Fermi Edge Research Articles

Tunneling into a nonequilibrium Luttinger liquid with impurity

We evaluate tunneling rates into/from a voltage biased quantum wire containing weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\hbar \omega \leq U$. The tunneling rates are split into two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge $E_F-U$ is negative if Coulomb interaction is not too strong.

Bosonization of one-dimensional fermions out of equilibrium

Bosonization technique for one-dimensional fermions out of equilibrium is developed in the framework of the Keldysh action formalism. We first demonstrate how this approach is implemented for free fermions and for the problem of non-equilibrium Fermi edge singularity. We then employ the technique to study an interacting quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green functions, which can be measured via tunneling spectroscopy technique and carry the information about energy distribution, zero-bias anomaly, and dephasing, are expressed in terms of functional determinants of single-particle "counting" operators. The corresponding time-dependent scattering phase is found to be intrinsically related to "fractionalization" of electron-hole excitations in the tunneling process and at boundaries with leads. Results are generalized to the case of spinful particles as well to Green functions at different spatial points (relevant to the problem of dephasing in Luttinger liquid interferometers). For double-step distributions, the dephasing rates are oscillatory functions of the interaction strength.

Quartet Structures of Particles and Quasiparticles in the BCS Model

We study the possibility of multiple paring for more than two particles or two quasiparticles in terms of the BCS model. We consider the multiple pairs of particles in terms of the BCS Hamiltonian for two different ground states: in a quiescent Fermi sea model and in the BCS ground state. In case of quasiparticles, we consider the multiple quasiparticle pairs in terms of the BCS ground state only. Although there is no interaction between Cooper’s type pairs in terms of the BCS Hamiltonian, yet we have shown that four particles or two/four quasiparticles can be paired and form a bound state in the singlet state with just twice the bound state energy of a single Cooper’s pair. In the case of a pair of quasiparticles, the bound state exists as a result of the large quasiparticle density of states and the residual interaction between two quasiparticles which is described by the off-diagonal terms in the BCS Hamiltonian written in terms of quasiparticles. In the case of four particles, the bound state exists only as a result of the Pauli principle and the sharp Fermi edge. In the BCS model, a quartet of bound fermions indeed represents a boson, and the many-particle system of the composite of bosons can undergo the conventional Bose condensation of a boson gas. The temperature of the Bose condensation corresponds to the conventional temperature of Bose condensation for non-interacting bosons where each boson has quadruple mass (4m) and the boson density is one-quarter (n/4) of fermions density. A similar conclusion remains valid in the case of the particle–hole resonance in a quiescent Fermi sea. We have shown that in the particle–hole channel there exists the multiple particle–hole resonance for four particles and four holes in a quiescent Fermi sea model similar to the case of two particles and two holes resonance. We have shown that there is no particle–hole resonance in the case of the BCS ground state because there is no hole-type of excitations in the BCS ground state. Nevertheless we have shown that in the BCS ground state quasiparticle pairs can form bound pairs similar to the Cooper’s pair of particles due to the off-diagonal terms in the BCS Hamiltonian. The bound pairs of quasiparticles exist as a result of extremely large quasiparticle density of states. We also discuss the formation of a quartet of quasiparticles and the Bose condensation of the multiple pairs of quasiparticles.

Development of Hard X-ray Photoelectron Spectroscopy for Laboratory Use

A hard X-ray photoelectron spectroscopy (HXPS) instrument has been developed for laboratory use by combining a monochromatic Cr Kα focused X-ray source, a wide acceptance angle objective lens and a high energy electron analyzer. The Cr Kα X-rays excited by a micro focused electron beam at 20 kV beam voltage are diffracted by an ellipsoidal bent crystal monochromator and focused on the sample. A wide acceptance angle objective lens was integrated as the first section of an input lens of a hemispherical analyzer. A 9.9 μm diameter minimum X-ray spot size was achieved and the energy resolution of 0.56 eV was obtained by Au Fermi edge measurements. The maximum acceptance angle and angular resolution were 70o and 0.54o, respectively. The typical acquisition time is about 30 min for a wide energy survey spectrum and about 1 h for Si 1s angle resolved spectra obtained without tilting the sample. The application of this instrument for the analyses of overlayers and multilayer thin films is also discussed.

Vacuum space charge effect in laser-based solid-state photoemission spectroscopy

We report a systematic measurement of the space charge effect observed in the few-picosecond laser pulse regime in laser-based solid-state photoemission spectroscopy experiments. The broadening and the shift of a gold Fermi edge as a function of spot size, laser power, and emission angle are characterized for pulse lengths of 6 ps and 6 eV photon energy. The results are used as a benchmark for an N-body numerical simulation and are compared to different regimes used in photoemission spectroscopy. These results provide an important reference for the design of time- and angle-resolved photoemission spectroscopy setups and next-generation light sources.

Threshold photoemission magnetic circular dichroism at the spin-reorientation transition of ultrathin epitaxial Pt/Co/Pt(111)/W(110) films

X-ray magnetic circular dichroism (MCD) is nowadays widely used for the investigation of magnetic properties of surfaces and thin films. Recently, similarly large effects have been observed for UV-VIS MCD effects both in single [1] and two-photon photoemission [2-3]. This threshold MCD effect is directly related to spin-orbit effects present at the Fermi edge. We report on the observation of threshold photoemission magnetic circular dichroism (TPMCD) in one-photon and two-photon photoemission (1PPE and 2PPE) at a Pt-capped ultrathin Co wedge grown on Pt(111)/W(110) using femtosecond laser light. TPMCD measurements result in asymmetries continuously increasing with the sample thickness. This indicates that the TPMCD asymmetry is dominantly influenced by the Co bulk properties. At 5 monolayers (ML) asymmetry values of 0.07 % for 1PPE and 0.11 % for 2PPE are derived. The spin reorientation transition is detected at a Co thickness of 5.5 ML. For the magnetically saturated sample the TPMCD does not depend on the orientation of the easy axis. Kerr ellipticities and rotations are measured and compared with the TPMCD data in the framework of optical transfer matrix calculations. The observed TPMCD asymmetry considerably deviates from the behaviour of the complex Kerr angle. Moreover, the TPMCD measurements are referred to Co bulk bandstructure calculations and the influence of a capping layer on the TPMCD asymmetry is discussed

Enhanced Pauli blocking of light scattering in a trapped Fermi gas

Pauli blocking of spontaneous emission by a single excited-state atom has been predicted to be dramatic at low temperature when the Fermi energy EF exceeds the recoil energy ER. The photon scattering rate of a ground-state Fermi gas can also be suppressed by occupation of the final states accessible to a recoiling atom; however, suppression is diminished by scattering events near the Fermi edge. We analyse two new approaches to improve the visibility of Pauli blocking in a trapped Fermi gas. Focusing the incident light to excite preferentially the high-density region of the cloud can increase the blocking signature by 14%, and is most effective at intermediate temperature. Spontaneous Raman scattering between imbalanced internal states can be strongly suppressed at low temperature, and is completely blocked for a final state EF > 4ER in the high imbalance limit.

Surface electronic structure of ferromagnetic Fe(001)

A thorough investigation of the surface electronic structure of ferromagnetic Fe(100) films, epitaxially grown on single-crystal W(100), has been conducted using spin- and angle-resolved photoemission combined with state-of-the-art density-functional theory slab computations. The dispersion of the surface emission close to the Fermi level has been assessed quantitatively. The experimental results are in a good agreement with the calculations and, in particular, the presence of a minority surface state with d{sub xz+yz} character along the {Gamma}{bar X} high-symmetry direction is unambiguously established. Additionally, the calculations predict the existence of a different unoccupied surface state localized at {Gamma}. The existence of the related minority interface resonance near the Fermi edge and outside of the surface-Brillouin-zone center {Gamma} is believed to control the tunneling magnetoresistance in Fe/MgO/Fe(001) for very thin MgO spacers thus our results serve as indirect confirmation to these predictions.

X-ray diffraction and photoelectron spectroscopy study of swift heavy ion irradiated Mn/p-Si structure

The electronic structure and interfacial chemistry of thin manganese films on p-Si (1 0 0) have been studied by photoelectron spectroscopy measurements using synchrotron radiation of 134 eV and from X-ray diffraction data. The Mn/p-Si structures have been irradiated from swift heavy ions (∼100 MeV) of Fe 7+ with a fluence of 1 × 10 14 ions/cm 2. Evolution of valence band spectrum with a sharp Fermi edge has been obtained. The observed Mn 3d peak has been related to the bonding of Mn 3d–Si 3sp states. Mn 3p (46.4 eV), Mn 3s (81.4 eV) and Si 2p (99.5 eV) core levels have also been observed which show a binding energy shift towards lower side as compared to their corresponding elemental values. From the photoelectron spectroscopic and X-ray diffraction results, Mn 5Si 3 metallic phase of manganese silicide has been found. The silicide phase has been found to grow on the irradiation.

Angle-dependent ultraviolet photoelectron spectroscopy of sputter cleaned polycrystalline noble metals

Polycrystalline noble metal films are commonly used in practical applications across a variety of different fields. However, the surface electronic structure of the noble metals has primarily only been studied on single crystal substrates. In addition, sputter cleaned polycrystalline noble metal films are commonly used substrates in ultraviolet photoelectron spectroscopy (UPS) studies, but have yet to be systematically studied in terms of their photoemission anisotropy. The angle-dependence of the valence band spectra of sputter cleaned polycrystalline Au, Ag and Cu were studied using angle-resolved UPS. It is found that the photoemission is anisotropic with respect to photoelectron take-off angle. The results for Ag and Cu are in good agreement with previous reports of surface d-band narrowing in polycrystalline noble metal films. However, significant anisotropies in the d-band, s-band and Fermi edge of sputter cleaned Au are observed, which cannot be attributed to surface d-band narrowing alone. The unusual results for Au are attributed to drastic changes in the film morphology near the surface as a result of sputter cleaning.

Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states

We consider the problem of a single level quantum dot coupled to the edge of a one-dimensional Luttinger liquid wire by both a hopping term and electron–electron interactions. Using bosonization and Coulomb gas mapping of the Anderson–Yuval type we show that thermodynamic properties of the level, in particular, its occupation, depend on the various interactions in the system only through a single quantity—the corresponding Fermi edge singularity exponent. However, dynamical properties, such as the level density of states, depend in a different way on each type of interaction. Hence, we can construct different models, with and without interactions in the wire, with equal Fermi edge singularity exponents, which have identical population curves, although they originate from very different level densities of states. The latter may either be regular or show a power law suppression or enhancement at the Fermi energy. These predictions are verified to a high degree of accuracy using the density matrix renormalization group algorithm to calculate the dot occupation, and classical Monte Carlo simulations on the corresponding Coulomb gas model to extract the level density of states.

Solvent and temperature-dependent conductive behavior of poly(3-hexylthiophene)

Impedance characterization at different temperatures has been used to investigate the conductive behavior of Poly(3-hexylthiophene) (P3HT), prepared in different solvents, as the semiconductor layer in organic multilayer capacitor. It has been found that the P3HT films using chloroform and toluene solvents exhibit an enhancement in conductivity by heating following an Arrhenius law with an activation energy transition from 0.004 to 0.026 eV and from 0.002 to 0.015 eV at ~313 K, respectively, which originates from band tail hopping that occurs around the Fermi edge. The boiling point of the used solvents can affect P3HT crystallization process, which causes the difference in conduction and activation energy.

Fermi edge singularity observed in GaN/AlGaN heterointerfaces

We observe sharp spectral lines, at energies which are higher than the bulk GaN band gap, in the photoluminescence and photoluminescence excitation spectra of GaN/AlGaN heterointerfaces grown by molecular beam epitaxy. The spectra and their temperature dependence are in accord with the Fermi edge singularity expected for two dimensional electron gas systems. The associated localized hole energy in the AlGaN interface side was extracted directly from the spectra.

Near band‐gap photoluminescence of InN due to Mahan excitons

AbstractThe luminescence spectrum of degenerately n‐type doped hexagonal InN extends to energies significantly higher than the renormalized band edge of the material. The line shape cannot be explained by simple band‐filling. Reflectivity spectra reveal at low temperatures a strongly enhanced intensity at the Fermi energy which we ascribe to a Fermi edge singularity of the electrons interacting with holes to form so‐called Mahan excitons. High k ‐values of the holes recombining with Fermi edge electrons are provided by localization at acceptors. A weak binding energy for a Mahan exciton is expected due to screening of the electron liquid in the conduction band. The concept of Mahan excitons allows us to understand the observed near band gap photoluminescence spectra (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

MAGNETIC FIELD DEPENDENCE OF MANY-BODY ENHANCED ELECTRON TUNNELLING THROUGH A QUANTUM DOT

We consider many-body enhanced electron tunnelling through an InAs quantum dot in magnetic field applied perpendicular to the tunneling direction. Critical exponent of Fermi edge singularity in tunneling current is calculated as a function of magnetic field. We use lowest Landau level approximation for electrons in emitter and perform scattering matrix calculation in Born approximation. Results are compared with recent experiments.

Direct evidence of electron spin polarization from an organic-based magnet:[FeII(TCNE)(NCMe)2][FeIIICl4]

Direct evidence of an organic-based magnet with a finite electron spin polarization at the Fermi edge is shown from spin-resolved photoemission of the $[{\text{Fe}}^{\text{II}}(\text{TCNE}){(\text{NCMe})}_{2}][{\text{Fe}}^{\text{III}}{\text{Cl}}_{4}]$ organic-based magnet. The 23% majority-based spin polarization at the Fermi edge is observed at 80 K in zero applied field. Ab initio calculations at the density functional level (0 K) are in accord with a semiconductor with 100% majority-based electron spin polarization at the band edges, commensurate with our experimental results and model prediction for a half-semiconductor. Organic-based magnets may prove to be important for realizing polarized electron injection into semiconductors for magnetoelectronic applications.

Temperature dependent conductive behavior of pentacene in organic field-effect transistor

Impedance characterization at different temperature has been used to investigate the conductive behavior of pentacene as the semiconductor layer in organic field-effect transistor. It has been found that the pentacene exhibits an enhancement in conductivity by heating following an Arrhenius law with an activation energy transition from 0.004 to 0.018 eV at ∼323 K, which originates from band tail hopping that occurs around the Fermi edge.

Band offsets of a ruthenium gate on ultrathin high-κoxide films on silicon

Valence-band and conduction-band edges of ultrathin oxides (${\text{SiO}}_{2}$, ${\text{HfO}}_{2}$, ${\text{Hf}}_{0.7}{\text{Si}}_{0.3}{\text{O}}_{2}$, and ${\text{Al}}_{2}{\text{O}}_{3}$ grown on silicon) and their shifts upon sequential metallization with ruthenium have been measured using synchrotron-radiation-excited x-ray, ultraviolet, and inverse photoemissions. From these techniques, the offsets between the valence-band and conduction-band edges of the oxides, and the ruthenium metal gate Fermi edge have been directly measured. In addition the core levels of the oxides and the ruthenium have been characterized. Upon deposition, Ru remains metallic and no chemical alteration of the underlying oxide gates, or interfacial ${\text{SiO}}_{2}$ in the case of the high-$\ensuremath{\kappa}$ thin films, can be detected. However a clear shift of the band edges is measured for all samples due to the creation of an interface dipole at the ruthenium-oxide interface. Using the energy gap, the electron affinity of the oxides, and the ruthenium work function that have been directly measured on these samples, the experimental band offsets are compared to those predicted by the induced gap states model.

Reversible Phase Transformation and Doubly Charged Anions at the Surface of Simple CubicRbC60

The simple cubic phase of a RbC60 thin film has been studied using photoelectron spectroscopy. The simple cubic-to-dimer transition is found to be reversible at the film surface. A sharp Fermi edge is observed and a lower limit of 0.5 eV is found for the surface Hubbard U, pointing to a strongly correlated metallic character of thin-film simple cubic RbC60. A molecular charge state is identified in the valence band and core-level photoemission spectra which arises from C60(2-) anions and contributes to the spectral intensity at the Fermi level.

Electron excitations in grazing diffraction of fast He on a Ag(1 1 0) surface. A tribute to Hannspeter Winter

Grazing incidence diffraction of fast atoms (GIFAD) on surfaces has first been discovered on ionic insulators where electronic excitations are strongly reduced due to the large band gap. At variance no threshold exists for electronic excitations close to the Fermi edge of a metal surface. New results of energy resolved diffraction of keV helium atoms on a Ag(110) surface are presented which considerably extend the application range of GIFAD. The combined analysis of the energy loss and diffraction data could help providing a detailed description of the collision of helium with the surface electrons.