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# Calculated Cleavage Behavior and Surface States of LaOFeAs 

Helmut Eschrig, Alexander Lankau, Klaus Koepernik ∗ 

IFW Dresden, PO Box 270116, D-01171 Dresden, Germany 

The layered structure of the iron based superconductors gives rise to a more or less pronounced two-dimensionality of their electronic structure, most pronounced in LaOFeAs. A consequence are distinct surface states to be expected to influence any surface sensitive experimental probe. In this work a detailed density functional analysis of the cleavage behavior and the surface electronic structure of LaOFeAs is presented. The surface states are obtained to form two-dimensional bands with their own Fermi surfaces markedly different from the bulk electronic structure. 

About two years after the discovery of the high-T$_{c}$ su- perconductor La(O,F)FeAs 1 its normal state electronic structure remains badly understood. Although there is growing opinion that it is not a highly correlated case of Mott-Hubbard type $^{2}$, its magnetic properties for in- stance are not at all well described by the local den- sity approximations (LDA) of density functional theory (DFT) or gradient corrections to it (GGA). In contrast to the cuprates where it was nearly immediately clear that the electronic structure of the cuprate plane is dom- inated by a 3 d 9 shell with a correlation localized hole in a single band, here a complex multi-band case is obviously operative. 3 Like in the cuprates the electronic structure and most properties are highly anisotropic, though to varying extent. 4 

Many experimental probes of the electronic structure, photoemission in particular, are surface sensitive. To as- sess these experiments it is crucial to know something on the surface structure and possible surface states of the material. So far, as a rule those experiments are inter- preted in terms of the bulk electronic structure. Even if bulk properties show up in the experiment, the possible presence of surface states remains an important issue to be taken into account. 

In this paper the formation of surfaces in cleaving a sin- gle crystal and their properties are analyzed by means of DFT calculations for the most two-dimensional case, un- doped LaOFeAs. A pronounced surface electronic struc- ture is found for both forming surfaces, As and La ter- minated, which dramatically differs from the bulk elec- tronic structure. All calculations are done within the non-magnetic GGA model of LaOFeAs which fairly cor- rectly describes the crystal structure of the material. Al- though the relevance of this model for electronic many- body behavior may be debated, the results on the surface relaxation and on the character of surface states must be considered relevant. 

The computational approach is described in the follow- ing section, while the results are presented and discussed in Section III. A short summary completes the paper. 

PACS numbers: 68.35.bd, 74.20.Pq, 74.25.Jb, 74.70.Db 

Keywords: surface relaxation, surface band structure 

## I. INTRODUCTION 

All calculations were done by using the full-potential local-orbital (FPLO) code version FPLO9.00. 7 Relativis- tic effects were incorporated on a scalar relativistic level. The k -mesh input parameters were set to 6,6,4 (number of k intervals along the a, b, and c axes of the Brillouin zone) for bulk calculations and to 6,6,2 for slab supercell calculations. Some calculations were repeated with pa- rameters 12,12,4 and 12,12,2, resp., with essentially no changes in the results. The density convergence parame- ter was always put to 10 − $^{6}$. 

Since the surface structures were relaxed before cal- culating the surface Kohn-Sham band structure, relaxed bulk reference structures had to be used for compari- son. The obtained structure parameters together with experimental values are shown in Table I. Since as usu- ally the GGA 8 results are closer to experiment than the LDA 9 results, the GGA functional was used in all further calculations. In this text tetragonal structures are con- sidered only, therefore the low temperature experimental structure data from Ref. 10 were tetragonally averaged in Table I. As usual, z O was put to zero and z Fe to 1/2. We are interested in the (001) surfaces of bulk crystals, so the a lattice constant is kept fixed at the GGA bulk value a = 4 . 041 ˚ A in all what follows. In this text, the tetragonal axis of the structure is referred to as c -axis and its direction as z -direction. 

<img src='content_image/392715.jpg'>

The Kohn-Sham band structure of the GGA relaxed bulk crystal is shown in Fig. 1. The ‘fat bands’ (online in red) on this figure indicate the O-2 p and La-4 f, 5 d, 6 s orbital character of the bands. The thickness of those fat bands is proportional to the sum of squares of co- efficients for these basis states in the expansion of the Kohn-Sham wavefunction into the FPLO orbital basis. 

## II. COMPUTATIONAL APPROACH 

