Short-range order in linear binary alloys: Delocalization of states versus memory
of ordered band structures
R. Rey-Gonzalez and P. A. Schulz
Instituto de Fı ´sica Gleb Wataghin, Universidade/Estadual de Campinas, 13083-970 Campinas, Sa ˜ o Paulo, Brazil
Received 15 February 1996
We discuss the electronic properties of a one-dimensional tight-binding model for binary alloys with corre-
lated disorder. The correlation inhibits the bonds between atoms of one of the atomic species, leading to what
is called repulsive binary alloys. As it is well known, the transmission probability of repulsive binary alloys
shows resonances due to the delocalization of states in this peculiar disordered one-dimensional system. We
show that this delocalization can be related to the memory of the band structures of different ordered chains,
since short segments of these ordered chains constitute the repulsive binary alloy. This memory effect is
revealed in the localization length as a function of energy. The same argument is used to show that competing
correlations in the same linear chain destroy delocalization, as can be inferred from the properties of binary
alloys with no correlations at all. We also show that, complementary to delocalized bands, smooth transmission
gaps should also exist at specific energy ranges only for correlated disorder cases. S0163-18299610133-8
I. INTRODUCTION
Disordered one-dimensional 1D systems, exhibiting
nontrivial extended states, have been investigated theoreti-
cally in the past few years.
1–11
It has been shown that the
existence of extended states is a consequence of introducing
short-range correlations on the disorder. The correlations
considered are constraints to the site neighborhood in binary
alloys. These results opened an interesting scenario, since the
framework introduced by the Anderson model
12
has been
widened. The usefulness in this new scenario lies in the new
possibilities of understanding some transport properties in
polymers,
4,13–15
as well as the general interest in having a
one-dimensional model which intrinsically exhibits mobility
edges. It should also be mentioned that linear chains with
correlated disorder are strongly related to some quasiperiodic
and aperiodic systems that show similar delocalization
effects.
16–19
A prototype example of the situation where delocalization
of states in 1D disordered chains occurs is the so-called bi-
nary repulsive alloy. The repulsive binary alloy model has
been suggested by Dunlap, Wu, and Phillips
2
and has been
used to analyze transport mechanisms in polyanilines.
15
Con-
sidering a binary random alloy, the bond between one of the
atomic species is inhibited, thus introducing the above-
mentioned short-range order. In other words, in a chain of A
and B sites, only A - A and A - B nearest-neighbor bonds are
allowed. The introduction of this short-range order leads to
delocalization of states in the disordered chain, provided that
the hopping between A and B sites is different from the
hopping between A sites. Hence, the B sites, viewed as im-
purities in a host A -site chain, must have an internal structure
in order to show resonances in the transmission probabilities.
Having in mind a tight-binding framework, this internal
structure for the repulsive binary alloy implies introducing
off-diagonal disorder. Other variations for disorder correla-
tions have been discussed in the literature. The first, and
most discussed, is the random dimer model, where the inter-
nal structure of the impurities is provided by the fact that the
impurities now are dimers of B atoms. In this case the hop-
ping between different site species can be taken to be the
same, suppressing the off-diagonal disorder and delocaliza-
tion still may occur. In the present work we analyze the
electronic structure of finite chains of repulsive binary alloys
which are naturally described by a tight-binding model, con-
sidering one s -like orbital per atomic site. Our aim is to
relate the delocalization mechanism with the memory of the
electronic band structure of ordered binary alloys that persist
in the disordered counterparts, disregarding the presence of
correlation or not.
II. MODEL
The tools we use in our work are the calculation of trans-
mission probabilities and localization lengths, as well as
probability densities along the chains. We begin by ‘‘charac-
terizing’’ finite disordered linear chains connected to ordered
semi-infinite contact chains. This is the usual configuration
finite segments connected to ordered contacts to obtain in-
formation about the electronic structure via the transmission
probability of the finite chain segment considered. The
method to calculate the transmission probability of this sys-
tem, starting from a tight-binding Hamiltonian
H =
n
n
| n n | +V
n , n +1
| n n +1 | +V
n +1,n
| n +1 n | ,
1
is described elsewhere.
15
The atomic site energies used throughout this work are
A
=0.3 eV host chain and
B
=-0.3 eV. The bonding be-
tween A -like and B -like sites is represented by the hopping
parameter V
AB
=0.3 eV. For the hopping between A -like
sites V
AA
=0.8 eV is taken. For chains without bond con-
straints uncorrelated disorder, the allowed hopping between
B -like sites is taken as V
BB
=0.5 eV. These parameters are
taken from a previous work,
15
where a specific situation re-
PHYSICAL REVIEW B 1 SEPTEMBER 1996-II VOLUME 54, NUMBER 10
54 0163-1829/96/5410/71036/$10.00 7103 © 1996 The American Physical Society