Brillouin zone unfolding of complex bands in a nearest neighbour tight binding scheme

Abstract

Complex bands k(⊥)(E) in a semiconductor crystal, along a general direction n, can be computed by casting Schrödinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary n. It is, however, possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. In this paper, we present a unified method to unfold real and complex bands. Our method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy E.

Phonon dispersion unfolding in the presence of heavy breaking of spatial translational symmetry

“…The main advantage of this method is the ability to handle systems with heavy breaking of spatial translational symmetry. Its validity is tested by pure diamond, diamond with Si substitution, and diamond with C vacancies.Since the discovery of effective energy bands in semiconductors [1,2] and alloys [3], unfolding methods for treating the electronic band structures of the weakly periodic solid systems have been rapidly developed [4][5][6][7][8][9][10][11][12][13][14]. Moreover, it has also stimulated the study of phonon dispersion unfolding method [14][15][16][17].…”

A general group theoretical method to unfold band structures and its application

“…In this case, the unfolded energy bands contain information of the defects or reconstruction and can be directly compared with ARPES or other measurements. Since the main difference of computing real and complex bands lies in the choice of basis, our method can be used for complex bands too, if some modifications are included [27,28].…”

Multiscale model for phonon-assisted band-to-band tunneling in semiconductors

“…We believe that this is a reasonable approximation while computing BTBT currents, since the density of states scales as ∼ mass 1.5 , unlike the tunneling probability which depends exponentially on the effective masses of the complex bands, via the action for tunneling. We begin by extracting energy dependent effective masses m V B (E), m CB (E) of the imaginary parts of the valence and conduction bands from a computation 22,23 of the direction-dependent complex bandstructure k (E; k ⊥ ) in an sp 3 d 5 s * tight binding scheme. The valence band maxima are assumed to be at k = 0 to simplify the description that follows.…”