Tunable Fermi-edge resonance in an open quantum dot

Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(1+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.

Microscopic theory of resonant soft-x-ray scattering in materials with charge order: the example of charge stripes in high-temperature cuprate superconductors

We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.

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.

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.

S-matrix formulation of mesoscopic systems and evanescent modes

Validity of the Landauer-Buttiker formalism for studying linear transport in mesoscopic systems is well established theoretically as well as experimentally. Akkermans et al (1991 Phys. Rev. Lett. 66 76) have shown that the formalism can be extended to study thermodynamic properties like persistent currents. This extension was verified for simple one-dimensional systems. We study the applicability of Akkermans et al' s formula for quasi-one-dimensional systems with several conducting channels. In the case that all modes are propagating the formula is still valid but in the case of evanescent modes it requires reinterpretation.

Polarization of a charge qubit strongly coupled to a voltage-driven quantum point contact

We study a charge qubit with level splitting epsilon, coupled to a quantum point contact driven by voltage V. In the limit of weak coupling, the qubit polarization shows cusps at epsilon=+/-eV. We show that, for stronger couplings, prominent peculiarities occur at fractions epsilon=+/-eV/2. Further increase of the coupling leads to a polarization corresponding to a pseudo Boltzmann distribution with an effective temperature approximately eV.

Tunneling exponents sensitive to impurity scattering in quantum wires

We show that the scaling exponent for tunneling into a quantum wire in the "Coulomb Tonks gas" regime of impenetrable, but otherwise free, electrons is affected by impurity scattering in the wire. The exponent for tunneling into such a wire thus depends on the conductance through the wire. This striking effect originates from a many-body scattering resonance reminiscent of the Kondo effect. The predicted anomalous scaling is stable against weak perturbations of the ideal Tonks gas limit at sufficiently high energies, similar to the phenomenology of a quantum critical point.

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.