Fermi-edge singularity of the Tomonaga-Luttinger liquids with spin-split Fermi points

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.

Quantum condensation in electron-hole systems: excitonic BEC-BCS crossover and biexciton crystallization

Quantum condensation of electron-hole (e-h) systems in photoexcited semiconductors is reviewed from a theoretical viewpoint, stressing the exciton Bose-Einstein condensation (BEC), the e-h BCS-type condensed state, the exciton Mott transition, and the biexciton crystallization. First, we discuss the crossover between the exciton BEC and the e-h BCS states at low temperature using the self-consistent t-matrix and local approximations, applied to the high-dimensional two-band Hubbard model with both repulsive and attractive on-site interactions. We also study the metal-insulator transition (called the 'exciton Mott transition') at zero and finite temperatures, investigated with the dynamical mean-field theory. Away from half-filling we find excitonic/biexcitonic insulating phases and the first-order transition between metallic and insulating states. Second, in a one-dimensional e-h system, we employ the exciton bosonization and renormalization-group techniques to clarify quantum orders at zero temperature. The most probable ground state exhibits the biexciton crystallization, which reflects the Tomonaga-Luttinger liquid properties, the e-h backward scattering, and the long-range Coulomb interaction. The one-dimensional e-h system is insulating even at the high-density limit, hence the exciton Mott transition never occurs at zero temperature in one dimension.

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.