An investigation of the momentum dependence of the electronic spectrum for a disordered system

The spectral properties of disordered systems are investigated using twodimensional examples in the tight-binding approximation. The spectra are examined as functions of the momentum wavevector for two-dimensional systems. A particular example is the directional dependence of the spectrum for a quasicrystal, represented by a two-dimensional Penrose lattice. The spectrum changes dramatically, as expected, when the momentum vector moves off a symmetry axis of the system. The value of this approach for analysing the electronic properties of structurally disordered systems is discussed.