Local Density of States for Solids in an Electric Field

Abstract

The local densities of states (LDOSs) in electrified simple cubic crystals have been studied within the semi‐empirical tight‐binding (TB) model. One‐dimensional (1D), two‐dimensional (2D) and three‐dimensional (3D) cases are investigated, taking into account first neighbours and one band, when an external constant electric field with arbitrary direction is applied. The increasing strength of the field in a given direction turns smoothly the LDOSs of an n‐dimensional crystal (n = 1, 2, 3) into the LDOSs of an (n — 1)‐dimensional crystal. The Wannier‐Stark ladder phenomenon for crystals of different dimensionalities is discussed and the role of the electric field strength for the effective crystal dimension is assessed. The LDOSs are calculated by means of a new convolution technique which allows to compute the results faster than any conventional method.

Modelling Electronic Spectra of Crystals in Electric Fields with Various Orientations

“…When the LDOS of the central atom of a cluster in a field is known, Wannier's theorem [1,21,23] allows to obtain the LDOS of any other atom in the cluster.…”

“…For low indexed directions taking into account neighbours of the first few orders give LDOS with non-zero dimensionality at Conversely, observing a LDOS in the form of an isolated level tells that not enough orders of neighbours have been taken into account. (This is relevant for some earlier results [3,23].) Of course not all direction are given by rational numbers but in any finite consideration a satisfactory rational approximation can be made.…”

“…Thus, it was possible to observe the effects of an electrical field at practically accessible values for its intensity [6]. Theoretical investigations most commonly envisage the effect of an electric field on the electronic spectrum of 1D crystals [18][19][20][21][22][23]. The 2D case has been considered by Nakanishi et al [3] and the authors have discussed the dependence of the LDOS on the electric field direction.…”

“…In a previous work [23] we also used a first neighbours only model but the investigation covered three different dimensionalities. A new technique utilizing the separability of the Hamiltonian [22] allowed to treat easily a large array of cases.…”

“…This was a step by step demonstration that a strong field in an arbitrary direction (not along a single axis) will shrink the LDOS of a simple crystal down to an isolated level. Indeed, these results [3,23] reflect some of the shortcomings of this most simple model: accounting for neighbours after the first produces a new type of results. In the present investigation we used the TB model of 2D crystals with one s-orbital per atom and accounting for interactions with neighbours up to fourth order.…”