Fermi Surface Contours Research Articles

Dimensional crossover and symmetry transformation of charge density waves in VSe2

Collective phenomena in solids can be sensitive to the dimensionality of the system; a case of special interest is VSe2, which shows a (r7 x r3) charge density wave (CDW) in the single layer with the three-fold symmetry in the normal phase spontaneously broken, in contrast to the (4 x 4) in-plane CDW in the bulk. Angle-resolved photoemission spectroscopy (ARPES) from VSe2 ranging from a single layer to the bulk reveals the evolution of the electronic structure including the Fermi surface contours and the CDW gap. At a thickness of two layers, the ARPES maps are already nearly bulklike, but the transition temperature TC for the (4 x 4) CDW is much higher than the bulk value of 110 K. These results can be understood as a result of dimensional crossover of phonon instability driven by a competition of nesting vectors. Our study provides key insights into the CDW mechanisms and offers a perspective in the search and control of emergent phases in quantum materials.

Observation of Surface Fermi Arcs in Weyl Semimetal via Scanning Tunneling Microscopy

Weyl semimetals host topologically protected surface states, with arced Fermi surface contours that are predicted to penetrate through the bulk when their momentum matches that of the surface projections of the bulk's Weyl nodes. Here, we describe our experiment in which we used spectroscopic mapping with a scanning tunneling microscope (STM) to visualize quasi-particle interference at the surface of the Weyl semimetal TaAs. Our measurements revealed multitude of scattering wavevectors, which can be reproduced by taking into account the shape and spin texture of the Fermi arc surface states and their momentum-dependent penetration into the bulk. Our result exemplifies an atomic-scale manifestation of surface-bulk connectivity of Weyl semimetal.

Comparative study of rare earth hexaborides using high resolution angle-resolved photoemission

Strong electron correlations in rare earth hexaborides can give rise to a variety of interesting phenomena like ferromagnetism, Kondo hybridization, mixed valence, superconductivity and possibly topological characteristics. The theoretical prediction of topological properties in SmB6 and YbB6 has rekindled the scientific interest in the rare earth hexaborides, and high-resolution ARPES has been playing a major role in the debate. The electronic band structure of the hexaborides contains the key to understand the origin of the different phenomena observed, and much can be learned by comparing the experimental data from different rare earth hexaborides. We have performed high-resolution ARPES on the (001) surfaces of YbB6, CeB6 and SmB6. On the most basic level, the data show that the differences in the valence of the rare earth element are reflected in the experimental electronic band structure primarily as a rigid shift of the energy position of the metal 5d states with respect to the Fermi level. Although the overall shape of the d-derived Fermi surface contours remains the same, we report differences in the dimensionality of these states between the compounds studied. Moreover, the spectroscopic fingerprint of the 4f states also reveals considerable differences that are related to their coherence and the strength of the d–f hybridization. For the SmB6 case, we use ARPES in combination with STM imaging and electron diffraction to reveal time dependent changes in the structural symmetry of the highly debated SmB6(001) surface. All in all, our study highlights the suitability of electron spectroscopies like high-resolution ARPES to provide links between electronic structure and function in complex and correlated materials such as the rare earth hexaborides.

Fermi surface contours obtained from scanning tunneling microscope images around surface point defects

We present a theoretical analysis of the standing wave patterns in scanning tunneling microscope (STM) images, which occur around surface point defects. We consider arbitrary dispersion relations for the surface states and calculate the conductance for a system containing a small-size tunnel contact and a surface impurity. We find rigorous theoretical relations between the interference patterns in the real-space STM images, their Fourier transforms and the Fermi contours of two-dimensional electrons. We propose a new method for reconstructing Fermi contours of surface electron states, directly from the real-space STM images around isolated surface defects.

Combined large spin splitting and one-dimensional confinement in surface alloys

We have found and characterized, by angle-resolved photoelectron spectroscopy (ARPES), quasi-one-dimensional spin-split states in chain-like surface alloys formed by large Z elements (Bi and Pb) at the Cu(110) surface. The ARPES results are supported by first-principles relativistic calculations, which also confirm the spin polarization of these states, characteristic of the Rashba–Bychkov effect. The Fermi surface contours are open, but warped, as a result of the interaction with the bulk Cu conduction band. This interaction introduces a k dependence of the spin splitting perpendicular to the chains direction. We have also investigated the influence of the atomic spin–orbit parameter in substitutional isostructural Bi1−xPbx overlayers, and found that the magnitude of the spin splitting can be continuously tuned as a function of stoichiometry.

Fermi surface of Mo(112) and indirect interaction between adsorbed atoms

A comprehensive examination of the Fermi surface of Mo(112) is presented. The Fermi surface contours for the Mo(112) surface, obtained by density functional theory calculations, agree well with the direct observations via angle-resolved photoemission spectroscopy and indicate the existence of flattened segments in the Fermi contours perpendicular to the direction of the atomic furrows. Both the calculation and the experiment indicate significant surface weight for these states. Such flattened Fermi contours at the surface can give rise to long-range charge density waves (CDW) and long-range indirect lateral interactions, especially in the case of adsorption of electropositive atoms. When mediated by the surface electrons, exhibiting flattened Fermi contours, the oscillatory potential of the indirect interaction between adsorbed atoms decays very slowly (∼1/r) in the direction along the furrows, which can explain the formation of long-period chain structures of electropositive adsorbates on the furrowed surface of Mo(112).

Nonadiabatic effects on surfaces: Kohn anomaly, electronic damping of adsorbatevibrations, and local heating of single molecules

Three aspects of electron–phonon coupling at metal surfaces are reviewed. One aspect isthe Kohn effect, which describes an anomalous dispersion relation of surface phonons dueto quasi-one-dimensional nesting of Fermi surface contours. The combination of electronenergy loss spectroscopy and angle-resolved photoelectron spectroscopy allows us tounambiguously characterize Kohn anomaly systems. A second aspect is the nonadiabaticdamping of adsorbate vibrations. Characteristic spectroscopic line shapes of vibrationalmodes allow us to estimate the amount of energy transfer between the vibrationalmode and electron–hole pairs. Case studies of a Kohn anomaly and nonadiabaticdamping are provided by the hydrogen- and deuterium-covered Mo(110) surface. As athird aspect of interaction between electrons and phonons, local heating of aC60 molecule adsorbed on Cu(100) and in contact with the tip of a scanning tunnellingmicroscope is covered.

Fermi surface nesting and the origin of charge density waves in metals

The concept of a charge density wave (CDW), which is induced by Fermi-surface nesting, originated from the Peierls idea of electronic instabilities in purely one-dimensional metals and is now often applied to charge ordering in real low-dimensional materials. The idea is that if Fermi surface contours coincide when shifted along the observed CDW wave vector, then the CDW is considered to be nesting derived. We show that, in most cases, this procedure has no predictive power, since Fermi surfaces either do not nest at the right wave vector or nest more strongly at the wrong vector. We argue that only a tiny fraction, if any, of the observed charge ordering phase transitions are true analogs of the Peierls instability because electronic instabilities are easily destroyed by even small deviations from perfect nesting conditions. By using prototypical CDW materials ${\text{NbSe}}_{2}$, ${\text{TaSe}}_{2}$, and ${\text{CeTe}}_{3}$, we show that such conditions are hardly ever fulfilled and that the CDW phases are actually structural phase transitions driven by the concerted action of electronic and ionic subsystems, i.e., a $\mathbf{q}$-dependent electron-phonon coupling plays an indispensable part. We also mathematically show that the original Peierls construction is so fragile that it is unlikely to apply to real materials. We argue that no meaningful distinction between a CDW and an incommensurate lattice transition exists.

Final state effects in photoemission studies of Fermi surfaces

Photoelectron spectroscopy is one of the most important methods for extractinginformation about the Fermi surface (FS) of materials. An electron photoexcited from theFS is emitted from the crystal conserving the parallel momentum, , while the perpendicular momentum is reduced due to the surface potential barrier. A simple interpretation of the process assumes thefinal state is free-electron-like allowing one to ‘map’ the detected photoelectron back to its initialk momentum. There are multiple final state effects that can complicate the interpretation ofphotoelectron data and these effects are reviewed here. These can involve both energy andk broadening, which can give rise to shadow or ghost FS contours, scattering and final statediffraction effects that modify intensities, and matrix element effects which reflect thesymmetries of the states involved and can be highly dependent on photon polarization. Thesematrix elements result in contours of photoelectron intensity that follow the dispersion ink-space of the initial state, the FS, and the final state. Locations where intensities go tozero due to matrix element and symmetry effects can result in gaps where FScontours ‘disappear’. Recognition that these effects can play a significant role indetermining the measured angular distributions is crucial in developing an informedmodel of where the FS contours actually lie in relation to measured intensitycontours.

Two-domains bulklike Fermi surface of Ag films deposited ontoSi(111)−(7×7)

Thick metallic silver films have been deposited onto $\mathrm{Si}(111)\ensuremath{-}(7\ifmmode\times\else\texttimes\fi{}7)$ substrates at room temperature. Their electronic properties have been studied by using angle-resolved photoelectron spectroscopy (ARPES). In addition to the electronic band dispersion along the high-symmetry directions, the Fermi surface topology of the grown films has been investigated. Using ARPES, the spectral weight distribution at the Fermi level throughout large portions of the reciprocal space has been determined at particular perpendicular electron-momentum values. Systematically, the contours of the Fermi surface of these films reflected a sixfold symmetry instead of the threefold symmetry of the Ag single crystal. This symmetry loss has been attributed to the fact that these films appear to be composed by two sets of domains rotated $60\ifmmode^\circ\else\textdegree\fi{}$ from each other. Extra photoemission features at the Fermi level were also detected, which have been attributed to the presence of surface states and $\mathrm{sp}$-quantum states. The dimensionality of the Fermi surface of these films has been analyzed, studying the dependence of the Fermi surface contours with the incident photon energy. The behavior of these contours measured at particular points along the Ag $\ensuremath{\Gamma}L$ high-symmetry direction puts forward the three-dimensional character of the electronic structure of the investigated films.

Comparative study of the electronic structure of XRu2Si2: probing the Anderson lattice

The k-resolved single particle excitations, as determined by angle-resolved photoemission spectroscopy (ARPES), are compared and contrasted for, LaRu2Si2, CeRu2Si2, ThRu2Si2, and URu2Si2, isostructural layered compounds with differing nominal f-occupations of f0, f1, f0, and f2, respectively. ARPES measurements include 4d and 5d-edge resonant photoemission to distinguish f-character and Fermi-energy intensity mapping of Fermi surface contours. Comparison to RLAPW band structure calculations shows very good agreement of the d-band structure away from EF. Discrepancies in the near EF region highlight k-dependent effects of f-correlation and f-d hybridization. Approximately equal dimensions of Fermi contours for X=(La, Ce) suggest the exclusion of 4f electrons from the CeRu2Si2 Fermi surface at temperatures far above the Kondo temperature. High-resolution spectra for X=(Ce, U) allow comparison of f-d mixing to predictions of the Anderson lattice model. Published by Elsevier Science B.V.

Angle-resolved photoemission study of clean and hydrogen-saturated Mo(110)

We present the development of Fermi-level crossings from the clean to the hydrogen-saturated (110) surface of molybdenum at room temperature. The well-known adsorbate-induced phonon anomaly is discussed in terms of a quasi-one-dimensional Fermi-surface nesting and giant Kohn anomaly. Our experiment resolved an existing discrepancy between earlier photoemission data and Fermi-surface contours calculated within density-functional theory. Moreover, it is found that the Fermi-surface nesting is fully established at hydrogen coverages where the phonon anomaly just barely forms.

New aspects of the QC-phase in layered 1T-TaS2

Abstract We present Fermi surface (FS) mapping measurements obtained by photoemission for the quasi-commensurate charge density wave (CDW) phase of layered 1T-TaS2. The topology of the FS is rather dominated by the undistorted (1×1) symmetry than by the CDW-induced ( 13 × 13 ) phase. CDW effects can be seen in terms of nesting properties of the FS. Compared to one-electron band structure calculations we observe changed FS contours of Ta 5d-derived electron pockets around the M,M′ points of the (1×1) Brillouin zone. Low energy electron diffraction measurements support the view of a quasi-commensurate CDW.

High-resolution photoemission study of hcp-Co(0001)

Using a monochromatized high-flux He discharge lamp, we have investigated the electronic bands of hexagonal-closed packed (hcp) Co(0001) near the Fermi energy at room temperature. Particularly, sections through the Fermi surface have been measured by high-resolution photoemission using photon energies of 21.2 eV and 40.8 eV. Compared to analogous measurements from copper and nickel surfaces, the features here are less sharp, even though LEED patterns indicate a similar degree of surface order. Still, an interpretation of these data in terms of calculated Fermi surface contours is possible. The Fermi wave vectors of the minority d-hole pocket centered at the Γ-point, are well reproduced. This is furthermore corroborated by polar-angle dependent dispersion measurements along two high-symmetry azimuths.

Evidence for a driving mechanism of the W(001) reconstruction

We report the first experimental observation of a gap-opening and changes of the Fermi surface contours upon reconstruction of the W(001) surface. A gap Δ ≥ 0.6 eV is found to form at X̄', a new surface Brillouin zone boundary along the \\ ̄ bE azimuth of the reconstructed ( 2 × 2 ) R45° structure. The large gap and the Fermi surface contours of which the curvatures remain essentially unaltered through reconstruction suggest that the reconstruction is driven primarily by a strong-coupling charge density wave mechanism.

Bulk Fermi surface determination by tuning the photoelectron kinetic energy

The three‐dimensional Fermi surface of a Cu single crystal has been measured by angle‐resolved photoemission (ARUPS). Well‐defined two‐dimensional (2D) cuts through the bulk fcc Cu Brillouin zone have been mapped by adjusting the incident photon energy of a tunable light source. This method, conceived of as an extension of the traditional ARUPS, allows the direct visualization of Fermi surface contours from experimental two‐dimensional patterns. The surface shape of constant energy at the Fermi level and its link with the translational bulk symmetries could be clearly seen by the determination of the Fermi photoelectron momentum distribution along several Brillouin zones. In addition, the 2D sections of the Fermi surface measured by photoemission have been well reproduced by a semiempirical tight binding calculation.