Density of Quantum States in Quasi-1D layers
  Recently, new quantum effects have been studied in thin nano-grating layers. Nano-grating on the surface imposes additional boundary conditions on the electron wave function and reduces the density of states (DOS). When the nano-grating dimensions are close to the de Broglie wavelength, the DOS reduction is considerable and leads to changes in the layer properties. DOS calculations are challenging to perform and are related to the quantum billiard problem. Performing such calculations requires finding the solutions for the time-independent Schrodinger equation with Dirichlet boundary conditions. Here, we use a numerical method, namely the method of auxiliary sources, which offers significant computational cost reduction relative to other numerical methods. We found the first five eigenfunctions for the nano-grating layer and compared them with the corresponding eigenfunctions for a plain layer by calculating the correlation coefficients. Furthermore, the numerical data were used to analyze the DOS reduction. The nano-grating is shown to reduce the probability of occupation of a particular quantum state, reducing the integrated DOS by as much as 4.1 -fold. This reduction in the DOS leads to considerable changes in the electronic properties. 
D. Kakulia, A. Tavkhelidze, V. Gogoberidze and M. Mebonia
cond-mat.mes-hall cond-mat.supr-con