16 research outputs found
Dimensional reduction of the Luttinger-Ward functional for spin-degenerate -dimensional electron gases
We consider an isotropic spin-degenerate interacting uniform -dimensional
electron gas (DDEG) with within the Luttinger-Ward (LW) formalism. We
derive the asymptotically exact semiclassical/infrared limit of the LW
functional at large distances, , and large times, , where and are the Fermi wavelength and the Fermi
energy, respectively. The LW functional is represented by skeleton diagrams,
each skeleton diagram consists of appropriately connected dressed fermion
loops. First, we prove that every -dimensional skeleton diagram consisting
of a single fermion loop is reduced to a one-dimensional (1D) fermion loop with
the same diagrammatic structure, which justifies the name dimensional
reduction. This statement, combined with the fermion loop cancellation theorem
(FLCT), agrees with results of multidimensional bosonization. Here we show that
the backscattering and the spectral curvature, both explicitly violate the FLCT
and both are irrelevant for a 1DEG, become relevant at and ,
respectively. The reason for this is a strong infrared divergence of the
skeleton diagrams containing multiple fermion loops at . These diagrams,
which are omitted within the multidimensional bosonization approaches, account
for the non-collinear scattering processes. Thus, the dimensional reduction
provides the framework to go beyond predictions of the multidimensional
bosonization. A simple diagrammatic structure of the reduced LW functional is
another advantage of our approach. The dimensional reduction technique is also
applicable to the thermodynamic potential and various approximations, from
perturbation theory to self-consistent approaches.Comment: 15 pages, 4 figure
Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential
Copyright © 2014 American Physical SocietyWe analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.URCOEU FP7 ITN NOTEDEVFP7 IRSES project SPINMETFP7 IRSES project QOCaNFP7 IRSES project InterNo
Mechanisms for Strong Anisotropy of In-Plane g-Factors in Hole Based Quantum Point Contacts
In-plane hole g factors measured in quantum point contacts based on p-type heterostructures strongly
depend on the orientation of the magnetic field with respect to the electric current. This effect, first reported
a decade ago and confirmed in a number of publications, has remained an open problem. In this work, we
present systematic experimental studies to disentangle different mechanisms contributing to the effect and
develop the theory which describes it successfully. We show that there is a new mechanism for the
anisotropy related to the existence of an additional Bþk4
−σþ effective Zeeman interaction for holes, which is
kinematically different from the standard single Zeeman term B−k2
−σþ considered until now