Angle-resolved photoemission study of the iron-based superconductors PrFeAsO 1 y and BaFe 2 (As 1 x P x ) 2

Transcription

1 Angle-resolved photoemission study of the iron-based superconductors PrFeAsO 1 y and BaFe (As 1 x P x ) Master Thesis Ichiro Nishi Department of Physics, Graduate School of Science, The University of Tokyo January, 11

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3 Abstract The recent discovery of iron-based superconductors has attracted keen attention in the materials science community from both experimental and theoretical points of view because they are the only class of superconductors which show critical temperatures exceeding 5 K other than the cuprates. In the iron-based materials, many Fe 3d-derived bands cross the Fermi level, resulting in complicated holeand electron-like Fermi surfaces (FS s), whereas only a single band with one FS exists in the cuprates. As the mechanism of superconductivity in iron pnictides, it has been proposed that superconductivity is driven by spin fluctuations or their characteristic dynamical spin susceptibilities, which basically originate from FS nestings. Therefore, in order to understand the mechanism of superconductivity in iron-based superconductors, it is necessary to clarify the relationship between the band structures, the FS shapes, and the existence or absence of superconductivity. In the present work, we have performed angle-resolved photoemission spectroscopy (ARPES) studies of the iron-based superconductors PrFeAsO 1 y (y =.3, ) and BaFe (As 1 x P x ) (x =.6,.9) to investigate their band structures and FS shapes. As for PrFeAsO 1 y, heavily hole-doped electronic states have been observed due to the polar nature of cleaved surfaces. Nevertheless, we have found that the ARPES spectra basically agree with band dispersions calculated in the local density approximation (LDA) if the bandwidth is reduced by a factor of.5 and then the chemical potential is lowered by 7 mev. Comparison with previous ARPES results on LaFePO reveals that the energy positions of the d 3z r- and d yz,zx -derived bands are considerably different between the two materials, which we attribute to the different pnictogen height as predicted by the LDA calculation. As for BaFe (As 1 x P x ), the three-dimensional electronic structure has been observed as predicted by band-structure calculation. We have estimated the area of electron FS s and the effective masses of electron bands, and found that their P content dependences agree well with the results of de Haas-van Alphen measurements. We have observed a disconnection of the hole Fermi surface along the k z direction for the non-superconducting compound x =.9. The disconnection deteriorates nesting properties and, therefore, may lead to the suppression of superconductivity.

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5 Contents 1 Introduction 1 Principles of photoemission spectroscopy 3.1 Photoemission spectroscopy Angle-resolved photoemission spectroscopy Effect of matrix element Angle-resolved photoemission study of PrFeAsO 1 y Introduction Physical properties of PrFeAsO 1 y Experiment Results and discussion Pnictogen height dependence of the electronic structure Oxygen concentration dependence of the Fermi surfaces and band dispersions of PrFeAsO 1 y Energy gaps Electron bands around the Γ point taken with low photon energies Angle-resolved photoemission study of BaFe (As 1 x P x ) Introduction Physical properties of BaFe (As 1 x P x ) Experiment Results and discussion Three-dimensional electronic structure Composition dependence of Fermi surface size and effective mass Nesting properties Summary and conclusion 51 Acknowledgments iii

6 References

7 Chapter 1 Introduction The recent discovery of superconductivity in iron pnictides [1] has attracted keen attention in the materials science community from both experimental and theoretical points of view because they are the only class of superconductors which show critical temperatures (T c ) exceeding 5 K [] other than the cuprates. This new class of iron-based systems share some common properties with the cuprates such as the layerd crystal structures [1] and the antiferromagnetic ordering in the parent compounds [3,4]. However, many differences exist between the two families especially in their electronic structures. These differences were apparent from the early stage when local-density-approximation (LDA) band-structure calculations predicted that many Fe 3d-derived bands cross the Fermi level (E F ), resulting in complicated holeand electron-like Fermi surfaces (FS s) [5 7], whereas only a single band with one FS exists in the cuprates. The predictions of the LDA calculations were confirmed by photoemission experiments, which demonstrated that Fe 3d states are predominant near E F [8 1] with moderate p-d hybridization and electron correlations [9]. Moreover, angle-resolved photoemission spectroscopy (ARPES) studies have revealed (i) disconnected hole- and electron-like FS sheets [11], (ii) moderately renormalized energy bands due to electron correlations [1,13], (iii) kinks in band dispersions, suggesting coupling of quasiparticles to Boson excitations [14, 15], and (iv) FS-dependent nodeless, nearly-isotropic superconducting gaps [16 19]. Although the mechanism of superconductivity has not been elucidated yet, there is remarkable correlation between the T c and the position of pnictogen atoms relative to the Fe plane []. The ARPES observations mentioned above were mainly obtained for the socalled 1 system (such as AFe As, A(Fe 1 x Co x ) As ) while few studies have been reported for the so-called 1111 system (such as LaFeAsO 1 y F y ) [13,17,1 3] owing to the difficulty in obtaining high quality, sizable single crystals. Because the 1111 system has higher T c s than those of the 1 system, detailed knowledge of the electronic structure of the 1111 system and its differences from that of the 1 sys- 1

8 Chapter 1. Introduction tem may give a clue for understanding the mechanism of superconductivity in the iron-based superconductors. Therefore, we have performed ARPES measurements on the 1111 system PrFeAsO 1 y, which has a T c as high as 4 K, and the parent compound PrFeAsO and compared the results with a band-structure calculation of PrFeAsO. As reported by the previous ARPES studies on the 1111 system [13,1], heavily hole-doped electronic states have been observed probably due to the polar nature of the cleaved surfaces. We have found that the ARPES spectra agree well with the LDA band dispersions and FS s if the calculated bandwidth is reduced by a factor of.5 and then the chemical potential is lowered by 7 mev, resulting in the heavily hole-doped correlated electronic states. We have thus found remarkable differences in the electronic structures between PrFeAsO.7 and LaFePO [13], which can be attributed to the change of the pnictogen height, the distance between the Fe plane and the pnictogen atoms, as predicted by the band-structure calculation [4]. Recently, penetration depth, thermalconductivity [5], and NMR studies [6] have shown signatures of a superconducting gap with line node in BaFe (As 1 x, P x ) [7]. Early angle-resolved photoemission spectroscopy (ARPES) studies on Ba 1 x K x Fe As have revealed the importance of FS nesting for the superconductivity based on two-dimensional (D) electronic structure. However, it is necessary to investigate the three-dimensional electronic structure of the 1 ironbased superconductors because band-structure calculation identified strong threedimensionality in the FS s of the family of BaFe As [8] and recent ARPES studies confirmed this [9, 3]. Therefore, we have performed ARPES measurements on the 1 system BaFe (As 1 x P x ) (x =.6 and.9) in order to elucidate the relationship between superconductivity and nesting properties. We have found that one of the hole FS s is disconnected between the Z points in x =.9, which may be the main reason for the suppresion of superconductivity in the x =.9 compound. In Chapter, we describe the basic principles of photoemission spectroscopy. In Chapter 3, we describe the experiment on PrFeAsO 1 y and mainly discuss the dependence of the electronic structure on the pnictogen height. In Chapter 4, we describe the experiment on BaFe (As 1 x P x ) and mainly discuss the three-dimensional electronic structure. Finally, in Chapter 5, we summurize the results of this thesis.

9 Chapter Principles of photoemission spectroscopy Angle-resolved photoemission spectroscopy (ARPES) is one of the most direct methods of studying the electronic structure of solids. In this chapter, we describe the principles of photoemission spectroscopy (PES) and ARPES..1 Photoemission spectroscopy Photoemission spectroscopy (PES) is a powerful tool to directly investigate the electronic structure of materials. Photoemission is a phenomenon that a material emits electrons when an electron in the solid absorbs a photon of sufficiently high energy hν. Knowing the kinetic energy Ekin v of the emitted electron in the vacuum, one can deduce how strong the electron was bound to the material. From the energy conservation law, E v kin = hν Φ E B, (.1) where hν is the energy of the incident photons, E B is the binding energy relative to the Fermi level E F (chemical potential µ) and Φ is a work function of the material under study. The work function Φ is the energy required for the electron to escape from the solid through the surface and to reach the vaccum level E vac, that is, Φ = E vac E F. In real experiments the kinetic energy (E kin ) measured from E F rather than Ekin v is directly observed. Then we obtain E kin = hν E B. (.) Here, we take the chemical potential µ as a standard of all energies. Since both the sample and the electron energy analyzer are grounded, the measured kinetic energy E kin of the emitted electron is referred to µ (E F ). 3

10 4 Chapter. Principles of photoemission spectroscopy In the mean-field (Hartree-Fock) approximation, the energy E B is regarded as the energy ϵ of the electron inside the solid before it was emitted. Therefore, the energy distribution of the electrons inside the material can be directly mapped by the distribution of the kinetic energyies of photoelectrons emitted with monochromatic incident photons. Figure.1 illustrates a schematic diagram of the principles of photoemission spectroscopy. In real systems, the photoemission spectra are affected by the relaxation of the whole electron system in the solid, in addition to the one-electron energy ϵ in the simple view (frozen-orbital approximation). In response to the hole produced by the photoemission process, the surrounding electrons tend to screen the hole to lower the total energy of the system. Therefore, considering the whole electron system, the binding energy E B is given by the energy difference between the N-electron initial state Ei N and the (N 1)-electron final state E N 1 f. In other words, E B is the energy of the hole produced by the photoemission process, including the relaxation energy of the total electron system. Hence, much information of the electron correlations can be derived by analyzing the photoemission spectra.. Angle-resolved photoemission spectroscopy Angle-resolved photoemission spectroscopy (ARPES) is one of experimental techniques to determine the structure of a material. In ARPES not only the energies but also the momenta of the electrons in the materials are proved. Here, we briefly review the principle of ARPES [3]. In the photoexcitation process by photons with low energy, the wave number of the incident photon can be neglected, and the wave number of the electron is conserved before and after the photoexcitation except for the reciprocal lattice vector. Therefore, we obtain k f = k i + G, (.3) where k i and k f are the crystal momentum of the electron in the initial and final states, respectively, and G = (n x π/a, n y π/b, n z π/c) is an arbitrary reciprocal lattice vector. When the photoelectron escapes from the solid to the vacuum, part of the momentum perpendicular to the surface is lost due to the finite work function Φ, whereas the momentum parallel to the surface is preserved owing to the translational symmetry along the surface. Therefore, when the momentum of the electron outside the sample is denoted by p p / = k f + G. (.4) In Fig.., the geometry of an ARPES experiment is sketched. A beam of monochromatized radiation supplied either by a gas-discharge lamp or by a synchrotron beamline is incident on a sample. As a result, electrons are emitted by photoelectric effect

11 Chapter. Principles of photoemission spectroscopy 5 Figure.1: Schematic energy diagram showing the principle of photoemission spectroscopy (PES) [31]. Using the relationship E kin = hν E B, the electronic structure of the solid is mapped as an electronic distribution curve (EDC), i.e., a photemission spectrum.

12 6 Chapter. Principles of photoemission spectroscopy and escape in vacuum in all directions. By collecting the photoelectrons with an electron energy analyzer characterized by a finite acceptance angle, one measures their kinetic energy Ekin v for given emission direction. In this way, the momentum p of the photoelectrons in vacuum is also completely determined: its modulus is given by p = mekin v and its components parallel (p = p x + p y ) and perpendicular (p = p z ) to the sample surface are obtained in terms of the polar (θ) and azimuthal (ϕ) emission angles defined by the experiment: p x = mekin v sin θ cos ϕ, (.5) p y = mekin v sin θ sin ϕ, (.6) p z = mekin v cos θ, (.7) where m is the free electron mass. Summarizing Eqs. (.1), (.3), (.4), (.5), (.6), we can directly observe both the energy E E B and the parallel momentum k = (k x, k y ) of the hole produced in the sample by the photoemission process as k x = k y = m(hν Φ EB ) m(hν Φ EB ) sin θ cos ϕ + n xπ a, (.8) sin θ sin ϕ + n yπ, (.9) b where n x and n y are integers. As for the determination of k = k z, which is not conserved during the photoemission process, a different approach is required [Fig..3]. If we adopt a nearlyfree-electron description for the final bulk Bloch state: E f (p) = p m + E = p + p m + E, (.1) where the electron momenta are defined in the extended-zone scheme, and E is the energy of the bottom of the free electron band as indicated in Fig..3. Because E f = Ekin v + Φ + µ and Eqs. (.5) and (.6), one obtains from Eq. (.1), m (E v k = kin cos θ + V ). (.11) Here V = Φ + µ E = E vac E is the inner potential, which corresponds to the energy of the bottom of the valence band referenced to vacuum level E vac. From Eq. (.11) and the measured values of E v kin and θ, if V is also known, one can obtain the corresponding value of k. Based on this principle, one can investigate the cross-section of Fermi surface in k -k z plane. Figure.4 schematically illustrates the procedure for the band mapping by the ARPES spectra.

13 Chapter. Principles of photoemission spectroscopy 7 Figure.: Geometry of an ARPES experiment; the emission direction of the photoelectron is specified by the polar (θ) and azimuthal (ϕ) angles [33]. Figure.3: Kinematics of the photoemission process within the three-step nearly-freeelectron final-state model [3]. (a) Direct optical transition in the solid (the lattice supplies the required momentum). (b) Free-electron final state in vacuum. (c) Corresponding photoelectron spectrum with a background due to scattered electrons.

14 8 Chapter. Principles of photoemission spectroscopy Figure.4: Schematic diagram showing the principle of ARPES taken from [34]. The band dispersions in the material are directly mapped by the ARPES spectra..3 Effect of matrix element The matrix element of the photoemission process is responsible for the dependence of the photoemission data on photon energy and experimental geometry, and may even result in complete suppression of the intensity. The matrix element is given by M k f,i ϕ k f ϵ x ϕ k i, (.1) where ϵ is an unit vector of the electric field of the incident light or an unit vector along the polarization direction of the vector potential A [33]. As shown in Fig..5, we consider photoemission from a d x y orbital, with the detector located in the mirror plane. In order to have a non-vanishing photoemission intensity, the integrand in the overlap integral must be an even function under reflection with respect to the mirror plane. Because odd parity final states would be zero everywhere on the mirror plane and therefore also at the detector, the final state wavefunction ϕ k f

15 Chapter. Principles of photoemission spectroscopy 9 Figure.5: Mirror plane emission from a d x y orbital [33]. Table.1: Forbidden orbital symmetries assuming that the zx-plane is the mirror plane. d xy d yz d zx d x y d 3z r σ-geometry forbidden forbidden forbidden π-geometry forbidden forbidden itself must be even. In particular, at the detector the photoelectron is described by an even parity plane-wave state e ik r with momentum in the mirror plane. In turn, this implies that ϵ x ϕ k i must be even. In the case depicted in Fig..5 where ϕ k i is also even, the photoemission process is allowed for A: even or in-plane (i.e., ϵ p x depends only on in-plane coordinates and is therefore even under reflection with respect to the plane) and forbidden for A: odd or normal to the mirror plane (i.e., ϵ s x is odd as it depends on normal-to-the-plane coordinates). For a generic initial state of either even or odd symmetry with respect to the mirror plane, the polarization conditions resulting in an overall even matrix element can be summarized as: ϕ k f ϵ x ϕ k i { ϕ k i : even A : even ϕ k i : odd + A : odd. (.13) We refer to A: even or E p (A: odd or E s ) as π- (σ-) geometry [Fig..5]. With respect to the zx-plane, the d yz and d xy orbitals are odd, and the d zx, d x y, and d 3z r orbitals are even as shown in Fig..6. Therefore, if we take the zx-plane as the mirror plane, the condition in which ARPES intensity is forbidden can be summurized as indicated in Table.1.

16 1 Chapter. Principles of photoemission spectroscopy Figure.6: Momentum direction for ARPES (left) and the symmetries of the five 3d orbitals with respect to the zx-plane (right) [35].

17 Chapter 3 Angle-resolved photoemission study of PrFeAsO 1 y 3.1 Introduction So far ARPES experiments have been performed on several 1111 iron pnictides, such as LaFePO [13], NdFeAsO.9 F.1 [17], CeFeAsO [], and LaFeAsO [36] [Figs ]. In all these compounds, at least a large hole-like Fermi surface centered at the Γ point of the D BZ was observed. That is, heavily hole-doped electronic states have been observed by ARPES. This problem occurs for the following reason. A cleaved surface of 1111 system is electronically polar. Therefore, in order to prevent the divergence of electric potential in a macroscopic crystal, electronic charges at the surface must reconstruct. Thus, a FeAs layer at the surface must lose electrons. Regaring the electronic states observed by ARPES, it has been claimed from the ARPES study of LaFeAsO that both the bulk bands and the surface bands have been Figure 3.1: FS mapping of LaFePO taken from [13]. Figure 3.: FS mapping of NdFeAsO.9 F.1 taken from [17]. 11

18 1 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y Figure 3.3: FS mapping of CeFeAsO taken from []. Figure 3.4: FS mapping of LaFeAsO taken from [36]. Figure 3.5: Summary of (a) the bulk and (b) the surface band structures of LaFeAsO. (c) Diagram for the origin of the measured bands. This figure is taken from [36]

19 3.. Physical properties of PrFeAsO 1 y 13 Figure 3.6: Band structure of the (LaO) 4 (FeAs) 6 slab taken from [37]. The thickness of the red lines represents the weight of bulk Fe 3d states. Figure 3.7: Element dependence of the T c of 1111 iron pnictides taken from [38]. observed as shown in Fig. 3.5 [36]. Eshchrig et al. have performed band-structure calculations of (LaO) 4 (FeAs) 6 slabs as shown in Fig. 3.6 [37]. The thickness of the red lines represents the weight of bulk Fe 3d states and, therefore, thin lines represent surface Fe 3d states. One can see that the surface bands can be obtained by shifting the bulk bands approximately by a constant energy of.1 ev and, therefore, one can say that the surface states contain information of the bulk states.

20 14 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y Figure 3.8: Temperature dependence of the resistivity of the PrFeAsO 1 y (y =,.3) samples. Figure 3.9: Temperature dependence of the magnetic susceptibility of the PrFeAsO.7 samples. 3. Physical properties of PrFeAsO 1 y PrFeAsO 1 y belongs to the family of 1111 iron-based superconductors. It can achieve relatively high T c among the 1111 iron pnictides as shown in Fig. 3.7 [38]. Therefore, it may give us a clue to understand the mechanism of the high-t c superconductivity of iron-based superconductors. Figure 3.8 shows the temperature dependence of the resistivity of PrFeAsO 1 y (y =,.3). PrFeAsO is not superconducting and shows a kink of resistivity curve around 15 K due to structural transition. PrFeAsO.7 is superconducting and has T c = 4 K. The T c of PrFeAsO.7 has been also confirmed from temperature dependence of magnetic susceptivility [Fig. 3.9].

21 3.3. Experiment Experiment High-quality single crystals of the electron-doped compound PrFeAsO 1 y (T c 4 K for y =.3) and its parent compound (y = ) were synthesized by a high-pressure method as described in Ref. [39]. The ARPES measurements were carried out at BL5-4 of Stanford Synchrotron Radiation Lightsource (SSRL), at BL1..1 of Advanced Light Source (ALS), and at BL-8A of Photon Factory (PF) using incident photons of hν = 5 ev linearly-polarized, hν = 4.5 ev linearly-polarized, and hν = 36-8 ev circularly-polarized, respectively. SCIENTA R4 analyzers were used at SSRL and ALS and a SCIENTA SES- analyzer was used at PF, with the momentum resolution of. π/a, where a = 4. Å is the in-plane lattice constant. The total energy resolution was 1 mev, 15 mev, and 1 mev for SSRL, ALS, and PF, respectively. The crystals were cleaved in situ at T = 1 K in an ultra-high vacuum better than Torr giving flat mirror-like surfaces which stayed clean all over the measurement time ( days). The calibration of E F was achieved by referring to that of gold which was in electrical connect with the samples. In the measurements at ALS, the electric field vector E of incident photons was in the Fe plane and its direction along the Fe-Fe nearest-neighbor. In the measurements at SSRL, although the direction of the in-plane component of E was the same as that at ALS, E had also a finite component perpendicular to the plane. Density functional calculation was done within the LDA by using a WIENk package [4], where the experimental tetragonal lattice parameters of PrFeAsO at room temperature were used. As for Pr 4f bands, we have adopted the LSDA+U method in order to move the bands away from E F. 3.4 Results and discussion Pnictogen height dependence of the electronic structure Figures 3.1 (a) and 3.1 (b) show the results of FS mapping for the PrFeAsO.7 sample at low temperature ( 1 K) using photon energies hν = 5 ev and 4.5 ev, respectively. Here, we choose the local coordinate system around the Fe atom such that the x and y axes point toward the nearest-neighbor Fe atoms. The x and y direction are indicated by E x and E y in Fig 3.1. In these plots, the photoemission intensity has been integrated over E F ±5 mev. In both plots one can clearly observe a large nearly circular hole pocket with k F.6(π/a) centered at the Γ point of the the two-dimensional (D) Brillouin zone (BZ). A smaller, nearly circular hole pocket with k F.3(π/a) is also seen in Fig. 3.1 (b) while the intensity is very weak in Fig. 3.1 (a). In Fig. 3.1 (b), the momentum with strong intensities on the FS are opposite between the large and small FS sheets around the Γ point, im-

22 16 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y 1 (a) PrFeAsO.7 X hn = 5 ev Μ (b) PrFeAsO.7 X hn = 4.5 ev Μ k Y (π/a) Γ Γ -1 E y (+E z ) E y k X (π/a) Figure 3.1: Fermi surface mapping of PrFeAsO.7 obtained by integrating the EDCs over an energy window of E F ± 5 mev. The white square highlights the boundary of the first Brillouin zone. a is the in-plane lattice constant. The direction of polarization vector is indicated in each panels. Red dots indicate k F positions determined by the peak positions of momentum distribution curves (MDC s). (a) Fermi surface mapping taken with hν = 5 ev. (b) Fermi surface mapping taken with hν = 4.5 ev. plying that they have different orbital characters. The large size of the hole pocket has been reported by the previous ARPES studies for the 1111 iron-based superconductors [13, 17, 1, ] and reflects heavily hole-doped electronic states. One can also observe clover-shaped FS s around the corner (the M point) of the D BZ. This occurs because the Fermi level is lowered below the four Dirac points around M caused by excess hole doping. The excess hole doping occurs because the cleaved surface in the 1111 iron pnictides is electronically polar and electronic charges must reconstruct after cleaving [41]. Note that the heavily hole-doped electronic states in the surface region have been observed in spite of the fact the oxygen deficiency of the bulk samples produces negative carrier. The clover-shaped FS s have been also observed in previous ARPES studies of heavily hole-doped KFe As [4, 43]. The ARPES intensity plots in energy-momentum (E-k) space along Γ-M taken at hν = 5 ev and 4.5 ev are shown in panels (a) and (b) of Fig. 3.11, respectively. The direction of the electrical polarization vector of incident light is indicated in Fig In Fig (a) and (b), the band dispersions of PrFeAsO.7 deduced from the second derivative plots of EDC s and those of MDC s are also shown (see caption). In order to understand the multiband electronic structure of this material, we plot the experimentally deduced band structure and compare with the LDA dispersions in Fig (c). We have found that the band structure basically agree with the calculated band dispersions if the bandwidth is reduced by a factor of.5

23 3.4. Results and discussion 17 E - E F (mev) Μ 5 (a) PrFeAsO.7-5 Γ hn = 5 ev k Y (π/a) 1 (d) X Γ hn = 5 ev Μ -1-1 E y (+E z ) E - E F (mev) 5-5 (b) PrFeAsO.7 hn = 4.5 ev k Y (π/a) 1 (e) -1 1 X Μ Γ hn = 4.5 ev E y E - E F (mev) -5 (c) PrFeAsO.7 d yz,zx d xy d xy d yz,zx -1 1 k X (π/a) d 3z -r k // (p/a) Figure 3.11: Comparison between the ARPES spectra of PrFeAsO.7 and the LDA band structure along the Γ-M direction. The directions of momentum and polarization vector of (a) and (b) are indicated in Fig (a) The ARPES data taken with hν = 5 ev. Experimental band structure deduced from the second derivative plots of EDCs and MDCs is also shown. Diamond: EDC peak positions for hν = 5 ev, circle: MDC peak positions for hν = 5 ev. (b) The same as (a) with hν = 4.5 ev. Triangle: EDC peak positions for hν = 4.5 ev, square: MDC peak positions for hν = 4.5 ev. (c) Experimental band structure of PrFeAsO.7 deduced from of EDCs and MDCs of (a) and (b). The calculated band dispersions are plotted after reducing the bandwidth by a factor of.5 and then shifting down the chemical potential by 7 mev. (d) Calculated Fermi surface plotted on the Fermi surface mapping taken with hν = 5 ev. (e) The same as (d) with hν = 4.5 ev.

24 18 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y and then the chemical potential is lowered by 7 mev. The band narrowing is due to electron correlation, which is not taken into account in the LDA calculation, and the chemical potential shift is due to the electronic reconstruction of the surface layers to prevent the polar catastrophe [41]. One can also reproduce the observed FS s using the same shift as shown in Fig (d) and 3.11 (e). According to the LDA calculation [Fig (c)], the outer two FS s around the Γ point are nearly degenerate and consist of d yz,zx and d xy bands while the inner one consists of only a d yz,zx band. Since the spectral intensity of the d xy band would be weak and may not be seen near the Γ point due to matrix element effects [35], one can conclude that the intensities of both the outer and inner FS s in Figs. 3.1 (b) and 3.11 (b) mainly come from the d yz,zx bands. Furthermore, if we take into account matrix element effects for the electric vector E in Fig. 3.1 (b), the outer and inner FS s have d zx (d yz ) and d yz (d zx ) orbital character in the k x (k y ) direction, respectively 1. However, the band-structure calculation predicts opposite orbital characters between them, namely, d yz (d zx ) character for the outer FS and d zx (d yz ) character for the inner one along the k x (k y ) direction [44]. Although the origin of the discrepancy between experiment and calculation is not clear at present, a similar discrepancy has been reported in a previous ARPES results on 1 a iron-based superconductor [35]. Here, we shall discuss the orbital character of the other bands seen in Figs (a) and (b). As for the band observed 5 mev below E F around the Γ point, one can notice that the spectral intensity in Fig (a), where the E z component is finite, is strong compared to that in Fig (b). Therefore, this band is considered to have d 3z r character as predicted by the band-structure calculation. From Fig (c), One can also see that the FS around the M point has a hole-like feature arising from the intersection of the d yz,zx band and the d xy band near E F. Calculation of the volume enclosed by the hole FS s yields hole counts of.7,.8 and.5 per Fe atom, respectively, for the inner FS around the Γ point, the outer FS around the Γ point, and the FS s around the M point. As mentioned above, the spectral intensity of the d xy band should be weak and cannot be observed near the Γ point and, therefore, we cannot evaluate the size of d xy band-origin FS. For three possible cases, (1) the d xy FS has the same size as the outer FS, () it has the same size as the inner FS, and (3) it does not exist, the total hole concentration, respectively, becomes (1).68, ().47, and (3).4 holes per Fe atom. These values are comparable to the predicted value of.5 which is necessary to avoid the polar catastrophe [41]. Now, let us compare the present results with the previous ARPES results on LaFePO with T c 6 K [45], which has also the same crystal structure as PrFeAsO 1 The data of Figs. 3.1 (b), 3.11 (b), and 3.1 (b) have been taken with σ geometry [35]. Therefore, the spectral intensity of d zx band cannot be observed.

25 3.4. Results and discussion 19. hn (a)prfeaso = 5 ev.7 (b)prfeaso.7 hn = 4.5 ev. E - E F (ev) Μ (c)prfeaso.7 Γ Μ (d)lafepo Γ hn = 4.5 ev d yz,zx d 3z -r. d yz,zx d xy d yz,zx E - E F (ev) d xy d yz,zx d 3z -r d 3z -r d xy d yz,zx d yz,zx d xy d 3z -r -.6 d x -y Μ Γ Μ Γ Figure 3.1: Comparison between ARPES spectra and LDA band structures along the Γ-M direction. The directions of momentum and polarization vector of (a) and (b) are indicated in Fig (a) The same as Fig (a). (b) The same as Fig (b). (c) The same as Fig (c). (d) The ARPES data of LaFePO taken from Ref. [13].

26 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y with lower pnictogen height than that of PrFeAsO.7. Band-structure calculation [4] predicts that if the pnictogen height is lowered, the d 3z r band is raised and may cross E F around the Γ point. In order to see differences in the electronic structure between PrFeAsO.7 and LaFePO, in Fig. 3.1 we compare the present ARPES intensity E-k plot with that of LaFePO [13] along the Γ-M line. For the same reason as mentioned above, PrFeAsO.7 has two bands at the Γ point 5 mev and. ev below E F with d 3z r character as predicted by the band-structure calculation [Fig. 3.1 (c)]. In LaFePO, in contrast to PrFeAsO.7, one of the d 3z r bands crosses E F and forms a quite large hole FS as shown in Fig. 3.1 (d). In addition, in LaFePO, the d yz,zx bands around the M point are lowered compared to those in PrFeAsO.7 and recover the electron FS s. Although we have not been able to observe the spectral intensity of the d xy band near the Γ point as mentioned above, it seems from comparison between the data and band-structure calculation [Figs. 3.1 (c) and (d)] that PrFeAsO.7 has a d xy FS around the Γ point while LaFePO does not. According to the theory of spin-flucutuation-mediated superconductibity [46], in which the d xy FS plays an important role to induce high T c superconductivity, the difference in the d xy band may be the main reason why the T c of PrFeAsO.7 is higher than that of LaFePO. In the previous ARPES study of another 1111 superconductor LaFeAsO [36], the Dirac points around the M point are below E F like LaFePO [Fig. 3.1 (d)], while they are slightly above E F in PrFeAsO.7 [Figs (c) and 3.1 (c)]. This difference can also be explained by the different pnictogen heights based on bandstructure calculation Oxygen concentration dependence of the Fermi surfaces and band dispersions of PrFeAsO 1 y Oxygen deficiency produces electron carriers in PrFeAsO 1 y. Therefore, one may expect electron-doped-electronic states of PrFeAsO 1 y, or rigid band shifts, can be observed by ARPES. Figure 3.13 shows the results of FS mapping for the PrFeAsO sample at low temperature ( 1 K) using photon energy hν = 5 ev. In this plot, the photoemission intensity has been integrated over E F ± 5 mev. One can clearly observe a large nearly circular hole pocket with k F.6 (π/a) centered at the Γ point. A smaller nearly circular hole pocket with k F.3 (π/a) is also seen in Fig One can also observe clover-shaped FS s around the M point. We compare FS s of PrFeAsO to those of PrFeAsO.7 in Fig One can notice that the formation of FS s of PrFeAsO observed by ARPES is similar to that of PrFeAsO.7 observed by ARPES. This indicates that the electronic structures of the cleaved surface of PrFeAsO.7 and PrFeAsO are almost identical in spite of the fact the oxygen dificiency of the bulk

27 3.4. Results and discussion 1 1 PrFeAsO X hn = 5 ev Μ k Y (π/a) Γ -1 E y (+E z ) -1 1 k X (π/a) Figure 3.13: Fermi surface mapping of PrFeAsO taken with hν = 5 ev obtained by integrating the EDCs over an energy window of E F ± 5 mev. The white square highlights the boundary of the first Brillouin zone. a is the in-plane lattice constant. The direction of polarization vector is indicated in the panel. Red dots indicate k F positions determined by the peak positions of momentum distribution curves (MDC s). 1 PrFeAsO hn = 5 ev.7 PrFeAsO k Y (π/a) Γ -1 M X -1 1 k X (π/a) Figure 3.14: Comparison of the Fermi surfaces between PrFeAsO.7 and PrFeAsO. The dots indicate k F positions obtained from Figs. 3.1 (a) and 3.13.

28 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y 5 Μ (a) PrFeAsO Γ hn = 5 ev Μ (b) PrFeAsO Γ E - E F (mev) -5 d xy d yz,zx d xy d yz,zx d 3z -r k // (p/a) -1 1 k // (p/a) Figure 3.15: Comparison between the ARPES spectra of PrFeAsO and the LDA band structure along the Γ-M direction. The directions of momentum and polarization vector of (a) are indicated in Fig (a) The ARPES data taken with hν = 5 ev. Experimental band structure deduced from the second derivative plots of EDCs and MDCs is also shown. Diamond: EDC peak positions for hν = 5 ev, circle: MDC peak positions for hν = 5 ev. (b) Experimental band structure of PrFeAsO deduced from (a). The calculated band dispersions are plotted after reducing the bandwidth by a factor of.5 and then shifting down the chemical potential by 7 mev. PrFeAsO.7 samples produces negative carrier and chemical potential of the bulk PrFeAsO.7 is considered as higher than that of the bulk PrFeAsO. The reason why this occurs may be because the charge reconstruction mentioned in the section is so large that it considerably modify the chemical potential and mask the difference in the chemical potential between PrFeAsO.7 and PrFeAsO. The ARPES intensity plots in E-k space along Γ-M taken at hν = 5 ev are shown in Figs and The direction of the electrical polarization vector of incident light is indicated in Fig In Figs (a) and 3.16 (a), the band dispersions of PrFeAsO deduced from the secound derivative plots of EDC s and those of MDC s are also shown (see caption). We plot the deduced band structure and compare with tha LDA dispersions in Figs (b) and 3.16 (b). We have found that the band structure basically agree with the calculated band dispersions if the bandwidth is reduced by a factor of.5 and then the chemical potential is lowered by 7 mev, which are same values in the case of PrFeAsO.7. However, the position of the band at the Γ point 1 mev is different from that of the band at the Γ point 5 mev. The origin of this difference is not clear at present. In Figs and 3.18, we have summurized the obtained band dispersions of PrFeAsO 1 y (y =.3, ).

29 3.4. Results and discussion 3.. (a) PrFeAsO hn = 5 ev hn = 5 ev (b) PrFeAsO d yz,zx d yz,zx d xy d 3z -r E - E F (ev) d xy d yz,zx d 3z -r -.6 d x -y Μ Γ Μ Γ Figure 3.16: Comparison between ARPES spectra of PrFeAsO and LDA band-structure calculation along the Γ-M direction. The directions of momentum and polarization vector of (a) are indicated in Fig (a) The same as Fig (a). (b) The same as Fig (b). E - E F (mev) 5-5 d xy d yz,zx d xy PrFeAsO.7 hn = 5 ev PrFeAsO.7 hn = 4.5 ev PrFeAsO hn = 5 ev d yz,zx d 3z -r k // (p/a) Figure 3.17: Comparison of band dispersions between PrFeAsO.7 and PrFeAsO along the Γ-M direction. The band dispersions are obtained from Figs and 3.15.

30 4 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y.. d yz,zx d yz,zx d xy d 3z -r E - E F (ev) d xy d yz,zx d 3z -r -.6 Μ PrFeAsO.7 hn = 5 ev PrFeAsO.7 hn = 4.5 ev d x -y PrFeAsO hn = 5 ev Γ Figure 3.18: Comparison of band dispersions between PrFeAsO.7 and PrFeAsO along the Γ-M direction. The band dispersions are obtained from Figs. 3.1 and 3.16.

31 3.4. Results and discussion 5 E - E F (mev) B (a) A PrFeAsO.7 hν=5 ev, T=1 K k // (π/a) Intensity (arb. units) B A A B (b) -1 1 E-E F (mev) Figure 3.19: Energy gaps of PrFeAsO.7 ovserved by hν = 5 ev. The directions of momentum and polarization vector of (a) are indicated in Fig. 3.1 (a). (a) The ARPES data taken with hν = 5 ev and T = 1 K. (b) The symmetrized EDC s of (a) Energy gaps Kondo et al. have reported energy gaps on a hole FS around the Γ point in NdFeAs O.9 F.1, which belongs to the family of 1111 iron-based superconductor [17]. The energy gaps have opened on the entire FS and k B T c = 6.7. However, they have not shown the temperature dependence of the energy gaps, and therefore, the origin of the gaps have been still unclear. Figure 3.19 shows the ARPES intensity plot in E-k space along Γ-M and symmetrized EDC s of PrFeAsO.7 taken with hν = 5 ev and T = 1 K. The directions of momentum axes and the electrical polarization vector of incident light are indicated in Fig. 3.1 (a). By the symmetrization of EDC s, one can remove the effect of the Fermi-Dirac function. One can see in Fig that we have not observed energy gap at k F point B on the outer hole FS around the Γ point while we have observed energy gaps at k F point A on the inner hole FS around the Γ point. In order to confirm the existence of the energy gaps, we have investigated other ARPES data which are taken at a different photon energy and polariation. Figure 3. shows the ARPES intensity plot in E-k space along Γ-M and symmetrized EDC s of PrFeAsO.7 taken with hν = 5 ev and T = 1 K. The directions of

32 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y E - E F (mev) (a) PrFeAsO.7 A hν=4.5 ev, T=1 K Intensity (arb. units) A A k // (π/a) (b) -1 1 E-E F (mev) Figure 3.: Energy gaps of PrFeAsO.7 ovserved by hν = 4.5 ev. The directions of momentum and polarization vector of (a) are indicated in Fig. 3.1 (b). (a) The ARPES data taken with hν = 4.5 ev and T = 1 K. (b) The symmetrized EDC s of (a). momentum and the electrical polarization vector of the incident light are indicated in Fig. 3.1 (b). In this case, spectral intensity of the outer FS around the Γ point is suppressed due to the effect of the matrix element. One can see in Fig. 3. that we have again observed energy gaps on the inner hole FS around the Γ point indicated by A. The observed gaps have the magnitude of 15 mev. In order to clarify the momentum dependence of the energy gaps, we have examined several EDC s at different k F points and summurized them in Fig In Fig. 3.1 (b), we plot the symmetrized EDC s at k F points indicated in Fig. 3.1 (a). We have observed energy gaps on the inner hole FS around the Γ point, similar to Figs and 3.. In Fig. 3.1 (c), we plot the momentum dependence of the energy gaps of the inner hole FS around the Γ point. From this plot, we conclude that the energy gap is nearly isotropic and has a value of 16.5 mev, that is, k B T c = 9.1. In order to have a clue for the origin of the ovserved energy gaps, we have performed temperature-dependent measurement of the energy gaps. In Fig. 3., we plot E-k ARPES intensity plots [(a) and (d)], symmetrized EDC s of four k F points with four temperature points [(b), (c), (e), and (f)], and FS mapping [(g)],

33 3.4. Results and discussion 7 1 (a) X PrFeAsO.7 = 4.5 ev Μ k Y (π/a) -1 (c) 18 Γ -1 1 k X (π/a) Angle θ Gap Intensity (arb. units) (b) -4 4 E-E F (mev) Figure 3.1: Momentum dependence of the energy gaps of PrFeAsO.7. (a) The same as Fig. 3.1 (b). (b) Symmetrized EDC s at k F points indicated in (a). (c) Angular dependence of the energy gaps of the inner FS around the Γ point. The red circle corresponds to = 16.5 mev.

34 8 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y ν=4.5 ev, T= K ν=4.5 ev, T= K ( /a) ( /a) = 4.5 ev = 4.5 ev PrFeAsO.7 (T c =4 K) hν=8 ev, T= K = 4.5 ev = 4.5 ev k Y ( /a) (1) () Γ g Μ k X ( /a) Figure 3.: Temparature dependence of the energy gaps of PrFeAsO.7. (a) ARPES data taken with hν = 4.5 ev and T = K. The direction of momentum is indicated as (1) in (g). (b) and (c) Temperature dependence of symmetrized EDC s at k F points indicated in (a). (d) ARPES data taken with hν = 4.5 ev and T = K. The direction of momentum is indicated as () in (g). (e) and (f) Temperature dependence of symmetrized EDC s at k F points indicated in (d). (g) Fermi surface mapping of PrFeAsO.7 obtained by integrating the EDCs over an energy window of E F ± 5 mev.

35 3.4. Results and discussion 9 which incidates the momentum direction of the E-k plots. As for the outer k F s [(c) and (f)], we have obaserved peak-like fetures aroud E E F 1 mev. The peak-like features disappear above T c = 4 K. On the other hand, as for the inner k F s [(b) and (e)], we have observed the suppression of the density of states at E F. The gap features remained even if we increased the temperature as high as 11 K, much higher than T c. From this observation, the observed energy gaps may be called pseudo gap and may have a different origin from superconductivity Electron bands around the Γ point taken with low photon energies We have observed an electron-like band around the Γ point which is not predicted by bulk band-structure calculations. It has been observed strong with low photon energies around 7-14 ev as shown in Fig For convenience, we have summurized the observed band structures in Fig We refer to the band dispersions as A-D as indicated in the figure. Bands A, B, and C correspond to the d yz band, the d yz band, and the d 3z r band, respectively [Fig. 3.18]. With low photon energies 7-9 ev, we have observed only band D. With increasing photon energy, the other bands A-C can be observed and the intensity of band D is weakened [Fig. 3.3]. The electron-like band possibly has an origin of the LaO terminated surface as calculated by Eschrig et al. [37]. The calculated band structure of the surface La 5d+6s has a similar band structure as shown in Fig. 3.5.

36 3 Chapter 3. Angle-resolved photoemission study of PrFeAsO 1 y Energy relative to E F (ev) hν= 7 ev hν= 8 ev hν= 9 ev Energy relative to E F (ev) hν=1 ev hν=11 ev hν=1 ev Energy relative to E F (ev) hν=13 ev hν=14 ev -1.. k // (p/a) PrFeAsO.7 X Γ hn = 5 ev Μ E y (+E z ) k // (p/a) k // (p/a) Figure 3.3: Photon energy dependence of the electron band in PrFeAsO.7. The direction of momentum is indicated by the black arrow in the FS mapping. The FS mapping is the same as Fig. 3.1 (a).

37 3.4. Results and discussion 31 Energy relative to E F (ev) PrFeAsO.7 hν=11 ev A B C D -1.. k // (p/a) Figure 3.4: Observed band dispersions of PrFeAsO.7. Black lines are guide for eyes and indicate the band dispersions (A-D). The superimposed ARPES spectra is the same as those in Fig Figure 3.5: Band structure of the (LaO) 1 (FeAs) 8 slab taken from [37]. The thickness of the red lines represents the weight of surface La 5d+6s states. The black ellipse highlights the electron-like band which may be observed in Fig. 3.3.

38

39 Chapter 4 Angle-resolved photoemission study of BaFe (As 1 x P x ) 4.1 Introduction Many experimental results on the iron-based superconductors have indicated that their superconducting gaps have s±-wave symmetry, that is, the superconducting gap opens on the entire Fermi surfaces (FS s) [16, 18]. However, signatures of line node in the superconducting gap have been formed for BaFe (As 1 x P x ) [7] in recent penetration depth, thermal conductivity [5], and NMR studies [6]. Early angle-resolved photoemission spectroscopy (ARPES) studies on Ba 1 x K x Fe As have revealed the importance of FS nesting for the superconductivity based on two-dimensional (D) electronic structure. However, strong three-dimensionality in the FS s of the family of BaFe As has been identified by the band-structure calculation [8] and confirmed by ARPES studies [9, 3]. As shown in Fig. 4.1, band-structure calculation predicts that the shapes of hole FS s in BaFe (As 1 x P x ) become more three-dimensional with P substitution [7, 47, 48] because P substitution reduces the c-axis length as well as the pnictogen height. Therefore, it is necessary to reveal the three-dimensional electronic structure of BaFe (As 1 x P x ) in order to clarify the relationship between FS nesting, superconductivity, and gap symmetry. 4. Physical properties of BaFe (As 1 x P x ) BaFe (As 1 x P x ) belongs to the family of 1 iron-based superconductors. In this system, the substitution of P for As suppresses magnetic order without changing the number of Fe 3d electrons and induces superconductivity with a maximum T c 3 K at x.3 [Figs. 4. and 4.3]. 33

40 34 Chapter 4. Angle-resolved photoemission study of BaFe (As 1 x P x ) Figure 4.1: Fermi surfaces of BaFe As (x = ) (a) and BaFe P (x = 1) (b) [7]. Crosssectional views on the (11) plane are also shown for x = (c),.3 (d), and 1 (e). Figure 4.: Transport properties of BaFe (As 1 x P x ) [7]. (a), (b) ρ xx (T ) curves in zero field. (c) ρ xx (T ) and dc-magnetization curve, M(T ), for a x =.33 crystal. (d) T dependence of the Hall coefficient R H (T ).

41 4.. Physical properties of BaFe (As 1 x P x ) 35 Figure 4.3: Phase diagram of BaFe (As 1 x P x ) against the P content x [7]. (a) Lattice constants determined from x-ray diffraction as a function of x. (b) z coordinate z Pn of pnictogen atoms in the unit cell and the pnictogen height from the iron plane h Pn = (z Pn.5) c. (c) Phase diagram. Colors in the nonmagnetic normal state represent the evolution of the exponent of temperature dependence in resistivity. Figure 4.4 shows the results of a penetration depth measurement on BaFe (As.67 P.33 ). In sharp contrast to the exponential behavior at low temperature observed in (Ba.45 K.55 )Fe As, λ(t ) in the BaFe (As.67 P.33 ) crystal exhibits a strong quasilinear temperature dependence, indicating line nodes in the superconducting gap [Fig. 4.4 (a)]. The normalized superfluid density λ ()/λ (T ) also clearly shows the difference between the P-doped and K-doped samples [Fig. 4.4 (b)]. The low-temperature data of the P-doped sample is nearly T -linear dependent. This is completely different from the exponential dependence observed in the fully gapped superconductors, and indicates low-lying quasiparticle excitations in this system. Results of thermal conductivity measurements have also indicated the line nodes of superconducting gaps in BaFe (As 1 x P x ). Figure 4.5 shows the temperature dependence of κ/t at zero field. In (Ba.45 K.55 )Fe As, κ/t is nearly identical to the phonon contribution obtained from nonsuperconducting BaFe As, consistent with fully gapped superconductivity, in which few quasiparticles are excited at T T c. On the other hand, the magnitude of κ/t in BaFe (As.67 P.33 ) is strongly enhanced from that in (Ba.45 K.55 )Fe As. Besides, at low temperature, the data of BaFe (As.67 P.33 ) are well fitted to κ/t = at + b. Accoding to [5], these behavior of BaFe (As.67 P.33 ) can be explained by the existence of line nodes in the superconducting gaps. NMR experiment on BaFe (As 1 x P x ) also supports the line nodes in the super-

42 36 Chapter 4. Angle-resolved photoemission study of BaFe (As 1 x P x ) Figure 4.4: Results of a penetration depth measurement on BaFe (As.67 P.33 ) [5]. (a) The change λ(t ) λ(t ) λ() in the penetration depth of BaFe (As.67 P.33 ) along with the data for (Ba.45 K.55 )Fe As T c = 33 K [49]. In the inset, the results obtained by the microwave and rf techniques are compared. (b) Normalized superfluid density λ ()/λ (T ) as a function of T/T c. The data follow a T -linear dependence (dashed line) down to T/T c.5. The upper inset is the data up to T c. The lower inset shows λ(t ) at low temperatures for two samples.