Fermi Surface Dimensions Research Articles

On the multi‐orbital band structure and itinerant magnetism of iron‐based superconductors

AbstractThis paper explains the multi‐orbital band structures and itinerant magnetism of the iron‐pnictide and chalcogenide superconductors. We first describe the generic band structure of a single, isolated FeAs layer. Use of its Abelian glide‐mirror group allows us to reduce the primitive cell to one FeAs unit. For the lines and points of high symmetry in the corresponding large, square Brillouin zone, we specify how the one‐electron Hamiltonian factorizes. From density‐functional theory, and for the observed structure of LaOFeAs, we generate the set of eight Fe d and As p localized Wannier functions and their tight‐binding (TB) Hamiltonian, h (k) . For comparison, we generate the set of five Fe d Wannier orbitals. The topology of the bands, i. e. allowed and avoided crossings, specifically the origin of the d6 pseudogap, is discussed, and the role of the As p orbitals and the elongation of the FeAs4 tetrahedron emphasized. We then couple the layers, mainly via interlayer hopping between As pz orbitals, and give the formalism for simple tetragonal and body‐centered tetragonal (bct) stackings. This allows us to explain the material‐specific 3D band structures, in particular the complicated ones of bct BaFe2As2 and CaFe2As2 whose interlayer hoppings are large. Due to the high symmetry, several level inversions take place as functions of kz or pressure, and linear band dispersions (Dirac cones) are found at many places. The underlying symmetry elements are, however, easily broken by phonons or impurities, for instance, so that the Dirac points are not protected. Nor are they pinned to the Fermi level because the Fermi surface has several sheets. From the paramagnetic TB Hamiltonian, we form the band structures for spin spirals with wavevector q by coupling h (k) and h (k + q). The band structure for stripe order is studied in detail as a function of the exchange potential, Δ, or moment, m, using Stoner theory. Gapping of the Fermi surface (FS) for small Δ requires matching of FS dimensions (nesting) and d‐orbital characters. The interplay between pd hybridization and magnetism is discussed using simple 4 × 4 Hamiltonians. The origin of the propeller‐shaped Fermi surface is explained in detail. Finally, we express the magnetic energy as the sum over band‐structure energies and this enables us to understand to what extent the magnetic energies might be described by a Heisenberg Hamiltonian, and to address the much discussed interplay between the magnetic moment and the elongation of the FeAs4 tetrahedron.

Positron annihilation study for cadmium (electronic structure and enhancement effect)

AbstractThe three dimensional electron density in momentum space ρ(p) and in wave vector space n(k) was reconstructed for cadmium (Cd). The measurements were performed using the two dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Enhanced contributions in the spectra were observed around 5.5 mrad, discussed in terms of a Kahana-like enhancement effect. From another viewpoint, Fermi radii were analyzed in the (λM K), (ALM) and (AHK) planes, and they showed a maximum deviation of about 4% from the free electron Fermi radius. Moreover, comparisons to a radio-frequency size effect (RFSE) experiment and theoretical band structure calculations (using augmented plane wave (APW), linear combination of atomic orbital (LCAO) and linear muffin tin orbital (LMTO) methods) were examined. The results showed a qualitative agreement with both APW and LCAO calculations. However, a favorable agreement with the APW method was determined via Fermi surface dimensions. The differences of bands' occupation of n(k) between the current work and the APW method were argued in view of positron wave function in Cd.

Fermi surface of the ferromagnetic semimetal,EuB6

We report the results of magnetoresistance and magnetization measurements on single crystal ${\mathrm{EuB}}_{6}$ for temperatures above and below the ferromagnetic ordering temperatures ${T}_{C}^{+}=15.3 \mathrm{K}$ and ${T}_{C}^{\ensuremath{-}}=12.5 \mathrm{K},$ in magnetic fields as large as 30 T. Shubnikov--de Haas and de Haas--van Alphen oscillations were observed with four fundamental frequencies. By comparison to band-structure calculations, we ascribe the orbits to small pockets of electrons and holes, centered at the X points. The effective masses and extremal areas of the pockets are in good agreement with the predictions of band-structure calculations. We conclude that ${\mathrm{EuB}}_{6}$ is an intrinsic semimetal and not a doped insulator. The intrinsic carrier concentration is $1.2\ifmmode\times\else\texttimes\fi{}{10}^{20} {\mathrm{cm}}^{\ensuremath{-}3},$ although our sample is somewhat uncompensated, with a 65% surplus of holes. There is no appreciable modification to the Fermi-surface dimensions or carrier masses with the onset of ferromagnetism.

The Fermi surface dimensions of disordered Cu 3Au as determined by angle resolved photoemission spectroscopy

The bulk Fermi surface of the disordered phase of Cu 3Au has been experimentally mapped using angle resolved constant initial state (CIS) photoemission spectroscopy. The shape of the Fermi surface in the (11 2 ) plane has been determined using only those transitions which could be identified from the Fermi surface to primary cone free electron bands. A Fourier series formula, using a linear combination of coefficients for the Fermi surfaces of Cu and Au has been found to be in good agreement with the experimentally determined Fermi surface of disordered Cu 3Au. Furthermore, the neck radius, determined absolutely in k-space, was found to be smaller than the neck radius of Cu by ∼ 10%; a difference which may be explained by the presence of Au and the sensitivity of the neck region to changes in the crystal potential.

Exact-diagonalization study of the Hubbard model with nearest-neighbor repulsion.

An exact-diagonalization technique on small clusters is used to study the ground states and single-particle excitations of the Hubbard model with on-site (U) and nearest-neighbor (V) Coulombic repulsive interactions. It is shown that the long-range charge-density-wave state realized in a half-filled two-dimensional square lattice for 4V\ensuremath{\gtrsim}U persists up to quarter filling, and that the doped carriers form a small Fermi surface that encloses an area corresponding to the number of doped carriers rather than the total number of electrons involved in the system. The present result offers a well-defined counterexample in the discussion of the Fermi-surface dimensions of strongly correlated electron systems, and may provide a complementary understanding of the large Fermi surface believed to exist in the ordinary Hubbard model.

Electronic structure and magnetism of the semimetals ErAs and ErxSc1-xAs.

We present results of linear muffin-tin-orbital band-structure calculations of ErAs in the local-spin-density approximation. While the exchange splitting and cyclotron masses are in good agreement with experimental data, we find the Fermi surface dimensions of this semimetal to be significantly overestimated. A good fit to recently measured Shubnikov-de Haas oscillations in ${\mathrm{Er}}_{\mathrm{x}}$${\mathrm{Sc}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As is obtained when the ${\mathrm{\ensuremath{\Delta}}}_{2}^{\ensuremath{'}}$ band is shifted upward by a quasiparticle self-energy correction. The effects due to alloying with Sc are taken into account in a virtual-crystal approximation.

The Fermi surface and pseudopotentials of aluminium

The accurately determined energy levels at the W point of the FCC Brillouin zone obtained from low-temperature galvanometric measurements of the Fermi surface of aluminium are used to determine an empirical local pseudopotential and to test the precision of the standard scheme for calculations of band structure. While satisfactory for cohesive and structural properties, the standard scheme appears to reproduce the third-zone Fermi surface dimensions and topology rather poorly. Since there still remains some flexibility in the definition of ab initio pseudopotentials, it is suggested that agreement with the major cohesive and structural properties can be maintained, but that with relatively minor adjustment Fermi surface properties can also be reproduced. This notion is illustrated for the empirical local pseudopotential which is applied to the evaluation of the interatomic pair potential (which is found to be in good agreement with other calculated pair potentials) and also to a redetermination of the conductivity of molten aluminium which reveals rather clearly the limitations of the first-order Born approximation.

Structural dependence of the oscillatory exchange interaction across Cu layers.

A structure-dependent exchange coupling across wedge-shaped Cu layers in fcc (100) Co/Cu/Co and bcc (100) Fe/Cu/Fe epitaxial sandwiches has been determined from analysis of longitudinal magneto-optical Kerr effect hysteresis loops. In the fcc Co/Cu/Co system, the variation of the coupling with Cu thickness can be described as a superposition of two oscillatory terms, with periods of 2.6 and 8.0 monolayers (ML). The bcc Fe/Cu/Fe system shows oscillations with a period of 2 ML. These periodicities are related to the Fermi surface dimensions and topology of fcc and hypothetical bcc bulk Cu.

Electronic structure of Mg, Zn and Cd

Electronic structures for Mg, Zn and Cd have been completed using the linear muffin tin orbital method. The results include plots of band structure, Fermi-surfaces in extended and reduced zone schemes and density-of-states functions. Generally, good agreement with some other ab initio band results as well as with experiment is found for the Fermi surface dimensions except for an absence of needles in Zn. For the d bands, it is found that in Zn they are localised above the conduction-band minimum, while in Cd they lie only partially above the conduction band.

Electronic structure and properties of CoSi2.

The energy-band structure and related electronic properties of cubic ${\mathrm{CoSi}}_{2}$ have been calculated self-consistently with the use of the linear augmented-plane-wave method. The results are qualitatively similar to those determined previously for ${\mathrm{NiSi}}_{2}$, assuming a rigid-band adjustment of the Fermi level. The ${\mathrm{CoSi}}_{2}$ Fermi surface is quite simple, consisting of three nested hole sheets centered at the Brillouin-zone origin. The calculated Fermi-surface dimensions and topology are in excellent agreement with the de Haas--van Alphen data of Newcombe and Lonzarich (preceding paper). The calculated Drude plasma energy and Fermi velocity are combined with the observed resistivity to estimate transport properties such as low-temperature carrier mean free paths (l\ensuremath{\approxeq}340 A\r{}). The kinematics of carrier transmission through Si/${\mathrm{CoSi}}_{2}$ interfaces and its dependence on interface orientation is analyzed in terms of the projected band structure.

Fermi surface changes and electron scattering anisotropy in alkali metal alloys II. The rubidium-cesium system

The de Haas-van Alphen effect has been used to study the changes in Fermi surface (FS) dimensions and the electron scattering in dilute Rb(Cs) and Cs(Rb) alloys. The initial FS cross-section changes indicate that at each end of the system the actual lattice constant changes lie slightly below a linear interpolation between the host lattice constants. The changes in FS anisotropy are relatively large (up to −10−3 / at % in FS radius for Cs(Rb)): a phase-shift fit with a combination ofs andp terms gives a good representation of the changes in Rb(Cs), but that for Cs(Rb) is relatively poor. The electron scattering has less forward-scattering component than in the K-Rb system, the ratio xρ/x0 between the resistivity temperature and the average Dingle temperature being 0.73 in Rb(Cs) and 0.74 in Cs(Rb). The scattering rate anisotropies are large, 20% in Rb(Cs) and 63% in Cs(Rb). In both cases the maximum scattering rate occurs at 〈110〉. Phase-shift fits give a good representation of the scattering anisotropy at both ends of the alloy system: a combination ofs andp terms appears best for Rb(Cs) and ofs andd for Cs(Rb). However, these phase shifts give poor values for xρ/x0, and no agreement with a lattice-distortion prediction for the Friedel sum.

A Pseudopotential Band Structure Calculation of Bismuth, Antimony, and Their Alloys

AbstractA semiempirical pseudopotential band structure calculation with account of spin—orbit‐interaction is performed for Bi, Sb, and Bi1−xSbx alloys considering the alloy potential in the framework of VCA. The parameter of Fermi surfaces are evaluated on the basis of the calculated energies. The resulting Fermi surfaces of the pure elements correspond better to experimental data than those of previous work. The composition dependences as well of gap and overlap as the Fermi surface dimensions agree qualitatively with the measured dependences.

Fermi surface changes and electron scattering anisotropy in the potassium-rubidium alloy system

The de Haas-van Alphen effect has been used to study the changes in Fermi surface (FS) dimensions and the electron scattering in dilute K(Rb) and Rb(K) alloys. Small discrepancies, around 10%, have been found between the observed FS cross-section changes and those calculated from a linear interpolation of the lattice constant between the two host values, the cross-section changing more rapidly than expected in each case: these discrepancies appear to reflect rather accurately a real nonlinearity in the lattice constant change with solute concentration. There are also measurable changes in the FS anisotropy, which are described well by a combination ofs andp phase shifts in K(Rb) and bys andd in Rb(K). The electron scattering has a significant forward-scattering component, the ratiox ρ/x 0 between the resistivity temperature and the average Dingle temperature being 0.63 and 0.59 for K(Rb) and Rb(K), respectively. The scattering rate anisotropy in Rb(K) is about 7%, with the maximum rate at 〈110〉: this can be fitted rather well by a combination ofs andp phase shifts.

Band structure changes through the structural and band inversion transitions in Pb1−xSnxTe

Abstract Changes in Fermi surface dimensions and effective masses have been measured through the structural and band inversion transitions and are found to be in good agreement with band structure calculations.

An angle-resolved photoemission study of Cu96Ge4and Cu89Ge11single crystals

The authors present angle-resolved photoemission spectra from (100) faces of Cu96Ge4 and Cu89Ge11 single crystals using 16.85 eV radiation, together with the corresponding Korringa-Kohn-Rostoker coherent potential (KKR CPA) complex band computations. The results are compared and contrasted with an earlier photoemission study of Cu87Al13 single crystals. Among the features of the alloy spectrum discussed are the characteristic shifts in the Cu d bands and in the s-p-type valence bands, changes in the Fermi surface dimensions and the disorder smearing of states. The computations provide a good understanding of the various observed effects of alloying on the bulk electronic structure of Cu.

The Fermi surface properties of aluminium from a phase shift parametrisation

Accurate de Haas-van Alphen measurements in aluminium have been parametrised using a KKR model with three phase shifts as parameters. Over a wide range of the Fermi energy parameter EF an accurate fit to the data can be obtained. The Fermi surface dimensions deduced from the parametrisation confirm those obtained from the Ashcroft model. Over the same range of EF Green function coefficients have been obtained by performing the necessary Brillouin zone integrals. The coefficients in the partial wave expansion of the wavefunctions are examined in some detail. Orbital averages have been evaluated for orbits along symmetry directions and the anisotropy of the coefficients is found to be essentially independent of the choice of EF. The averages differ from OPW values by typically 20%; much of the discrepancy can be attributed to backscattering effects but there is some evidence that 'non-local', i.e. 'off the Fermi sphere' effects are also important. Comparison of KKR Z and APW pseudopotential form factors derived from the parametrisation shows quite large differences at smaller values of EF.

Fermi-surface radii in gold: Radio frequency size effect

Fermi-surface dimensions for electron orbits in the (110) plane of gold have been measured to a precision of 0.2%. The measured dimensions are found to deviate from the accepted values of Halse by as great as 1.6%.

Pseudoatom version of the rigid-muffin-tin approximation

The electron-phonon coupling parameter ($\ensuremath{\lambda}$) is calculated for the metals K, Al, Cu, and Nb using the rigid-muffin-tin approximation but with the Fermi energy as an adjustable parameter and phase shifts obtained by fitting the Fermi-surface dimensions. A pseudoatom muffin-tin potential is obtained by making a suitable choice of the Fermi-energy parameter. In simple metals the choice is defined in terms of the screening constraint. In transition metals an arbitrary choice (half the "band-structure" value) is suggested. For the simple metals $\ensuremath{\lambda}$ changes by a factor of 3 or more over the range of Fermi energies considered but agrees well with experimental estimates at the pseudoatom value. In niobium the shift leaves the average value of $\ensuremath{\lambda}$ essentially unaltered but changes the anisotropy so as to better match the experimental anisotropy. Provided the same criteria are used for determining the Fermi-energy parameter, very similar results are obtained using a scaling procedure suggested by Butler and based on the atomic-sphere approximation.

Magnetic field induced conduction electron polarization, magnetization density, and neutron magnetic form factor of Pt metal

Results are presented of a detailed relativistic augmented plane wave (RAPW) study of the magnetic field induced conduction electron polarization, magnetization density, and neutron magnetic form factor of Pt metal. We find that the spherical part of the total induced spin density is very localized spatially and almost entirely d-like in character, with the band 6 contribution differing substantially from its counterpart in Pd metal. The spin only estimate of the Weiss-Freeman asymmetry parameter is large (93% t 2g and 7% e g). Our predicted Fermi surface dimensions for both the electron and hole surfaces (and the suitably enhanced effective masses) show excellent agreement with the recent measurements of Dye et al.

Surface impedance of a metal in a magnetic field and cyclotron waves: Numerical calculations

A recently developed formalism (see ibid., vol.7, no.10, p.2109 (1977)) is applied to the calculation of the surface impedance of a metal in a magnetic field for two configurations: (i) a cylindrical Fermi surface and ERF perpendicular to B, and (ii) a spherical Fermi surface and ERF//B. In the former case, especially, the surface impedance anomalies observed above the fundamental Azbel-Kaner resonance are calculated, whereas in the latter case the fundamental Azbel-Kaner resonance is considered. The calculations aim at illustrating the convergence properties of formal expressions presented earlier, and, in case (i), at elucidating the physical nature of the surface impedance anomalies. In this connection a general condition for the occurrence of such anomalies is presented and a possible use for determination of Fermi surface dimensions is suggested.