in phosphorene
• Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides
• Interlayer interaction in general incommensurate atomic layers
• Spin-layer locking of interlayer excitons trapped in moiré potentials
• Electronic and optical properties of two-dimensional InSe from a DFT-parameterized tight-binding model
• Multifaceted moiré superlattice physics in twisted WSe${}_2$ bilayers
• Piezoelectric networks and ferroelectric moiré superlattice domains in twistronic WS${}_2$/MoS${}_2$ and WSe${}_2$/MoSe${}_2$ bilayers
• $k\cdot p$ theory for phosphorene: Effective g-factors, Landau levels, and excitons
• Theory of moiré localized excitons in transition-metal dichalcogenide heterobilayers
• Band energy landscapes in twisted homobilayers of transition metal dichalcogenides
• Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene
• Gate induced monolayer behavior in twisted bilayer black phosphorus
• Excitons in Phosphorene: A Semi-Analytical Perturbative Approach