1,524 research outputs found
A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume
We study the localization volumes (participation ratio) of electronic
wave functions in the 2d-Anderson model with diagonal disorder. Using a
renormalization procedure, we show that at the band edges, i.e. for energies
, is inversely proportional to the variance \var of the
site potentials. Using scaling arguments, we show that in the neighborhood of
, scales as V=\var^{-1}g((4-\ve E\ve)/\var) with the scaling
function . Numerical simulations confirm this scaling ansatz
Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux
Absence of localization is demonstrated analytically to leading order in weak
disorder in a one-dimensional Anderson model of a ring threaded by an
Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier
perturbation treatment of disorder in a superconducting ring subjected to an
imaginary vector potential proportional to a depinning field for flux lines
bound to random columnar defects parallel to the axis of the ring. The absence
of localization in the ring threaded by an A-B flux for sufficiently weak
disorder is compatible with large free electron type persistent current
obtained in recent studies of the above model
Sufficient Conditions for Topological Order in Insulators
We prove the existence of low energy excitations in insulating systems at
general filling factor under certain conditions, and discuss in which cases
these may be identified as topological excitations. This proof is based on
previously proven locality results. In the case of half-filling it provides a
significantly shortened proof of the recent higher dimensional
Lieb-Schultz-Mattis theorem.Comment: 7 pages, no figure
The Complexity of Vector Spin Glasses
We study the annealed complexity of the m-vector spin glasses in the
Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of
the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a
continuous band of positive eigenvalues in addition to an isolated eigenvalue
and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly,
the band does not extend to zero at any finite temperature. The isolated
eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1),
indicating that the same supersymmetry breaking recently found in Ising spin
glasses occurs in vector spin glasses.Comment: 4 pages, 2 figure
Stability of the shell structure in 2D quantum dots
We study the effects of external impurities on the shell structure in
semiconductor quantum dots by using a fast response-function method for solving
the Kohn-Sham equations. We perform statistics of the addition energies up to
20 interacting electrons. The results show that the shell structure is
generally preserved even if effects of high disorder are clear. The Coulomb
interaction and the variation in ground-state spins have a strong effect on the
addition-energy distributions, which in the noninteracting single-electron
picture correspond to level statistics showing mixtures of Poisson and Wigner
forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.
Bosons in one-dimensional incommensurate superlattices
We investigate numerically the zero-temperature physics of the
one-dimensional Bose-Hubbard model in an incommensurate cosine potential,
recently realized in experiments with cold bosons in optical superlattices L.
Fallani et al., Phys. Rev. Lett. 98, 130404, (2007)]. An incommensurate cosine
potential has intermediate properties between a truly periodic and a fully
random potential, displaying a characteristic length scale (the quasi-period)
which is shown to set a finite lower bound to the excitation energy of the
system at special incommensurate fillings. This leads to the emergence of
gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass
(BG) phases for strong quasi-periodic potential, both for hardcore and softcore
bosons. Enriching the spatial features of the potential by the addition of a
second incommensurate component appears to remove the IBI regions, stabilizing
a continuous BG phase over an extended parameter range. Moreover we discuss the
validity of the local-density approximation in presence of a parabolic trap,
clarifying the notion of a local BG phase in a trapped system; we investigate
the behavior of first- and second-order coherence upon increasing the strength
of the quasi-periodic potential; and we discuss the ab-initio derivation of the
Bose-Hubbard Hamiltonian with quasi-periodic potential starting from the
microscopic Hamiltonian of bosons in an incommensurate superlattice.Comment: 22 pages, 28 figure
Realistic model of correlated disorder and Anderson localization
A conducting 1D line or 2D plane inside (or on the surface of) an insulator
is considered.Impurities displace the charges inside the insulator. This
results in a long-range fluctuating electric field acting on the conducting
line (plane). This field can be modeled by that of randomly distributed
electric dipoles. This model provides a random correlated potential with
decaying as 1/k . In the 1D case such correlations give essential
corrections to the localization length but do not destroy Anderson
localization
Topological winding properties of spin edge states in Kane-Mele graphene model
We study the spin edge states in the quantum spin-Hall (QSH) effect on a
single-atomic layer graphene ribbon system with both intrinsic and Rashba
spin-orbit couplings. The Harper equation for solving the energies of the spin
edge states is derived. The results show that in the QSH phase, there are
always two pairs of gapless spin-filtered edge states in the bulk energy gap,
corresponding to two pairs of zero points of the Bloch function on the
complex-energy Riemann surface (RS). The topological aspect of the QSH phase
can be distinguished by the difference of the winding numbers of the spin edge
states with different polarized directions cross the holes of the RS, which is
equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys.
Rev. Lett. 95, 146802 (2005)].Comment: 9 pages, 10 figure
- …