five-orbital tight-binding model and effect of the tetrahedral distortion in iron pnictides

Iron pnictides are layered Iron pnictides are layered materials characterized by materials characterized by Pnictogen (Pn)-Fe layers, Pnictogen (Pn)-Fe layers, Pn=As,P. Fe-Pn bonds form Pn=As,P. Fe-Pn bonds form an angle an angle with the Fe plane. with the Fe plane.

Experiments and first principle calculations seem Experiments and first principle calculations seem to indicate a dependence of the superconducting and to indicate a dependence of the superconducting and magnetic properties on magnetic properties on . Inclusion of the five 3d-Fe . Inclusion of the five 3d-Fe orbitals is believed to be relevant to describe these orbitals is believed to be relevant to describe these materials. Interband scattering is sensitive to the materials. Interband scattering is sensitive to the orbital makeup of the Fermi surface sheets. orbital makeup of the Fermi surface sheets. We propose a 5-orbital tight-binding model to We propose a 5-orbital tight-binding model to describe the pnictogen-iron layers. We use it to study describe the pnictogen-iron layers. We use it to study the influence of the Fe-Pn angle the influence of the Fe-Pn angle on the band on the band structure. We find that small changes in structure. We find that small changes in have a have a strong impact on the bands and on the shape and strong impact on the bands and on the shape and orbital content of the Fermi surface. orbital content of the Fermi surface.

Five-orbital tight-binding model and Five-orbital tight-binding model and effect of the tetrahedral distortion in effect of the tetrahedral distortion in

iron pnictides iron pnictides M.J. Calderón(1), B. Valenzuela(1,2) and M.J. Calderón(1), B. Valenzuela(1,2) and E. BasconesE. Bascones(1)(1)(1) Instituto de Ciencias de Materiales de Madrid, ICMM-CSIC (Spain),

(2) Universidad Autónoma de Madrid (Spain).

.

Angle dependence in experiments, LDA and in our tight binding model

CONCLUSIONSCONCLUSIONS

Abstract

• We propose a five orbital Slater-Koster tight binding We propose a five orbital Slater-Koster tight binding model for the iron-pnictogen layers which allows to model for the iron-pnictogen layers which allows to analyze the depencence of the electronic properties of analyze the depencence of the electronic properties of iron pnictides on the Fe-As angle. It reproduces the iron pnictides on the Fe-As angle. It reproduces the bands and orbital component using only four bands and orbital component using only four parameters to parametrize all hopping terms. For the parameters to parametrize all hopping terms. For the angle dependence:angle dependence:

•The hopping amplitudes depend strongly on the Fe-The hopping amplitudes depend strongly on the Fe-As angle. This is expected to be important for weak As angle. This is expected to be important for weak coupling models (via nesting) and strong coupling coupling models (via nesting) and strong coupling models (via superexchange). models (via superexchange). • This angle-dependence is also present in the shape This angle-dependence is also present in the shape and topology of the Fermi surface (crucial for and topology of the Fermi surface (crucial for properties based on nesting).properties based on nesting).• In agreement with LDA calculations at M (in the In agreement with LDA calculations at M (in the extended Brillouin zone) close to the Fermi surface extended Brillouin zone) close to the Fermi surface the bands with 3z2-r2 and xy character switch in the bands with 3z2-r2 and xy character switch in energy as a function of the angle. energy as a function of the angle. •The orbital component of the Fermi surfaces also The orbital component of the Fermi surfaces also depends on the Fe-As angle, what could influence depends on the Fe-As angle, what could influence the symmetry of the superconducting order the symmetry of the superconducting order parameterparameter

Results: Fermi surfaces and orbital components of the Fermi surfaces

V. Vildosola, e al. PRB 78, 64518 (2008)

LaFeAsO (LaFeAsO (LaFeAsOLaFeAsO=33.2º) has =33.2º) has a magnetic transition and a magnetic transition and high Tc. LaFePO high Tc. LaFePO ((LaFePOLaFePO=29.9º) has no =29.9º) has no magnetic transition and low magnetic transition and low Tc. Tc.

From LDA: Fermi pocket with dxy character in LaFeAsO but with d3z2-r2 character in LaFePO

As in LDA it is found a switch in M between a d3z2-r2 pocket for

LaFePOLaFePO=29.9º=29.9º and a dxy pocket for LaFeAsOLaFeAsO=33.2º=33.2º

Slater-Koster five-orbital tight-binding model

Tight-binding model to describe the Pn-Fe layersTight-binding model to describe the Pn-Fe layers

onon

Results for the LaFeAsO bands

AB initio calculation of LaFeAsO bandsin the reduced Brillouin zone, Boeri, e al. PRL 101, 26403 (2008)

Tight-binding LaFeAsO bands in the extended Brilloun zone

Extended (Fe) Brilloun zone

ReducedBrilloun zone

Good agreement for the hole and electron pockets

and for the orbital character

of the bands

differs among compounds and depends differs among compounds and depends on doping or applied pressure. on doping or applied pressure. Differences in the value of Differences in the value of have been have been proposed as the origin of the different proposed as the origin of the different superconducting and magnetic properties superconducting and magnetic properties among compounds. among compounds.

The Fermi surface orbital makeup has been claimed to determine The Fermi surface orbital makeup has been claimed to determine the symmetry of the superconducting order parameterthe symmetry of the superconducting order parameter(Maier et al. PRB 79, 224510 (2009) ; Kuroki et al. , PRB 79, 224511 (2009)).(Maier et al. PRB 79, 224510 (2009) ; Kuroki et al. , PRB 79, 224511 (2009)).

Calderon, Valenzuela and Bascones, arXiv:0907.1259

Change on the orbital content of the Fermi surface when the Fe-Pn

angle varies

Change on the shape and topology of the Fermi surface when

the Fe-Pn angle varies

- Indirect hopping between Fe atoms via Pn - Indirect hopping between Fe atoms via Pn induces a dependence of the hopping amplitudes induces a dependence of the hopping amplitudes on on . .

- Hopping parameters are calculated within the Slater-- Hopping parameters are calculated within the Slater-Koster framework in terms of the Pn-Fe (pd) and Fe-Fe Koster framework in terms of the Pn-Fe (pd) and Fe-Fe (dd) orbital overlap integrals .(dd) orbital overlap integrals .

-All five d-Fe orbitals are included. - Pnictogen (As, P) atoms only enter via Fe-Fe hopping amplitudes

Slater and Koster, Phys. Rev 94, 1498 (1954).

-Hopping is restricted to second Fe nearest Hopping is restricted to second Fe nearest neighbours. There are 18 hopping terms which neighbours. There are 18 hopping terms which can can be given in terms of be given in terms of justjust four fitting parameters. four fitting parameters.

Hole pockets in can disappear in elongated compounds

C.H. Lee, e al., JPSJ 77,083704 (2008)

Zhao, e al. Nat. Mat. 7, 953 (2008)

Fe

Pn=As,P

pd pd dd dd dd

W.A. Harrison, “Elementary Electronic Structure”, World Scientific (2004)

CeFeAsO1-xF