Fermi-edge Singularity Research Articles

Hot luminescence of two-dimensional electron hole systems in modulation-doped silicon

Modulation doping of silicon has great potential for miniaturization, surface passivation, and third generation photovoltaics (PV). At a modulation-doped silicon surface, we observe the formation of a 2D hole layer at the silicon surface at low temperatures by means of photoluminescence (PL) measurements. A line shape analysis of band–band and hot luminescence reveals the hole density (which is equal to the modulation-doped acceptor density). A high excitation intensity leads to a Fermi edge singularity of the band–band and hot PL emission. While the 2D layer can be characterized by the observed luminescence, the spectral region of twice the bandgap is fully dominated by emission from this surface layer, impeding the measurement of bulk hot luminescence, e.g., from Auger electrons or from nonthermalized carriers in a hot carrier PV device.

Fermi-edge singularity and related emission from degenerate semiconductors: Transition from a spontaneous to a stimulated process

Fermi-edge singularity and related emission from degenerate semiconductors: Transition from a spontaneous to a stimulated process

Spatiotemporal spread of Fermi-edge singularity as time-delayed interaction and impact on time-dependent RKKY-type coupling

Fermi-edge singularity and Anderson's orthogonality catastrophe are paradigmatic examples of non-equilibrium many-body physics in conductors, appearing after a quench is created by the sudden change of a localised potential. We investigate if the signal carried by the quench can be used to transmit a long ranged interaction, reminiscent of the RKKY interaction, but with the inclusion of the full many-body propagation over space and time. We calculate the response of a conductor to two quenches induced by localised states at different times and locations. We show that building up and maintaining coherence between the localised states is possible only with finely tuned interaction between the localised states and the conductor. This puts bounds to the use of time controlled RKKY type interactions and may limit the speed at which some quantum gates could operate.

Signatures of the orthogonality catastrophe in a coherently driven impurity

We consider a fixed impurity immersed in a Fermi gas at finite temperature. We take the impurity to have two internal spin states, where the $\uparrow$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, while the $\downarrow$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states therefore allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity Green's functions with a variational approach to treat the Rabi driven dynamics, we find that the system features Rabi oscillations whose frequency scales as a non-trivial power of the Rabi drive at low temperatures. This reflects the power law of the Fermi-edge singularity and, importantly, this behavior is qualitatively different from the case of a mobile impurity quasiparticle where the scaling is linear. We therefore argue that the scaling law serves as an experimentally implementable probe of the orthogonality catastrophe. We additionally simulate rf spectroscopy beyond linear response, finding a remarkable agreement with an experiment using heavy impurities [Kohstall $\textit{et al.}$, Nature $\textbf{485}$, 615 (2012)], thus demonstrating the power of our approach.

Correlation between Optical Localization-State and Electrical Deep-Level State in In0.52Al0.48As/In0.53Ga0.47As Quantum Well Structure.

The peculiar correlationship between the optical localization-state and the electrical deep-level defect-state was observed in the In0.52Al0.48As/In0.53Ga0.47As quantum well structure that comprises two quantum-confined electron-states and two hole-subbands. The sample clearly exhibited the Fermi edge singularity (FES) peak in its photoluminescence spectrum at 10–300 K; and the FES peak was analyzed in terms of the phenomenological line shape model with key physical parameters such as the Fermi energy, the hole localization energy, and the band-to-band transition amplitude. Through the comprehensive studies on both the theoretical calculation and the experimental evaluation of the energy band profile, we found out that the localized state, which is separated above by ~0.07 eV from the first excited hole-subband, corresponds to the deep-level state, residing at the position of ~0.75 eV far below the conduction band (i.e., near the valence band edge).

Effect of growth temperature on surface morphology and optical properties of undoped Al0.32Ga0.68As

Undoped Al0.32Ga0.68As material which was grown by metal-organic chemical vapor deposition at different growth temperature. The evolution mechanism of surface morphology of Al0.32Ga0.68As was explained by the variation of step growth direction and growth rate, which were affected by growth temperature. Electrochemical capacitance-voltage results showed the dependence of conductivity type on carbon incorporation. Al0.32Ga0.68As changed from p-type to n-type conductivity and carrier concentration decreased as growth temperature increased from 640 °C to 740 °C. The disorder of Al0.32Ga0.68As ternary alloy originated from its structural defects, which were attributed to aluminum (Al) compositional fluctuations by the incorporation of carbon impurity. The crystal quality of undoped Al0.32Ga0.68As was characterized by the intensity of Fermi-edge singularity peak. The change rule of the intensity of Al0.32Ga0.68As and GaAs peaks was discussed in terms of carrier transport and recombination properties.

Charge transfer statistics and qubit dynamics at the tunneling Fermi-edge singularity

Tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD) is studied, when all Coulomb screening of charge variations on the dot is realized by the emitter channel and the system is mapped onto an exactly solvable model of a dissipative qubit. In this model we describe the qubit density matrix evolution with a generalized Lindblad equation, which permit us to count the tunneling electrons and therefore relate the qubit dynamics to the charge transfer statistics. In particular, the coefficients of its generating function equal to the time dependent probabilities to have the fixed number of electrons tunneled into the collector are expressed through the parameters of a non-Hermitian Hamiltonian evolution of the qubit pure states in between the successive electron tunnelings. From the long time asymptotics of the generating function we calculate Fano factors of the second and third order (skewness) and establish their relation to the extra average and cumulant, respectively, of the charge accumulated in the transient process of the empty QD evolution beyond their linear time dependence. It explains the origin of the sub and super Poisson shot noise in this system and shows that the super Poisson signals existence of a non-monotonous oscillating transient current and the qubit coherent dynamics. The mechanism is illustrated with particular examples of the generating functions, one of which coincides in the large time limit with the $1/3$ fractional Poissonian realized without the real fractional charge tunneling.

Taming convergence in the determinant approach for x-ray excitation spectra

A determinant formalism in combination with \emph{ab initio} calculations proposed recently has paved a new way for simulating and interpreting x-ray excitation spectra. The new method systematically takes into account many-electron effects in the Mahan-Nozi\'eres-De Dominicis (MND) theory, including core-level excitonic effects, the Fermi-edge singularity, shakeup excitations, and wavefunction overlap effects such as the orthogonality catastrophe, all within a universal framework using many-electron configurations. A heuristic search algorithm was introduced to search for the configurations that are important for defining spectral lineshapes, instead of enumerating them in a brute-force way. The algorithm has proven to be efficient for calculating \ce{O} $K$ edges of transition metal oxides, which converge at the second excitation order (denoted as $f^{(n)}$ with $n = 2$), i.e., the final-state configurations with two \emph{e-h} pairs (with one hole being the core hole). However, it remains unknown how the determinant calculations converge for general cases and at which excitation order $n$ one should stop the determinant calculation. Even with the heuristic algorithm, the number of many-electron configurations still grows exponentially with the excitation order $n$. In this work, we prove two theorems that can indicate the order of magnitude of the contribution of the $f^{(n)}$ configurations, so that one can estimate their contribution very quickly without actually calculating their amplitudes. The two theorems are based on the singular-value decomposition (SVD) analysis, a method that is widely used to quantify entanglement between two quantum many-body systems. We examine the $K$ edges of several metallic systems with the determinant formalism up to $f^{(5)}$ to illustrate the usefulness of the theorems.

Many-body theory of optical absorption in doped two-dimensional semiconductors

In this article, we use a many-body approach to study the absorption spectra of electron-doped two-dimensional semiconductors. Optical absorption is modeled by a many-body scattering Hamiltonian which describes an exciton immersed in a Fermi sea. The interaction between electron and exciton is approximated by an effective scattering potential, and optical spectra are calculated by solving for the exciton Green's function. From this approach, a trion state can be assigned as a bound state of an electron-exciton scattering process, and the doping-dependent phenomena observed in the spectra can be attributed to several many-body effects induced by the interaction with the Fermi sea. While the many-body scattering Hamiltonian can not solved exactly, we reduce the problem to two limiting solvable situations. The first approach approximates the full many-body problem by a simple scattering process between the electron and the exciton, with a self-energy obtained by solving a Bethe-Salpeter equation (BSE). An alternate approach assumes an infinite mass for the exciton, such that the many-body scattering Hamiltonian reduces to a Mahan-Nozieres-De Dominicis (MND) model. The exciton Green's function can then be solved numerically exactly by a determinantal formulation, and the optical spectra show signatures of the Fermi-edge singularity at high doping densities. The full doping dependence and temperature dependence of the exciton and trion lineshapes are simulated via these two approximate approaches, with the results compared to each other and to experimental expectations.

Current noise spectrum in a solvable model of tunneling Fermi-edge singularity

We consider tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD). When all Coulomb screening of sudden charge variations of the dot during the tunneling is realized by the emitter channel, the system is mapped onto an exactly solvable model of a dissipative qubit. The qubit density matrix evolution is described with a generalized Bloch equation which permits us to count the tunneling electrons and find the charge transfer statistics. The two generating functions of the counting statistics of the charge transferred during the QD evolutions from its stationary and empty state have been expressed through each other. It is used to calculate the spectrum of the steady current noise and to demonstrate the occurrence of the bifurcation of its single zero-frequency minimum into two finite-frequency dips due to the qubit coherent dynamics.

Threshold effects in one-dimensional strongly interacting nonequilibrium systems

In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop the perturbation theory with respect to tunneling and derive an asymptotic behavior of physical quantities close to threshold energies. We reproduce earlier results for the electron relaxation at the edge of an integer quantum Hall system and for the non-equilibrium Fermi edge singularity phenomenon. In contrast to the previous works, our analysis does not rely on the free-fermionic character of local tunneling, therefore we are able to extend our theory to wider class of systems, without well-defined electron excitations, such as spinless Luttinger liquids and chiral quantum Hall edge states at fractional filling factors.

Spectra of heavy polarons and molecules coupled to a Fermi sea

We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority atom in an ultracold gas, exciton in a solid) by attraction strong enough to form a molecule/trion. We introduce a diagrammatic scheme which allows treating a finite mass impurity while reproducing the Fermi edge singularity in the immobile limit. For large binding energies the spectrum is characterized by a semi-coherent repulsive polaron and an incoherent molecule-hole continuum, which is the lowest-energy feature in the single-particle spectrum. The previously predicted attractive polaron seems not to exist for strong binding.

Experimental Detection and Control of Trions and Fermi-Edge Singularity in Single-Barrier GaAs/AlAs/GaAs Heterostructures Using Photocapacitance Spectroscopy

In this paper, we show how photocapacitance spectra can probe two dimensional excitonic complexes and Fermi edge singularity as a function of applied bias around 100 K. In lower density regimes (<1x1011cm^-2), the appearance of two distinct peaks in the spectra are identified as a signature of coexistence of both excitons and positively charged trions. We estimate the binding energy of these trions as ~2.0 meV. In the higher density regimes (>1x10^11 cm^-2), we observe a sharp spectral transition from trions to asymmetric shaped Fermi edge singularity in the photocapacitance spectra around a particular reverse bias. However, these signatures are absent from the photoluminescence spectra measured under identical circumstances. Such dissimilarities clearly point out that different many body physics govern these two spectral measurements. We also argue why such quantum confined dipoles of spatially indirect trions can have thermodynamically finite probability to survive even around 100 K. Finally, our observations demonstrate that photocapacitance technique, which was seldom used to detect trions in the past, can also be useful to detect the traces of these spatially indirect excitonic complexes as well as Fermi edge singularity even at 100 K. This is mainly due to enhanced sensitivity of such dielectric measurements to dipolar changes within such heterojunction.

Fermi-edge singularity and the functional renormalization group

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

On the Electronic Mechanisms of Specific Interactions between Surfactants and a Metal Surface

This work considers the electronic mechanism of specific interactions between a neutral surfactant and an uncharged metal surface during an elementary adsorption event. Special attention was paid to a role of the residual electronic interactions upon the exchange of electron density between the valence adsorbate orbital and the Fermi sea of metal electrons during adsorption. This interaction was simulated by the Coulomb electron–hole interactions through a potential barrier separating the surfactant and metal-electron systems. As this task concerns the problems associated with the Fermi edge singularities, the Nozieres–de Dominicis theory, which enables one to study an electron’s contribution to the energetics and kinetics of adsorption event, was used to interpret the donor–acceptor effects. The expressions of spectral characteristics of the localized electron density and tunneling time were analyzed in the context of the problem. There is a positive correlation between the surfactant adsorption parameters and the scattering phases of conductivity electrons screened in the metal by a potential field created by a hole at the valence surfactant orbital.

Manifestation of a Fermi edge singularity in the cotunneling regime

The Fermi edge singularity (FES) is a prominent manifestation of the Coulomb interaction. It can be observed in a controllable way by studying the transport through a quantum dot (QD), which is electrostatically coupled to the leads. In this paper we study how FES affects higher order tunneling processes (cotunneling). To address this problem we use the bosonic description of the electrons in the leads, which naturally accounts for the Coulomb interaction. We report the multiscale dependence of the current through the QD on the energy of the QD level and on the bias between the leads obtained for the limit of large and small bias. The new universal powers are determined by the scattering phases due to the interaction of electrons in the leads with the charge on the QD.

Probing qubit dynamics at the tunneling Fermi-edge singularity with alternating current

We consider tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot. When all Coulomb screening of sudden charge variations of the dot during the tunneling is realized by the emitter channel, the system is described with an exactly solvable model of a dissipative qubit. To study manifestations of the coherent qubit dynamics in the collector ac response we derive a solution to the corresponding Bloch equation for the model quantum evolution in the presence of the oscillating voltage of frequency $\ensuremath{\omega}$ and calculate perturbatively the ac response in the voltage amplitude. We have shown that in a wide range of the model parameters the coherent qubit dynamics results in the nonzero frequencies resonances in the amplitudes dependence of the ac harmonics and in the jumps of the harmonics phase shifts across the resonances. In the first order the ac response is directly related to the spectral decomposition of the corresponding transient current and contains only the first $\ensuremath{\omega}$ harmonic, whose amplitude exhibits resonance at $\ensuremath{\omega}={\ensuremath{\omega}}_{I}$, where ${\ensuremath{\omega}}_{I}$ is the qubit oscillation frequency. In the second order we have obtained the $2\ensuremath{\omega}$ harmonic of the ac response with resonances in the frequency dependence of its amplitude at ${\ensuremath{\omega}}_{I},\phantom{\rule{0.16em}{0ex}}{\ensuremath{\omega}}_{I}/2$ and zero frequency and also have found the frequency dependent shift of the average steady current.

Fermi-edge singularity and related interaction induced phenomena in multilevel quantum dots

We study the manifestation of the non-perturbative effects of interaction in sequential tunnelling between a quasi-one dimensional system of chiral quantum Hall edge channels and a multilevel quantum dot (QD). We use the formal scattering theory approach to the bosonization technique to present an alternative derivation of the Fermi-edge singularity (FES) effect and demonstrate the origin of its universality. This approach allows us to address, within the same framework, plasmon assisted sequential tunnelling to relatively large dots and investigate the interaction induced level broadening. The results are generalised by taking into account the dispersion in the spectrum of plasmons in the QD. We then discuss their modification in the presence of neutral modes, which can be realised either in a QD with two chiral strongly interacting edge channels or in a three dimensional QD in the Coulomb blockade regime. In the former case a universal behaviour of the tunnelling rate is discovered.

Fermi edge singularities in transport through lateral GaAs quantum dots

We measure tunnelling currents through electrostatically defined quantum dots in a GaAs/AlGaAs heterostructure connected to two leads. For certain tunnelling barrier configurations and high sample bias we find a pronounced resonance associated with a Fermi edge singularity. This many-body scattering effect appears when the electrochemical potential of the quantum dot is aligned with the Fermi level of the lead less coupled to the dot. By changing the relative tunnelling barrier strength we are able to tune the interaction of the localised electron with the Fermi sea.

Dynamical Excitonic Effects in Doped Two-Dimensional Semiconductors.

It is well-known that excitonic effects can dominate the optical properties of two-dimensional materials. These effects, however, can be substantially modified by doping free carriers. We investigate these doping effects by solving the first-principles Bethe-Salpeter equation. Dynamical screening effects, included via the sum-rule preserving generalized plasmon-pole model, are found to be important in the doped system. Using monolayer MoS2 as an example, we find that upon moderate doping, the exciton binding energy can be tuned by a few hundred millielectronvolts, while the exciton peak position stays nearly constant due to a cancellation with the quasiparticle band gap renormalization. At higher doping densities, the exciton peak position increases linearly in energy and gradually merges into a Fermi-edge singularity. Our results are crucial for the quantitative interpretation of optical properties of two-dimensional materials and the further development of ab initio theories of studying charged excitations such as trions.