77 research outputs found
D-Wave Superconductors near Surfaces and Interfaces: A Scattering Matrix Approach within the Quasiclassical Technique
A recently developed method [A. Shelankov and M. Ozana, Phys. Rev. B 61, 7077
(2000)] is applied to investigate d-wave superconductors in the vicinity of
(rough) surfaces. While this method allows the incorporation of arbitrary
interfaces into the quasiclassical technique, we discuss, as examples,
diffusive surfaces and boundaries with small tilted mirrors (facets). The
properties of the surface enter via the scattering matrix in the boundary
condition for the quasiclassical Green's function. The diffusive surface is
described by an ensemble of random scattering matrices. We find that the
fluctuations of the density of states around the average are small; the zero
bias conductance peak broadens with increasing disorder. The faceted surface is
described in the model where the scattering matrix couples m in- and m
out-trajectories (m>=2). No zero bias conductance peak is found for [100]
surfaces; the relation to the model of Fogelstrom et al. [Phys. Rev. Lett. 79,
281 (1997)] is discussed.Comment: RevTeX, 19 pages, 18 figure
Non-Equilibrium Quasiclassical Theory for Josephson Structures
We present a non-equilibrium quasiclassical formalism suitable for studying
linear response ac properties of Josephson junctions. The non-equilibrium
self-consistency equations are satisfied, to very good accuracy, already in
zeroth iteration. We use the formalism to study ac Josephson effect in a
ballistic superconducting point contact. The real and imaginary parts of the ac
linear conductance are calculated both analytically (at low frequencies) and
numerically (at arbitrary frequency). They show strong temperature, frequency,
and phase dependence. Many anomalous properties appear near phi = pi. We
ascribe them to the presence of zero energy bound states.Comment: 11 pages, 9 figures, Final version to appear in PR
Thermodynamics of a d-wave Superconductor Near a Surface
We study the properties of an anisotropically paired superconductor in the
presence of a specularly reflecting surface. The bulk stable phase of the
superconducting order parameter is taken to have symmetry.
Contributions by order parameter components of different symmetries vanish in
the bulk, but may enter in the vicinity of a wall. We calculate the
self-consistent order parameter and surface free energy within the
quasiclassical formulation of superconductivity. We discuss, in particular, the
dependence of these quantities on the degree of order parameter mixing and the
surface to lattice orientation. Knowledge of the thermodynamically stable order
parameter near a surface is a necessary precondition for calculating measurable
surface properties which we present in a companion paper.Comment: 12 pages of revtex text with 12 compressed and encoded figures. To
appear in J. Low Temp. Phys., December, 199
ac Josephson effect in superconducting d-wave junctions
We study theoretically the ac Josephson effect in superconducting planar
d-wave junctions. The insulating barrier assumed to be present between the two
superconductors may have arbitrary strength. Many properties of this system
depend on the orientation of the d-wave superconductor: we calculate the ac
components of the Josephson current. In some arrangements there is substantial
negative differential conductance due to the presence of mid-gap states. We
study how robust these features are to finite temperature and also comment on
how the calculated current-voltage curves compare with experiments. For some
other configurations (for small barrier strength) we find zero-bias conductance
peaks due to multiple Andreev reflections through midgap states. Moreover, the
odd ac components are strongly suppressed and even absent in some arrangements.
This absence will lead to a doubling of the Josephson frequency. All these
features are due to the d-wave order parameter changing sign when rotated
. Recently, there have been several theoretical reports on parallel
current in the d-wave case for both the stationary Josephson junction and for
the normal metal-superconductor junction. Also in our case there may appear
current density parallel to the junction, and we present a few examples when
this takes place. Finally, we give a fairly complete account of the method used
and also discuss how numerical calculations should be performed in order to
produce current-voltage curves
Effects of gap anisotropy upon the electronic structure around a superconducting vortex
An isolated single vortex is considered within the framework of the
quasiclassical theory. The local density of states around a vortex is
calculated in a clean type II superconductor with an anisotropy. The anisotropy
of a superconducting energy gap is crucial for bound states around a vortex. A
characteristic structure of the local density of states, observed in the
layered hexagonal superconductor 2H-NbSe2 by scanning tunneling microscopy
(STM), is well reproduced if one assumes an anisotropic s-wave gap in the
hexagonal plane. The local density of states (or the bound states) around the
vortex is interpreted in terms of quasiparticle trajectories to facilitate an
understanding of the rich electronic structure observed in STM experiments. It
is pointed out that further fine structures and extra peaks in the local
density of states should be observed by STM.Comment: 11 pages, REVTeX; 20 PostScript figures; An Animated GIFS file for
the star-shaped vortex bound states is available at
http://mp.okayama-u.ac.jp/~hayashi/vortex.htm
Zero-modes in the random hopping model
If the number of lattice sites is odd, a quantum particle hopping on a
bipartite lattice with random hopping between the two sublattices only is
guaranteed to have an eigenstate at zero energy. We show that the localization
length of this eigenstate depends strongly on the boundaries of the lattice,
and can take values anywhere between the mean free path and infinity. The same
dependence on boundary conditions is seen in the conductance of such a lattice
if it is connected to electron reservoirs via narrow leads. For any nonzero
energy, the dependence on boundary conditions is removed for sufficiently large
system sizes.Comment: 12 pages, 11 figure
Theory of charge transport in diffusive normal metal / unconventional singlet superconductor contacts
We analyze the transport properties of contacts between unconventional
superconductor and normal diffusive metal in the framework of the extended
circuit theory. We obtain a general boundary condition for the Keldysh-Nambu
Green's functions at the interface that is valid for arbitrary transparencies
of the interface. This allows us to investigate the voltage-dependent
conductance (conductance spectrum) of a diffusive normal metal (DN)/
unconventional singlet superconductor junction in both ballistic and diffusive
cases. For d-wave superconductor, we calculate conductance spectra numerically
for different orientations of the junctions, resistances, Thouless energies in
DN, and transparencies of the interface. We demonstrate that conductance
spectra exhibit a variety of features including a -shaped gap-like
structure, zero bias conductance peak (ZBCP) and zero bias conductance dip
(ZBCD). We show that two distinct mechanisms: (i) coherent Andreev reflection
(CAR) in DN and (ii) formation of midgap Andreev bound state (MABS) at the
interface of d-wave superconductors, are responsible for ZBCP, their relative
importance being dependent on the angle between the interface normal
and the crystal axis of d-wave superconductors. For , the ZBCP is due
to CAR in the junctions of low transparency with small Thouless energies, this
is similar to the case of diffusive normal metal / insulator /s-wave
superconductor junctions. With increase of from zero to , the
MABS contribution to ZBCP becomes more prominent and the effect of CAR is
gradually suppressed. Such complex spectral features shall be observable in
conductance spectra of realistic high- junctions at very low temperature
Theory of charge transport in diffusive normal metal / conventional superconductor point contacts
Tunneling conductance in diffusive normal metal / insulator / s-wave
superconductor (DN/I/S) junctions is calculated for various situations by
changing the magnitudes of the resistance and Thouless energy in DN and the
transparency of the insulating barrier. The generalized boundary condition
introduced by Yu. Nazarov [Superlattices and Microstructures 25 1221 (1999)] is
applied, where the ballistic theory by Blonder Tinkham and Klapwijk (BTK) and
the diffusive theory by Volkov Zaitsev and Klapwijk based on the boundary
condition of Kupriyanov and Lukichev (KL) are naturally reproduced. It is shown
that the proximity effect can enhance (reduce) the tunneling conductance for
junctions with a low (high) transparency. A wide variety of dependencies of
tunneling conductance on voltage bias is demonstrated including a -shaped
gap like structure, a zero bias conductance peak (ZBCP) and a zero bias
conductance dip (ZBCD)
Traffic and Related Self-Driven Many-Particle Systems
Since the subject of traffic dynamics has captured the interest of
physicists, many astonishing effects have been revealed and explained. Some of
the questions now understood are the following: Why are vehicles sometimes
stopped by so-called ``phantom traffic jams'', although they all like to drive
fast? What are the mechanisms behind stop-and-go traffic? Why are there several
different kinds of congestion, and how are they related? Why do most traffic
jams occur considerably before the road capacity is reached? Can a temporary
reduction of the traffic volume cause a lasting traffic jam? Under which
conditions can speed limits speed up traffic? Why do pedestrians moving in
opposite directions normally organize in lanes, while similar systems are
``freezing by heating''? Why do self-organizing systems tend to reach an
optimal state? Why do panicking pedestrians produce dangerous deadlocks? All
these questions have been answered by applying and extending methods from
statistical physics and non-linear dynamics to self-driven many-particle
systems. This review article on traffic introduces (i) empirically data, facts,
and observations, (ii) the main approaches to pedestrian, highway, and city
traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and
macroscopic (fluid-dynamic) models. Attention is also paid to the formulation
of a micro-macro link, to aspects of universality, and to other unifying
concepts like a general modelling framework for self-driven many-particle
systems, including spin systems. Subjects such as the optimization of traffic
flows and relations to biological or socio-economic systems such as bacterial
colonies, flocks of birds, panics, and stock market dynamics are discussed as
well.Comment: A shortened version of this article will appear in Reviews of Modern
Physics, an extended one as a book. The 63 figures were omitted because of
storage capacity. For related work see http://www.helbing.org
- …