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Analytic Theory of Wannier–Stark Quantization in Arbitrary‐Size Atomic Square Lattices
Author(s) -
Onipko Alexander,
Malysheva Lyuba
Publication year - 2018
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201700558
Subject(s) - physics , hamiltonian (control theory) , electric field , quantization (signal processing) , atom (system on chip) , quantum mechanics , condensed matter physics , second quantization , conductor , electron , square lattice , atomic physics , quantum , mathematics , geometry , ising model , mathematical optimization , algorithm , computer science , embedded system , creation and annihilation operators
The theory of electron energy quantization in an N atom long chain affected by a homogeneous electric fieldE eis extended to the 2D case of N atom long and N atom wide conductor with the lattice constant a . The conductor is modeled by the standard one‐parameter tight‐binding Hamiltonian (hopping integral t ) of an atomic rectangular square lattice, where the change of electron site energy from atom to atom across the conductor equals (in | t | units) to electric field parameter a e E e/ | t |(efp). Each field‐provoked levelE μ(transverse μ ‐mode energy) is shown giving rise to the μ th subband of field‐independent levels of extended states due to the electron resonant transfer in the longitudinal direction perpendicular to the electric field. The level spacing and, hence, the width of μ subbands, is dictated by the conductor width and hopping integral t . The spectra of arbitrary‐size atomic square lattices are classified in terms of subband center spacing (SBCS) within the transverse‐mode bands of extended states, edge‐localized states, and Wannier–Stark states. We identified special cases of integer and fractional SBCS quantization in efp‐portions and found the exact and/or highly accurate explicit approximate expressions for the weighted number of states within these bands. The presented novel results clarify and correct their analogs reported previously.