The Fermi surfaces of the alkali metals

Long before direct experimental studies of the Fermi surfaces of the alkali metals became technically feasible, evidence had accumulated to suggest that their low-lying energy bands are almost free-electron-like. Indeed, the importance of the free-electron model in the development of the theory of metals owes much t o the coincidence that sodium, now known to be the most free-electron-like of all the alkali metals, was the subject of the pioneering cohesive energy calculations of Wigner and Seitz.¹     

Fermi surfaces of single layer dielectrics on transition metals

Single sheets of hexagonal boron nitride on transition metals provide a model system for single layer dielectrics. The progress in the understanding of h-BN layers on transition metals of the last 10 years is shortly reviewed. Particular emphasis lies on the boron nitride nanomesh on Rh(1 1 1), which is a corrugated single sheet of h-BN, where the corrugation imposes strong lateral electric fields. Fermi surface maps of h-BN/Rh(1 1 1) and Rh(1 1 1) are compared. A h-BN layer on Rh(1 1 1) introduces no new bands at the Fermi energy, which is expected for an insulator. The lateral electric fields of h-BN nanomesh violate the conservation law for parallel momentum in photoemission and smear out the momentum distribution curves on the Fermi surface.     

Fermi surface of the noble metals

We report calculations of extremal areas of four Fermi surface (FS) orbits of the noble metals using the linear muffin tin orbital method in the atomic sphere approximation. Our calculations indicate that thel = 3 potential parameters and increase in the number of k-points in the Brillouin zone (BZ) summation from 240 to 916 have no significant effect on the FS. All calculations were performed self-consistently including up tol = 2 potential parameters and with 240 k points in the BZ summation. Calculations were performed with the exchange, correlation potentials (XCP) of Barth-Hedin, Barth-Hedin modified by Janak, SlaterX _α, and the Vosko-Wilk-Nussair. Results compared with other theoretical calculations indicate that none of the above XC potentials give an accurate representation of the FS for all the noble metals. We feel that the inclusion of the non-locality of XCP may give a better account of the FS geometry.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

Stability of Fermi surfaces and K theory

Nonrelativistic Fermi liquids in d+1 dimensions exhibit generalized Fermi surfaces: (d-p)-dimensional submanifolds in the (k,omega)-space supporting gapless excitations. We show that the universality classes of stable Fermi surfaces are classified by K theory, with the pattern of stability determined by Bott periodicity. The Atiyah-Bott-Shapiro construction implies that the low-energy modes near a Fermi surface exhibit relativistic invariance in the transverse p+1 dimensions. This suggests an intriguing parallel between nonrelativistic Fermi liquids and D-branes of string theory.     

Strength of metals at the Fermi length scale

Using silver and gold, we have measured the size‐dependence of the yield strength of atomic‐sized samples as small as a single‐atom bridge, with pico‐level resolution in the applied force and displacement. The strength approaches theoretical values as the diameter of the sample becomes comparable to the Fermi wavelength of electrons (～0.5 nm); in the limit of a single‐atom bridge, the strength is over four orders of magnitude higher than in bulk single crystals. Results provide direct evidence for Pauling's prediction of bond stiffening with reduced atomic coordination. Beginning with a single‐atom bridge, strength evolves in a staircase manner in Ag, instead of the intuitively assumed continuous approach to a saturating bulk value.

     

Oscillation phenomena and experimental determination of exact mathematical stability zones for magneto-conductivity in metals having complicated Fermi surfaces

We consider the problem of exact experimental determination of the boundaries of Stability Zones for magneto-conductivity in normal metals in the space of directions of magnetic field B. As can be shown, this problem turns out to be nontrivial since the exact boundaries of Stability Zones are in fact unobservable in direct measurements of conductivity. However, this problem can be effectively solved with the aid of the study of oscillation phenomena (cyclotron resonance, quantum oscillations) in normal metals, which reveal a singular behavior on the mathematical boundary of a Stability Zone.     

The Tolman parameter,self-absorption,and surface tension on flat and curved surfaces of liquid metals

Analytical expressions for Tolman parameter jg, self-absorption on a tension surface db, and surface tension σ on flat and curved surfaces were found using the thermodynamic Gibbs method. The jg, db, and σ values were determined for 50 liquid metals at the melting temperature. It was established that surface tension decreases with a decrease in the radius of an equimolecular dividing surface.     

The parametrization of the Fermi surfaces of the metallic elements

In the literature there is now much data available on the shapes of the Fermi surfaces of most of the metallic elements. It seems likely that the next few years will see the reduction of this data to parametric form; a start has already been made and the results published for a small number of metals. Parametrization schemes involving expansions in terms of appropriately symmetrized linear combinations of spherical harmonics or of plane waves are described. Tables of these symmetrized functions are already available in the literature. A plea is made for the standardization of procedure and of notation in future work on parametrizations of the Fermi surfaces of individual metals.     

Bonds and Fermi surfaces studied by photoelectron spectroscopy

Photoelectron spectroscopy with synchrotron radiation employing high energy and angular resolutions is a very efficient tool for experimental investigations of the electronic structure of solids and their surfaces. In addition to standard band-mapping applications, photoemission intensity and line-shape analyses provide valuable information about wave functions, bonds and interactions of a many-electron system. In this report we choose covalent semiconductor surfaces as well as metallic clean and nanostructured surfaces of layered materials to serve as model systems for assessing the spatial origin of photoelectrons and the three-dimensional shape of Fermi surfaces. Received: 11 July 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Models of bands and Fermi surfaces for electron-doped cuprates

The properties of Fermi surfaces and electron bands in electron-doped cuprates have been studied. The possible origins of a hole pocket in the nodal direction and a pseudogap at hot spots are discussed, including stripe phases and double bands in an antiferromagnetically correlated Fermi liquid. Within the framework of the mean field method, it is shown that both t-t′-t″-U Hubbard model solutions with a homogeneous antifer-romagnetic spin structure and those with a diagonal stripe structure can reproduce the fragmentar character of the Fermi surface. The appearance of hole pockets in various structures is related either to states in the lower Hubbard band or to states localized on domain walls. The behavior of a gap at the leading edge of the energy distribution of photoelectrons and its dependence on oxygen removal in the course of annealing are considered.     

Thermodynamics of an interacting Fermi system in the static fluctuation approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit were obtained. All expressions are given in the units of r _s , where r _s determines the ratio of a mean distance between electrons to the Bohr radius a ₀. In these expressions, we calculate terms of the respective order r _s and r _s ². It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r _s .     

Fragmentation of bands and Fermi surfaces in cuprate stripe phases

The band structure and evolution of the Fermi surfaces of stripe phases were studied using the t-t′-U Hubbard model in the mean field approximation. The appearance of quasi-one-dimensional “impurity” subbands caused by the localization of particles on domain walls inside the Hubbard gap is confirmed. Among vertical stripe phases parallel to y bonds, the Y₈ and Y₄ structures with distances l = 8a and 4a between domain walls were found to be stable. Fermi surface segments in antinodal or nodal directions were shown to correspond to an “ impurity” band or the main band related to the entire antiferromagnetic domain region. This is a probable explanation of the difference in the properties of ARPES spectra at different Fermi surface regions observed for La_2?xSr_xCuO₄. It was shown for the Y₈ structure that the topology of the Fermi surface changed and an isotropic pseudogap opened at the point corresponding to a p = 1/8 doping level. Attempts at relating this property to the anomalous suppression of T _c in LSCO at p = 1/8 encountered difficulties. The low dispersion of the impurity band and the wide gap separating it from the lower Hubbard band in diagonal stripe phases formed at p < 0.05 create prerequisites for the existence of the insulating state at nonzero doping.     

Recoil effect of photoelectrons in the Fermi edge of simple metals

High energy resolution photoelectron spectroscopy of conduction electrons in the vicinity of the Fermi edge in Al and Au at excitation energies of 880 and 7940 eV was carried out using synchrotron radiation. For the excitation energy of 7940 eV, the observed Fermi energy of Al shows a remarkable shift to higher binding energy as compared with that of Au, with accompanying broadening. This is due to the recoil effect of the emitted photoelectrons. The observed spectra are well reproduced by a simple model of Bloch electrons based on the isotropic Debye model.     

Destruction of the small Fermi surfaces in NaxCoO2 by disorder

We show using density functional calculations that the small e'g Fermi surfaces in NaxCoO2 are destroyed by Na disorder. This provides a means to resolve the prediction of these sections in band structure calculations with their nonobservation in angle resolved photoemission experiments.