Fermi-edge Singularity Research Articles

Fermionic full counting statistics with smooth boundaries: From discrete particles to bosonization

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher-Hartwig expansion for Toeplitz determinants, while in the continuous limit we recover the bosonization results. This example of full counting statistics with smoothing is also related to orthogonality catastrophe, Fermi-edge singularity and non-equilibrium bosonization.

Modeling the dielectric function of degenerately doped ZnO:Al thin films grown by ALD using physical parameters

Transparent conductive thin films are a key building block of modern optoelectronic devices. A promising alternative to expensive indium containing oxides is aluminum doped zinc oxide (AZO). By correlating spectroscopic ellipsometry and photoluminescence, we analyzed the contributions of different optical transitions in AZO grown by atomic layer deposition to a model dielectric function (MDF) over a wide range of photon energies. The derived MDF reflects the effects of the actual band structure and therefore describes the optical properties very accurately. The presented MDF is solely based on physically meaningful parameters in contrast to empirical models like e.g. the widely used Sellmeier equation, but nevertheless real and imaginary parts are expressed as closed-form expressions. We analyzed the influence of the position of the Fermi energy and the Fermi-edge singularity to the different parts of the MDF. This information is relevant for design and simulation of optoelectronic devices and can be determined by analyzing the results from spectroscopic ellipsometry.

Many-body effects of a two-dimensional electron gas on trion-polaritons

We theoretically investigate the trion-polariton and the effects of a two-dimensional electron gas on its single particle properties. Focussing on the trion and exciton transitions, we set up an effective model and calculate the optical absorption of the quantum well containing the 2DEG. Including the light-matter coupling, we compute the Rabi splitting and polariton lineshapes as a function of 2DEG density. The role of finite temperature is investigated. The spatial extent of the trion-polariton is also calculated. We find a substantial charge build-up at short distances as long as the Rabi frequency does not exceed the trion binding energy. All our calculations take into account the Fermi-edge singularity and the Anderson orthogonality catastrophe.

Potentials of electrochemical reactions and nature of singularities in electrode polarization dependences

The conditions of transition of the electrochemical polarization mode to a faradaic process are studied on the metal electrode within the framework of the microscopic approach when the value of polarization potential reaches the threshold value of the potential of the electrochemical reaction. It is suggested that the elementary act of electron transfer between the metal and redox electrolyte occurs at the interface under polarization bringing the local electron level of the reagent to the Fermi level of electrons of the metal. Discharge through the Helmholtz layer limited by electrons occurs due to resonance “lightening” of the potential barrier between the metal and localized redox state of the reagent. Estimates are obtained for the values of threshold potential and exchange current of the faradaic process. A method is suggested for consideration of the elementary act of the electrochemical reaction on the basis of the Hamiltonian describing the microscopic mechanism of Fermi edge singularities. Application of the known solutions allows the appearance of threshold singularities of polarization dependences in electrochemistry to be explained.

Fermi-edge singularity in chiral one-dimensional systems far from equilibrium

We study the effects of strong coupling of a localized state charge to one-dimensional electronic channels out of equilibrium. While the state of this charge and the coupling strengths determine the scattering phase shifts in the channels, the nonequilibrium partitioning noise induces the tunneling transitions to the localized state. The strong coupling leads to a nonperturbative backaction effect which is manifested in the orthogonality catastrophe and the Fermi-edge singularity in the transition rates. We predict an unusually pronounced manifestation of the non-Gaussian component of noise that breaks the charge symmetry, resulting in a nontrivial shape, and a shift of the position of the tunneling resonance.

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy.

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10(11) cm(-2) was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

Fermi-edge transmission resonance in graphene driven by a single Coulomb impurity.

The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude ≈e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.

Polariton formation in a microcavity with a doped quantum well: Roles of the Fermi edge singularity and Anderson orthogonality catastrophe

A theoretical investigation of the single particle polariton properties for a microcavity embedding a charged quantum well is presented. The electron gas optical susceptibility is calculated numerically using the method devised by Combescot and Nozi\`eres. The role of many-body effects, such as the Fermi edge singularity and Anderson orthogonality catastrophe, in the polariton formation is elucidated. By tuning the light-matter coupling the short time behaviour of the electron gas response function is probed and comparison with earlier results only using the long time response are made. Various single particle polariton properties such as the Rabi splitting, line shape, Hopfield coefficients and effective mass are discussed. These are experimentally accessible quantities and thus allow for a comparison with the presented theory.

Statistics of the work distribution for a quenched Fermi gas

The local quench of a Fermi gas, giving rise to the Fermi edge singularity and the Anderson orthogonality catastrophe, is an analytically tractable out-of-equilibrium problem in condensed matter. It describes the generic physics that occurs when a localized scattering potential is suddenly introduced in a Fermi sea, leading to a brutal disturbance of its quantum state. It has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra-cold atoms. In this work, we analyze the quench problem in a gas of trapped ultra-cold fermions from a thermodynamic perspective using the full statistics of the so-called work distribution. The work statistics are shown to provide an accurate insight into the fundamental physics of the process.

Linear response of a one-dimensional conductor coupled to a dynamical impurity with a Fermi edge singularity

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport set-up in which the impurity can be realised in a double quantum dot. The same Hamiltonian describes tunnelling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e. many fermion correlations result in an impurity decay rate with a non-trivial power law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand, and the linear response of the Fermi sea to external perturbations on the other. This results in a power law singularity in the space and time dependence of the non-local polarisability of the Fermi sea, which can be detected in transport experiments.

The mesoscopic X-ray edge problem: Boundary effects enhance photoabsorption in quantum dots

We investigate the X-ray edge problem and photoabsorption spectra of mesoscopic quantum dot systems, in particular those of rectangular shape. We find strong signatures of Fermi-edge singularities in the photoabsorption cross section that characteristically differ from the well-studied metallic behaviour. The averaged photoabsorption at K-edge, typically rounded in the metallic case, develops a peaked characteristics, comparable to the metallic and mesoscopic L-edge signature, in quantum dots. It stems from the contribution of the system boundary region to the photoabsorption signal and has its origin in the correlation between the single-particle wave functions and their derivatives near a system boundary.

Nonequilibrium dynamics in an optical transition from a neutral quantum dot to a correlated many-body state

We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intra dot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity model to include a static hole and a dynamic dot-electron scattering potential. The latter highlights the fact that an optically active dot acts as a tunable quantum impurity, enabling the investigation of a new dynamic regime of Fermi-edge physics.

Orthogonality Catastrophe and Decoherence in a Trapped-Fermion Environment

The Fermi-edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and to the degree of the non-Markovian nature of its dynamics.

Decoherence in a Fermion Environment: Non-Markovianity and Orthogonality Catastrophe

We analyze the non-Markovian character of the dynamics of an open two-level atom interacting with a gas of ultra-cold fermions. In particular, we discuss the connection between the phenomena of orthogonality catastrophe and Fermi edge singularity occurring in such a kind of environment and the memory-keeping effects which are displayed in the time evolution of the open system.

Visualization of wave function of quantum dot at Fermi-edge singularity regime

We consider in this work many-body enhanced electron tunneling through an InAs quantum dot in a magnetic field applied perpendicular to the tunneling direction. We have examined in details the anisotropic behavior of the amplitude and shape of the resonant peaks.

Time evolution of excitations in normal Fermi liquids

We inspect the initial and the long time evolution of excitations a Fermi liquids by analyzing the time behavior of the electron spectral function. Focusing on the short-time limit we study the electron-boson model for the homogenous electron gas and apply the first order (in boson propagator) cumulant expansion of the electron Green's function. In addition to a quadratic decay in time upon triggering the excitation, we identify non-analytic terms in the time expansion similar to those found in the Fermi edge singularity phenomenon. We also demonstrate that the exponential decay in time in the long-time limit is inconsistent with the GW approximation for the self-energy. The background for this is the Paley-Wiener theorem of complex analysis. To reconcile with the Fermi liquid behavior an inclusion of higher order diagrams (in the screened Coulomb interaction) is required.

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

Electronic transitions and fermi edge singularity in polar heterostructures studied by absorption and emission spectroscopy

Optically induced electronic transitions in nitride based polar heterostructures have been investigated by absorption and emission spectroscopy. Surface photovoltage (SPV), photocurrent (PC), and photo luminescence spectroscopy have been applied to high quality InAlN/AlN/GaN structures to study the optical properties of two dimensional electron gas. Energy levels within the two dimensional electron gas (2DEG) well at the interface between the GaN and AlN have been directly observed by SPV and PC. Moreover, a strong enhancement of the photoluminescence intensity due to holes recombining with electrons at the Fermi Energy, known as fermi energy singularity, has been observed. These analyses have been carried out on InAlN/AlN/GaN heterojunctions with the InAlN barrier layer having different In content, a parameter which affects the energy levels within the 2DEG well as well as the optical signal intensity. The measured energy values are in a very good agreement with the ones obtained by Schrödinger–Poisson simulations.

Non-Markovian effects at the Fermi-edge singularity in quantum dots

We study the electronic transport through a quantum dot in the Fermi-edge singularity regime, with emphasis on its non-Markovian attributes. These were quantified by the behavior of current noise as well as the trace-distance-based measure of non-Markovianity and found to be pronounced at low temperatures, where the interplay of many-electron correlations and quantum coherence present in the system leads to significant quantum memory effects and non-Markovian dynamics.

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined to a 1D trap. We review existing results for various dynamic correlation functions, in particular the density structure factor and the spectral function. Moreover, we show how a dispersion nonlinearity leads to finite particle lifetimes, and discuss its impact on the transport properties of 1D systems at finite temperatures. The conventional Luttinger liquid theory is a special limit of the new theory, and we explain the relation between the two.