Gradient catastrophe and Fermi-edge resonances in Fermi gas

Any smooth spatial disturbance of a degenerate Fermi gas inevitably becomes sharp. This phenomenon, called the gradient catastrophe, causes the breakdown of a Fermi sea to multiconnected components characterized by multiple Fermi points. We argue that the gradient catastrophe can be probed through a Fermi-edge singularity measurement. In the regime of the gradient catastrophe the Fermi-edge singularity problem becomes a nonequilibrium and nonstationary phenomenon. We show that the gradient catastrophe transforms the single-peaked Fermi-edge singularity of the tunneling (or absorption) spectrum to a sequence of multiple asymmetric singular resonances. An extension of the bosonic representation of the electronic operator to nonequilibrium states captures the singular behavior of the resonances.     

Fermi-edge singularities in the photoluminescence spectrum of modulation-doped GaAs v-groove quantum wires

We report the observation of strong Fermi-edge singularities in the photoluminescence spectrum of strongly-confined, modulation-doped GaAs v-groove quantum wires. The behaviour of the singularity has been investigated at high excitation intensity, and both lattice and electrical heating. The latter produces a strong reduction of the singularity due to Fermi surface smearing, whereas, increased photoexcitation produces complex electron–hole correlation effects.     

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.     

Observation of the Fermi-edge singularity in n-doped single asymmetric quantum wells: the influence of residual acceptors

The investigation of the evolution of the photoluminescence spectra, in single asymmetric quantum wells (SAQWs), from a typical emission spectrum to a Fermi-edge singularity, is carried out as a function of both the optical excitation intensity and the temperature. The three samples used here are n-doped, low carrier density (below 5×10¹¹ cm⁻²), GaAs/Al_0.35Ga_0.65As SAQWs grown by molecular beam epitaxy. The strong collective recombination of electrons with different k states up to the Fermi wave vector as well as the optical signature of the Fermi-edge singularity is observed in two samples containing residual acceptors inside the GaAs SAQW. In contrast, a third sample containing no experimental evidence of residual acceptors in the GaAs SAQW shows no optical signature of the Fermi-edge singularity.     

Strong Fermi-edge singularity in ultra-high-quality AlGaAs/GaAs quantum wires

We report the observation of a strong Fermi-edge singularity (FES), with the complete suppression of the band-edge peak, in the photoluminescence spectra of ultra-high-quality modulation-doped AlGaAs/GaAs quantum wires (QWRs). We find that the FES effect is very sensitive to the Fermi energy. The strong FES is observed only in QWRs having a Fermi energy of the order of a few meV, and disappears almost completely when the Fermi energy exceeds 10 meV. These results are expected to spark new research activities, both experimentally and theoretically, on many-body effects in one-dimensional electron gas.     

Bound states in optical absorption of semiconductor quantum wells containing a two-dimensional electron Gas

The dependence of the optical absorption spectrum of a semiconductor quantum well on two-dimensional electron concentration n(e) is studied using CdTe samples. The trion peak (X-) seen at low n(e) evolves smoothly into the Fermi edge singularity at high n(e). The exciton peak (X) moves off to high energy, weakens, and disappears. The X,X- splitting is linear in n(e) and closely equal to the Fermi energy plus the trion binding energy. For Cd0.998Mn0.002Te quantum wells in a magnetic field, the X,X- splitting reflects unequal Fermi energies for M = +/-1/2 electrons. The data are explained by Hawrylak's theory of the many-body optical response including spin effects.     

Fermi-edge resonance and tunneling in nonequilibrium electron gas

Fermi-edge singularity changes in a nonequilibrium system, acquiring features that reflect the structure of energy distribution. In particular, it splits into several components if the energy distribution exhibits multiple steps. While conventional approaches, such as bosonization, fail to describe the nonequilibrium problem, an exact solution for a generic energy distribution can be obtained with the help of the method of functional determinants. In the case of a split Fermi distribution, the "open loop" part of the Greens function possesses power law singularities. At the same time, the resulting tunneling density of states exhibits broadened peaks centered at Fermi sublevels.     

Interplay of collective excitations in quantum-well intersubband resonances

Intersubband resonances in a semiconductor quantum well (QW) display fascinating features involving various collective excitations such as Fermi-edge singularity (FES) and intersubband plasmon (ISP). Using a density matrix approach, we treated many-body effects such as depolarization, vertex correction, and self-energy consistently for a two-subband system. We found a systematic change in resonance spectra from FES- to ISP-dominated features, as QW width or electron density is varied. Such an interplay between FES and ISP significantly changes both line shape and peak position of the absorption spectrum. We found that a cancellation of FES and ISP undresses the resonant responses and recovers the single-particle features of absorption for semiconductors with a strong nonparabolicity such as InAs, leading to a dramatic broadening of the absorption spectrum.     

Fermi-edge singularity in the vicinity of the resonant scattering condition

Fermi-edge absorption theory predicting the spectrum A(ω) ∝ ω(-2δ(0)/π+δ(0)92)/π2) relies on the assumption that scattering phase δ(0) is frequency independent. The dependence of δ(0) on ω becomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, because of the finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate the finite time delay into the theory, solve the Dyson equation with a modified kernel, and find that, near the resonance, A(ω) behaves as ω(-3/4)|lnω|. Scattering off the core hole becomes resonant in 1D and 2D in the presence of an empty subband above the Fermi level; then a deep hole splits off a level from the bottom of this subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.     

Tunable Fermi-edge resonance in an open quantum dot

Resonant tunneling in an open mesoscopic quantum dot is proposed as a vehicle to realize a tunable Fermi-edge resonance with variable coupling strength. We solve the x-ray edge problem for a generic nonseparable scatterer and apply it to describe tunneling in a quantum dot. The tunneling current power law exponent is linked to the S matrix of the dot. The control of scattering by varying the dot shape and coupling to the leads allows us to explore a wide range of exponents. The sensitivity of mesoscopic coherence to the Wigner-Dyson ensemble symmetry is replicated in the Fermi-edge singularity.     

Fermi-edge singularities in AlxGa1-xAs quantum wells: extrinsic versus many-body scattering processes

A Fano resonance mechanism is evidenced to control the formation of optical Fermi-edge singularities in multisubband systems such as remotely doped AlxGa1-xAs heterostructures. Using Fano parameters, we probe the physical nature of the interaction between Fermi sea electrons and empty conduction subbands. We show that processes of extrinsic origin like alloy disorder prevail easily at 2D over multiple diffusions from charged valence holes expected by many-body scenarios.     

Low-temperature photoluminescence spectra of highly excited quantum wires

Optical spectra of highly excited quantum wires at low temperatures have been studied within the dynamical screening approximation. We found a strong Fermi-edge singularity (FES) in the photoluminescence spectra. The spectral shape and FES intensity strongly depend on temperature in agreement with recent experimental results.     

Many-body effects on intersubband resonances in narrow InAs/AlSb quantum wells

Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (QW) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons. The oscillator strength of intersubband resonances (ISBRs) strongly varies with QW parameters and electron density because of this coupling. Using the intersubband semiconductor Bloch equations for a two-conduction-subband model, we show that intersubband absorption spectra for narrow wells are dominated by the Fermi-edge singularity (via coupling to repellons) when the electron gas becomes degenerate and in the presence of large nonparabolicity. Thus the resonance peak position appears at the Fermi edge and the peak is greatly narrowed, enhanced, and red shifted as compared to the free particle result. Our results uncover a new perspective for ISBRs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBR line shape.     

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.     

Selection of dominant multi-exciton transitions in disordered linear J-aggregates

We show that the third-order optical response of disordered linear J-aggregates can be calculated by considering only a limited number of transitions between (multi-) exciton states. We calculate the pump-probe absorption spectrum resulting from the truncated set of transitions and show that, apart from the blue wing of the induced absorption peak, it agrees well with the exact spectrum.     

Optical absorption in degenerately doped semiconductors: Mott transition or Mahan excitons?

Electron doping turns semiconductors conductive even when they have wide fundamental band gaps. The degenerate electron gas in the lowest conduction-band states, e.g., of a transparent conducting oxide, drastically modifies the Coulomb interaction between the electrons and, hence, the optical properties close to the absorption edge. We describe these effects by developing an ab initio technique which captures also the Pauli blocking and the Fermi-edge singularity at the optical-absorption onset, that occur in addition to quasiparticle and excitonic effects. We answer the question whether free carriers induce an excitonic Mott transition or trigger the evolution of Wannier-Mott excitons into Mahan excitons. The prototypical n-type zinc oxide is studied as an example.     

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.     

Theoretical study of broadband near-field optical spectrum of twisted bilayer graphene

We theoretically study the broadband near-field optical spectrum of twisted bilayer graphene (TBG) at various twist angles near the magic angle using two different models. The spectrum at low Fermi energy is characterized by a series of peaks that are almost at the same energies as the peaks in the far-field optical conductivity of TBG. When the Fermi energy is near a van Hove singularity, an additional strong peak appears at finite energy in the near-field spectrum, which has no counterpart in the optical conductivity. Based on a detailed calculation of the plasmon dispersion, we show that these spectroscopic features are associated with interband and intraband plasmons, which can provide critical information about the local band structure and plasmonic excitations in TBG. The near-field peaks evolve systematically with the twist angle, so they can serve as fingerprints for identifying the spatial dependent twist angle in TBG samples. Our findings pave the way for future experimental studies of the novel optical properties of TBG in the nanoscale.     

Spin correlations in nonlinear optical response: light-induced Kondo effect

We study the role of spin correlations in nonlinear absorption due to transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons at the impurity leads to a logarithmic divergence in chi(3) at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump.