2017/07/17 by Alexander Onipko, Onipko, Alexander, L. A. Malysheva +1
Engineering · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Molecular Junctions and Nanostructures #Organic and Molecular Conductors Research #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1707.05084
openalex publication_date 2017/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the first time, one-particle theory of Wannier-Stark quantization for a a(N-1)-long chain affected by a homogeneous electric field Ee is extended to the 2D case of LN=a(N-1)-long and L\cal N=a(\cal N-1)-wide conductor, which is modeled by the atomic square lattice with the electron site-energy change from atom to atom in the direction parallel to \cal N axis by the amount of electric field parameter (efp) ε ≡ aeEe/|t| in units of |t|. It is shown that each field-provoked μ-level in the chain spectrum gives birth to the μ-subband of field-independent levels due to the electron-transfer interaction in the direction perpendicular to Ee. The level spacing and hence, the width of μ-subbands E0\rm bw, is dictated by the conductor length, the hopping integral t, and by the lattice constant a. Another principal result is that the levels, which are within the energy interval 0.5E0\rm bw on either sides of the spectrum (that is the edge spectrum), correspond to the delocalized states which are extended in the direction perpendicular to the electric field. In this direction, the electron spectrum width E⊥\rm bw is larger by E0\rm bw than the spectrum width in the field direction E∥\rm bw. Several special cases of the interrelation between the electron energy versus applied voltage are identified, when the spacing between the μ-subband centers is equal either to integer or fraction (>1) portion of dimensionless ε. Otherwise, the level spacing is shown to be irregular and, depending on N, \cal N, and ε, it can be equal to any portion of ε. It is argued that one of straightforward applications of the presented theory is the quantum-mechanical explanation of Hall effect in two dimensions.