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@ARTICLE{Kakulia:807104,
      author       = {Kakulia, D. and Tavkhelidze, A. and Gogoberidze, V. and
                      Mebonia, M.},
      title        = {{D}ensity of quantum states in quasi-1{D} layers},
      journal      = {Physica / E},
      volume       = {78},
      issn         = {1386-9477},
      address      = {Amsterdam [u.a.]},
      publisher    = {North-Holland, Elsevier Science},
      reportid     = {FZJ-2016-02124},
      pages        = {49 - 55},
      year         = {2016},
      abstract     = {Recently, new quantum effects have been studied in thin
                      nanograting layers. Nanograting on the surface imposes
                      additional boundary conditions on the electron wave function
                      and reduces the density of states (DOS). When the
                      nanograting 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 Schrödinger
                      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 nanograting 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
                      nanograting 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.},
      cin          = {JCNS-2 / PGI-4 / JARA-FIT / PGI-9},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JCNS-2-20110106 / I:(DE-Juel1)PGI-4-20110106 /
                      $I:(DE-82)080009_20140620$ / I:(DE-Juel1)PGI-9-20110106},
      pnm          = {144 - Controlling Collective States (POF3-144) / 524 -
                      Controlling Collective States (POF3-524) / 6212 - Quantum
                      Condensed Matter: Magnetism, Superconductivity (POF3-621) /
                      6213 - Materials and Processes for Energy and Transport
                      Technologies (POF3-621) / 6G4 - Jülich Centre for Neutron
                      Research (JCNS) (POF3-623)},
      pid          = {G:(DE-HGF)POF3-144 / G:(DE-HGF)POF3-524 /
                      G:(DE-HGF)POF3-6212 / G:(DE-HGF)POF3-6213 /
                      G:(DE-HGF)POF3-6G4},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000367534300009},
      doi          = {10.1016/j.physe.2015.11.033},
      url          = {https://juser.fz-juelich.de/record/807104},
}