Diverse Quantization Phenomena in Layered Materials

Abstract

The diverse quantization phenomena in 2D condensed-matter systems, being due to a uniform perpendicular magnetic field and the geometry-created lattice symmetries, are the focuses of this book. They cover the diversified magneto-electronic properties, the various magneto-optical selection rules, the unusual quantum Hall conductivities, and the single-and many-particle magneto-Coulomb excitations. The rich and unique behaviors are clearly revealed in few-layer graphene systems with the

Optical scatterings in layered systems

“…The Also, the rich intrinsic interactions, which arise from the stacking symmetries [4], the multi-orbital hybridizations [38] and spin-orbital couplings [38], are included in the various Hamiltonians. Reflectance and transmittance spectra of few-layer graphene systems are thus expected to exhibit the diverse magnetic quantization phenomena under the various stacking configurations [38]. But when a bulk system gradually reduces its thickness, electronic energy spectra and wave functions will display a dramatic transform and thus dynamic charge responses.…”

“…The former and the latter mainly arise from the initial and saddle-point π-electronic states near the K and M valleys, directly reflecting the main features of electronic energy spectra and wave functions {Fig. Also, the rich intrinsic interactions, which arise from the stacking symmetries [4], the multi-orbital hybridizations [38] and spin-orbital couplings [38], are included in the various Hamiltonians. Reflectance and transmittance spectra of few-layer graphene systems are thus expected to exhibit the diverse magnetic quantization phenomena under the various stacking configurations [38].…”

“…The gradient approximation is very convenient and reliable in resolving the second term, e.g., the successful evaluations on graphite intercalation compounds [33], carbon nanotubes [34], and few-layer graphenes [4,5,[35][36][37]. This linear Kubo formula, which is directly combined with the generalized model, is successful in exploring the diverse magneto-optical excitations of 2D layered structures, e.g., the systematic investigations on magnetic quantization phenomena of layered group-IV and group-V materials [38].…”

Na-intercalation compounds and Na-ion batteries

“…2 within a sufficiently wide energy range of −10 eV ≤ E c,v ≤ 3 eV, respectively, are fully supported by the carbon-and intercalant-atom dominances. Their main features cover the number of valence subbands (the active atoms and orbitals in a unit cell) [107,108], the enhanced asymmetry of valence and hole conduction electron energy spectra about the Fermi level (the intercalant-carbon interlayer interactions) [109], the blue shift of E F (the semimetal-metal transitions due to the charge transfer of metal adatoms) [110], the dependence of E F on the chemical intercalations (the densities of free conduction electrons under the various intercalation cases), the slight/major modifications of carbon 2p z -π and [2s, 2p x , 2p y ]-σ bands along the different wave-vector paths, the subband non-crossing/crossing/anti-crossing behaviors [111], the diverse energy dispersions near the highsymmetry points [112], and their band-edge states (the critical points in energy-wave-vector spaces with zero group velocities) [113]. The Fermi level is mainly determined by the concentration, distribution configuration, and charge transfer of intercalant metal atoms.…”

“…It displays that the higher concentrations of Na will provide more electrons transferring from sodium atoms to carbon atoms. Their magnitudes, which correspond to the 3D free electron densities, will have strong effects on the carrier excitations and transports [112,114], e.g., the optical plasmon modes of conduction electrons in the n-type graphite intercalation compounds [112,114].…”