Fermi-edge Singularity Research Articles

Mahan excitons in degenerate wurtzite InN: Photoluminescence spectroscopy and reflectivity measurements

Unintentionally degenerately doped $n$-type hexagonal wurtzite InN samples were studied by using Fourier-transform photoluminescence spectroscopy and reflectivity measurements. We found in luminescence overlapping band acceptor $(e,{A}^{0})$ transitions related to two different acceptors with a strong enhancement of their intensities close to the Fermi energy of the electrons recombining with the localized holes. Our explanation is in terms of a Fermi-edge singularity of the electrons due to strongly increased electron-hole scattering. Electron-hole pairs with such resonantly enhanced oscillator strengths have been referred to as Mahan excitons. Temperature-dependent reflectivity measurements confirm this interpretation.

Keldysh action of a multiterminal time-dependent scatterer

We present a derivation of the Keldysh action of a general multi-channel time-dependent scatterer in the context of the Landauer-B\"uttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering Full Counting Statistics and the Fermi Edge Singularity.

Fermi edge singularities in the mesoscopic regime: Photoabsorption spectra

We study Fermi edge singularities in photoabsorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photoexcitation of an electron into the conduction band. The photoabsorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozi\`eres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded $K$-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the ``bound state'' produced by the core hole.

Enhancement of the 2DEG density in AlGaAs/InGaAs/GaAs P-HEMTs structures grown by MBE on (311)A and (111)A GaAs substrates

The pseudomorphic high electron mobility transistor (P-HEMT) structure materials Al 0.33Ga 0.7As/In 0.1Ga 0.9As/GaAs have been grown by molecular beam epitaxy (MBE) on (311)A and (111)A GaAs substrates. The epitaxy of strain heterostructure on high index GaAs substrate has led to new growth phenomena, material properties and device applications. The photoluminescence (PL) spectra of the structures have been measured at low temperature. The dominant emission in the PL spectra is due to the recombination from the first electron (e1) subband to the first heavy-hole (hh1) subband ( E 11: e1–hh1). This feature ( E 11) is a relatively broad peak and has a typical asymmetric line shape. The transformation of the PL spectra in the close vicinity of the Fermi edge ( E F) under different excitation densities gives strong evidence for the Fermi Edge Singularity (FES) existence. The density of the quasi-two-dimensional electron gas (2DEG) determined by PL study ( n s PL), is in sufficient agreement with the values found from Hall measurements n s Hall at 77 K. The results prove an increase of the electron density in sample grown on GaAs (111)A and (311)A rather than in equivalent sample grown on (001) GaAs substrate. This effect is in good agreement with our theoretical prediction, which is based on a self-consistent solution of the coupled Schrödinger and Poisson equations.

Orthogonality catastrophe and Kondo effect in graphene

Anderson's orthogonality catastrophe [Phys. Rev. Lett. 18, 1049 (1967)] in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed due to the vanishing density of states at the Dirac point. In the presence of preexisting localized states at the Dirac energy, the orthogonality catastrophe shows features similar to those found in normal metals with a finite density of states at the Fermi level. The implications for the Kondo effect induced by magnetic impurities, and for the Fermi edge singularities in tunneling processes, are also discussed.

Linear optical responses of one-dimensional electron systems: Comparison of theories with experiments

We present a systematic study on the linear optical spectra of n-doped GaAs quantum wire. A Coulomb-correlated band-edge absorption peak appears at low doping density evolving from the exciton resonance. The Fermi-edge singularity is observed at high doping density. Based on theoretical calculations, we clarify the mechanism of the crossover among exciton, the band-edge and the Fermi-edge singularities.

Magnetic-field-induced Fermi-edge singularity in the tunnelling current through a self-assembled InAs quantum dot

Tunneling transport through a one-barrier GaAs/(AlGa)As/GaAs heterostructure containing self-assembled InAs quantum dots has been investigated at low temperatures. An anomalous increase in the tunneling current through quantum dots in magnetic fields oriented both parallel and perpendicular to the current is observed. This increase is a manifestation of the Fermi-edge singularity in the current as a result of the interaction of a tunneling electron with the electron gas in the emitter.

Magnetic-field-induced Fermi-edge singularity in the tunneling current through an InAs self-assembled quantum dot

The results of the investigation of tunneling transport through a GaAs/(AlGa)As/GaAs single-barrier heterostructure containing InAs self-assembled quantum dots at low temperatures are reported. An anomalous increase in the tunneling current through the quantum dots has been observed in the presence of a magnetic field both parallel and perpendicular to the current. This increase is a manifestation of a Fermi-edge singularity appearing in the current due to the interaction of a tunneling electron with the electron gas in an emitter.

Noise at a Fermi-edge singularity in self-assembled InAs quantum dots

We present noise measurements of self-assembled InAs quantum dots at high magnetic field. In comparison to $I\text{\ensuremath{-}}V$ characteristics at zero magnetic field, we notice a strong current overshoot that is due to a Fermi-edge singularity. We observe an enhanced suppression in the shot noise power simultaneous to the current overshoot that is attributed to the electron-electron interaction at the Fermi-edge singularity.

Fermi-Edge Singularity of Spin-Polarized Electrons

We study the absorption spectrum of a two-dimensional electron gas (2DEG) in a magnetic field. We find that at low temperatures, when the 2DEG is spin polarized, the absorption spectra, which correspond to the creation of spin up or spin down electrons, differ in magnitude, linewidth, and filling factor dependence. We show that these differences can be explained as resulting from the creation of a Mahan exciton in one case, and of a power law Fermi-edge singularity in the other.

ANDERSON-FANO TRANSITIONS IN PHOTOLUMINESCENCE OF A TWO DIMENSIONAL ELECTRON GAS

The many body interaction are investigated in polarization resolved photoluminescence in the magnetic field up to 23 T. The Fermi edge singularity, Anderson-Fano transition and neutral and negatively charged excitons (trions) are detected in the photoluminescence spectra. The experimental results are supplemented by realistic calculations.

Fermi edge singularities in ion-induced electron emission from plane metal surfaces

Auger electron emission – following low energy monoatomic ion impact on metal surfaces – is studied with a many body theory that includes both the band structure and the Fermi singular response of metal electrons (to the sudden neutralization of the projectiles). Application is made to the experimental kinetic energy distributions of electrons ejected from polycrystalline Al by Ar+-projectiles at varying incident energies and angles. Excellent agreement is found between the theory and the measurements.

Fermi-Edge Singularity in a Spin-Incoherent Luttinger Liquid

We theoretically investigate the Fermi-edge singularity in a spin-incoherent Luttinger liquid. Both cases of finite and infinite core hole mass are explored, as well as the effect of a static external magnetic field of arbitrary strength. For a finite mass core hole the absorption edge behaves as (omega-omega th)alpha/square root of absolute value (ln(omega-omega th)) for frequencies omega just above the threshold frequency omega th. The exponent alpha depends on the interaction parameter g of the interacting one dimensional system, the electron-hole coupling, and is independent of the magnetic field strength, the momentum, and the mass of the excited core hole (in contrast to the spin-coherent case). In the infinite mass limit, the spin-incoherent problem can be mapped onto an equivalent problem in a spinless Luttinger liquid for which the logarithmic factor is absent, and backscattering from the core hole leads to a universal contribution to the exponent alpha.

Auger electron emission from metals induced by low energy ion bombardment: Effect of the band structure and Fermi edge singularity

Calculations of the kinetic energy distributions of electrons ejected from plane metal surfaces by Auger neutralization of slow monoatomic ions are reported. A many body theory is used that includes both the band structure of the target material and the Fermi singular response of metal electrons (to the sudden neutralization of the projectile). Application is made to experiments of electron emission from polycrystalline Al by Ar +-ions, at varying incident energies and angles. Adjustment of the broadening parameters of the distribution of shake-up electrons leads to excellent agreement between the theory and the measurements.

The ‘strange metal’ is a projected Fermi liquid with edge singularities

The first measurements on single-crystalline high-temperature superconductors revealed that the ‘normal’ metal above the superconducting transition temperature, Tc, was as unusual as the superconductor: the large, temperature-dependent resistivity implied a scattering rate not just linear in T but of the order of the average excitation energy kBT/h, where kB is Boltzmann’s constant and h is Planck’s constant. This ‘strange metal’ phase continues to be of much theoretical interest. Here we show it is a consequence of projecting the doubly occupied amplitudes out of a conventional Fermi-sea wavefunction (Gutzwiller projection), requiring no exotica such as a mysterious quantum critical point. Exploiting a formal similarity with the classic problem of Fermi-edge singularities in the X-ray spectra of metals, we find a Fermi-liquid-like excitation spectrum, but the excitations are asymmetric between electrons and holes, show anomalous forward scattering and the renormalization constant Z=0. We explain the power-law frequency dependence of the conductivity, and predict tunnelling spectrum anomalies and the forms of photoelectron spectra.

Fermi-edge singularities in transport through quantum dots

We study the Fermi-edge singularity appearing in the current-voltage characteristics for resonant tunneling through a localized level at finite temperature. An explicit expression for the current at low temperature and near the threshold for the tunneling process is presented which allows to coalesce data taken at different temperatures to a single curve. Based on this scaling function for the current we analyze experimental data from a GaAs-AlAs-GaAs tunneling device with embedded InAs quantum dots obtained at low temperatures in high magnetic fields.

Dynamic Structure Factor of the Calogero-Sutherland Model

We evaluate the dynamic structure factor S(q, omega) of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small q, the structure factor differs from zero in a finite interval of frequencies of the width deltaomega proportional to q2/m. At the borders of this interval S(q, omega) exhibits power-law singularities with exponents depending on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the x-ray absorption spectra of metals.

Singularities in the magneto-photoluminescence spectra from isolated quantum dots

We have optically investigated quantum dots containing a few electrons each. In zero magnetic field, the photoluminescence (PL) should reflect the occupied density of states of such artificial atoms. However, the few-electron response to recombination of one of these electrons with a localized hole appears to be enhanced as the energy of the electrons approaches the highest occupied state. This phenomenon resembles the Fermi-edge singularity observed in the PL spectra from n-type two- and one-dimensional electron systems. Like in the case of doped n-type quantum wires, this singularity is seen to dominate the PL spectrum of the quantum dots at a low magnetic field with a sharp fall in intensity at a specific magnetic field.

Shot noise measurements of InAs quantum dots at a Fermi edge singularity

The noise properties of self-assembled InAs quantum dots were measured at high magnetic fields and for varying temperatures. We see a high current overshoot which we ascribe to a Coulomb interaction effect between a localized electron on the dot and the electrons at the Fermi edge of the emitter, a so-called Fermi edge singularity (FES) effect. We measure the shot noise at this point in detail for different temperatures.

Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at nonzero temperatures

We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise definition of the finite temperature Riemann-Hilbert problem and show that it is equivalent to a zero temperature problem. Using this equivalence, we discuss the solution of the nonequilibrium Fermi-edge singularity problem at finite temperatures.