Optical Fermi-edge singularities in a one-dimensional electron system with tunable effective mass

Singular responses of spin-incoherent Luttinger liquids

When a local potential changes abruptly in time, an electron gas responds by shifting to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called x-ray edge or Fermi-edge singularity, and for tunneling into an interacting one-dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: [Formula: see text], where ω(th) is a threshold frequency and α is an exponent characterizing the singular response. In this review singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.

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.