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Register a new userFermiology via the electron momentum distribution
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Authors
G. Kontrym-Sznajd
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Investigations of the Fermi surface via the electron momentum distribution reconstructed from either angular correlation of annihilation radiation (or Compton scattering) experimental spectra are presented. The basis of these experiments and mathematical methods applied in reconstructing three-dimensional densities from line (or plane) projections measured in these experiments are described. The review of papers where such techniques have been applied to study the Fermi surface of metallic materials with showing their main results is also done.
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The unoccupied states of complex materials are difficult to measure, yet play a key role in determining their properties. We propose a technique that can measure the unoccupied states, called time-resolved Compton scattering, which measures the time-dependent momentum distribution (TDMD). Using a non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a lattice in a pump-probe setup. We find a direct relation between temporal oscillations in the TDMD and the dispersion of the underlying unoccupied states, suggesting that both can be measured by time-resolved Compton scattering. We demonstrate the experimental feasibility by applying the method to a model of MgB$_2$ with realistic material parameters.
We investigate the electron momentum distribution function (EMD) in a weakly doped two-dimensional quantum antiferromagnet (AFM) as described by the t-J model. Our analytical results for a single hole in an AFM based on the self-consistent Born approximation (SCBA) indicate an anomalous momentum dependence of EMD showing hole pockets coexisting with a signature of an emerging large Fermi surface. The position of the incipient Fermi surface and the structure of the EMD is determined by the momentum of the ground state. Our analysis shows that this result remains robust in the presence of next-nearest neighbor hopping terms in the model. Exact diagonalization results for small clusters are with the SCBA reproduced quantitatively.
Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite- size errors. In the case of Quantum-Monte-Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real-space and momentum-space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surface-like systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and, hence, better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.
The electronic conductance of a molecule making contact to electrodes is determined by the coupling of discrete molecular states to the continuum electrode density of states. Interactions between bound states and continua can be modeled exactly by using the (energy-dependent) self-energy, or approximately by using a complex potential. We discuss the relation between the two approaches and give a prescription for using the self-energy to construct an energy-independent, non-local, complex potential. We apply our scheme to studying single-electron transmission in an atomic chain, obtaining excellent agreement with the exact result. Our approach allows us to treat electron-reservoir couplings independent of single electron energies, allowing for the definition of a one-body operator suitable for inclusion into correlated electron transport calculations.
We have carried out a study of the momentum distribution and of the spectrum of elementary excitations of liquid $^4$He across the normal-superfluid transition temperature, using the path integral Monte Carlo method. Our results for the momentum distribution in the superfluid regime show that a kink is present in the range of momenta corresponding to the roton excitation. This effect disappears when crossing the transition temperature to the normal fluid, in a behavior currently unexplained by theory.
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