Energy Spectrum of a Triangular Lattice in a Uniform Magnetic Field: Effect of Next-Nearest-Neighbor Hopping

Structural and electrical properties of FeMg0.7Cr0.6Co0.7−xAlxO4 (0≤x≤0.3) thick film NTC thermistors

“…The activation energy is primarily the energy for the hopping process from a cation M n+ to M (n+1)+ on the octahedral sites and, hence, for the mobility of the cations. [13][14][15][16][17][18][19] It is clear that the resistivity of all the samples followed basically the same thermally activated behavior represented by Eq. (1).…”

“…Several models invoke the small polaron theory, known as a "hopping" mechanism, which is associated with a phonon-assisted jump of carriers between cations of differing oxidation states on the octahedral sites of the spinel structure. [13][14][15][16][17][18][19] For example, in the nickel manganites, electrical conduction is due to an electron jump between the Mn 4+ and Mn 3+ cations present on the octahedral sites. 20 The octahedral cations in the spinel structure lie in chains along some <1 1 0> directions.…”

Magnetoelectronic properties of a graphite sheet

“…On the other hand, study of magnetoelectronic properties of a graphite sheet also provides a realistic system to understand the Hofstadter butterflies, the energy spectra of Bloch electrons in the magnetic field. So far, most of reports have focused on the hypertheoretical system, such as 2D square lattices [23], triangle lattices [24], hexagonal lattices [25], artificial structures [26], 3D cubic lattices [27], and 1D square lattices [28].…”

Energy band structures for electrons on the triangular lattice with uniform magnetic field

“…The case of anisotropic hopping was also taken into account [3,4]. The beauty of the results started the work with similar 2D structures in a magnetic field including the triangular [1,2] and rhombic [5] lattice, or by taking into account the influence of the next-nearest-neighbor hopping for the square [6] and triangular [7] lattice. The triangular lattice was first investigated just as a special case for the square lattice with next-nearest-neighbor hopping.…”