Anisotropic Band Dispersion Research Articles

Charge ordering in stoichiometric FeTe: Scanning tunneling microscopy and spectroscopy

We use scanning tunneling microscopy and spectroscopy to reveal a unique stripy charge order in a parent phase of iron-based superconductors in stoichiometric FeTe epitaxy films. The charge order has unusually the same---usually half---period as the spin order. We also found highly anisotropic electron band dispersions being large and little along the ferromagnetic (crystallographic $b$) and antiferromagnetic ($a$) directions, respectively. Our data suggest that the microscopic mechanism is likely of the Stoner type driven by interatomic Coulomb repulsion ${V}_{ij}$, and that ${V}_{ij}$ and charge fluctuations, so far much neglected, are important to the understanding of iron-based superconductors.

Probing 2D black phosphorus by quantum capacitance measurements

Two-dimensional materials and their heterostructures have emerged as a new class of materials, not only for fundamental physics but also for electronic and optoelectronic applications. Black phosphorus (BP) is a relatively new addition to this class of materials. Its strong in-plane anisotropy makes BP a unique material for making conceptually new types of electronic devices. However, the global density of states (DOS) of BP in device geometry has not been measured experimentally. Here, we report the quantum capacitance measurements together with the conductance measurements on an hBN-protected few-layer BP (∼six layers) in a dual-gated field effect transistor (FET) geometry. The measured DOS from our quantum capacitance is compared with density functional theory (DFT). Our results reveal that the transport gap for quantum capacitance is smaller than that in conductance measurements due to the presence of localized states near the band edge. The presence of localized states is confirmed by the variable range hopping seen in our temperature dependence conductivity. A large asymmetry is observed between the electron and hole side. This asymmetric nature is attributed to the anisotropic band dispersion of BP. Our measurements establish the uniqueness of quantum capacitance in probing the localized states near the band edge, hitherto not seen in conductance measurements.

Enhanced optical conductance in graphene superlattice due to anisotropic band dispersion

The optical response of a Kronig–Penney type graphene superlattice is investigated. When an external field is applied along the periodicity of the superlattice, the total optical response of the graphene superlattice is enhanced due to the formation of anisotropic Dirac fermions. Such anisotropy tunes up the total optical spectra while maintaining the same critical electric field regardless of the degree of anisotropy. The optical conductance of anisotropic Dirac fermions exhibits two contrasting behaviours: (i) inversely proportional to the anisotropy and (ii) directly proportional to the anisotropy, depending on the direction of the external field. Interestingly, the anisotropy-induced optical conductance enhancement also occurs in gapped graphene with band structure anisotropy. This suggests that the enhanced electron–photon couplings in the presence of anisotropy is a general feature of the relativistic nature of the Dirac fermions in both massless and massive form. It is also revealed that the strong optical nonlinearity is a consequence of the relativistic nature of the Dirac fermions and the Dirac cone isotropy is not required.

Anisotropic low-energy plasmon excitations in doped graphene: An ab initio study

Low-energy electronic excitations in free-standing graphene (gr) and gr(2×2)/K interface have been studied based on ab initio band structure and linear-response theory. For pristine graphene, the calculated linear dispersion of collective interband transitions around the Dirac cone is in good agreement with experiments. At the gr/K interface, in addition to the doping-enhanced linear mode, a nonlinear plasmon develops with increasing momentum transfers along the Γ K direction. Using a model-doped free-standing graphene, we revealed that the nonlinear mode originates from the anisotropic band dispersion at the Fermi level, and its collectivity emerges as the carrier density increases. These findings have implications for measurements of electronic excitations in metal-supported graphene sheet.

Momentum dependence of the single-particle self-energy and fluctuation spectrum of slightly underdopedBi2Sr2CaCu2O8+δfrom high-resolution laser angle-resolved photoemission

We deduce the normal-state angle-resolved single-particle self-energy $\ensuremath{\Sigma}(\ensuremath{\theta},\ensuremath{\omega})$ and the Eliashberg function (i.e., the product of the fluctuation spectrum and its coupling to fermions) ${\ensuremath{\alpha}}^{2}F(\ensuremath{\theta},\ensuremath{\omega})$ for the high-temperature superconductor ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ from the ultrahigh-resolution laser angle-resolved photoemission spectroscopy (ARPES). The self-energy $\ensuremath{\Sigma}(\ensuremath{\theta},\ensuremath{\omega})$ at energy $\ensuremath{\omega}$ along several cuts normal to the Fermi surface at the tilt angles $\ensuremath{\theta}$ with respect to the nodal direction in a slightly underdoped ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ were extracted by fitting the ARPES momentum distribution curves. Then, using the extracted self-energy as the experimental input, the ${\ensuremath{\alpha}}^{2}F(\ensuremath{\theta},\ensuremath{\omega})$ is deduced by inverting the Eliashberg equation employing the adaptive maximum entropy method. Our principal result is that the Eliashberg functions ${\ensuremath{\alpha}}^{2}F(\ensuremath{\theta},\ensuremath{\omega})$ collapse for all $\ensuremath{\theta}$ onto a single function of $\ensuremath{\omega}$ up to the upper cut-off energy despite the $\ensuremath{\theta}$ dependence of the self-energy. The in-plane momentum anisotropy is therefore predominantly due to the anisotropic band-dispersion effects. The obtained Eliashberg function has a small peak at $\ensuremath{\omega}\ensuremath{\approx}0.05\text{ }\text{eV}$ and flattens out above 0.1 eV up to the angle-dependent cutoff. It takes the intrinsic cutoff of about 0.4 eV or the energy of the bottom of the band with respect to the Fermi energy in the direction $\ensuremath{\theta}$, whichever is lower. The angle independence of the ${\ensuremath{\alpha}}^{2}F(\ensuremath{\theta},\ensuremath{\omega})$ is consistent only with the fluctuation spectra which have the short correlation length on the scale of the lattice constant. This implies among others that the antiferromagnetic fluctuations may not be the underlying physics of the deduced fluctuation spectrum.

Spontaneous exciton condensation in1T-TiSe2: BCS-like approach

Recently we found strong evidence in favor of a BCS-like condensation of excitons in $1T{\text{-TiSe}}_{2}$ [Cercellier et al., Phys. Rev. Lett. 99, 146403 (2007)]. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the exciton condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. The scope of this paper is to present the detailed calculations in the framework of this model. They represent an extension of the original excitonic insulator phase model of J\'erome et al. [Phys. Rev. 158, 462 (1967)] to three dimensional and anisotropic band dispersions. A detailed analysis of its properties and comparison with experiment is presented. Finally, the disagreement with density-functional theory is discussed.

Anisotropy in conductance of a quasi-one-dimensional metallic surface state measured by a square micro-four-point probe method.

We have devised a "square micro-four-point probe method" using an independently driven ultrahigh-vacuum four-tip scanning tunneling microscope, and succeeded for the first time to directly measure anisotropic electrical conductance of a single-atomic layer on a solid surface. A quasi-one-dimensional metal of a single-domain Si(111)4 x 1-In had a surface-state conductance along the metallic atom chains (sigma(axially)) to be 7.2(+/-0.6) x 10(-4) S/square at room temperature, which was larger than that in the perpendicular direction (sigma(radially)) by approximately 60 times. The sigma(axially) was consistently interpreted by a Boltzmann equation with the anisotropic surface-state band dispersion, while the sigma(radially) was dominated by a surface-space-charge-layer conductance.

Structural and electronic properties of the quasi-one-dimensional metallic chains of the Au-induced facets on the Si(5 5 12) surface

We have investigated the atomic arrangements and electronic properties of the quasi-one-dimensional (Q1D) atomic chains of the Au-induced facets formed on the clean Si(5 5 12)-$2\ifmmode\times\else\texttimes\fi{}1$ surface. The interchain distances of the two well ordered facet structures are estimated to be 30.2 and $22.8\mathrm{\AA{}}.$ By utilizing linearly polarized synchrotron photons, we also determine a complete band diagram of the surface bands and their symmetry characteristics along the two high symmetry azimuths $(\overline{\ensuremath{\Gamma}}\ensuremath{-}\overline{M}$ and $\overline{\ensuremath{\Gamma}}\ensuremath{-}\overline{X})$ of the surface Brillouin zone. The Q1D nature of the Au-induced atomic chains has been well demonstrated by the extremely anisotropic band dispersions of the Au-induced surface bands in addition to the $2\ifmmode\times\else\texttimes\fi{}1$ surface morphology. We find that while the clean reconstructed $\mathrm{Si}(5512)\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}1$ surface is insulating, the Au-induced chains form a highly anisotropic metallic system.

Angle-resolved photoemission study of the high-performance low-temperature thermoelectric materialCsBi4Te6

We report a study of the valence-band electronic structure of the newly discovered thermoelectric material, ${\mathrm{CsBi}}_{4}{\mathrm{Te}}_{6},$ using angle-resolved photoelectron spectroscopy. This material exhibits quasi-one-dimensional behavior, which is related to its unique crystal structure. The highly anisotropic band dispersions might explain the large value of the figure of merit, $ZT,$ observed in the hole-doped systems. Our experimental results are compared with a recent theoretical band-structure calculation.

Strongly Anisotropic Band Dispersion of an Image State Located above Metallic Nanowires

Indium can be grown on Si(111) in a $4\ifmmode\times\else\texttimes\fi{}1$ pattern that contains rows of In atoms spaced 13.3 \AA{} apart that have quasi-one-dimensional electronic structure. This ordered array of metallic wires produces an image-induced surface state series. We have measured the dispersion of the most tightly bound $(n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1)$ image state band and found it to be unconventional because it falls below the free electron parabola perpendicular to the In atom rows. The most straightforward explanation for this is that the electrons feel the surface corrugation potential produced by the rows of In atoms. We were able to infer the form of the potential from our measurements.

Ab initio pseudopotential calculation for (TMTSF)2ClO4

We have investigated the electronic structure of the quasi-one-dimensional organic conductor (TMTSF)2ClO4 by ab initio band calculation for the first time. Very anisotropic band dispersions and sheet-like Fermi surfaces are obtained. The present results are compared with previous tight-binding calculations. The overall agreement is good but some quantitative differences are observed. This work provides more accurate wave functions, which will be useful for estimating various physical properties and comparing with experimental results.