6 Impurity Nanostructures and Quantum Interference 227
screening of the Co atom located in the focus of
the corral through the formation of a Kondo reso-
nance in the Cu LDOS. In addition,they found that a
quantum image of the Kondo resonance was formed
in the empty focus. This projection of the Kondo
resonance from the occupied into the empty focus
utilized the specific spatial form of the corral’s low
energy electronic eigenmodes. As shown in detail
in a number of interesting theoretical studies [52],
these eigenmodes were created by quantum inter-
ference of electronic waves that are scattered off
the corral wall’s Co atoms (for a recent review, see
[53]). This experiment beautifully demonstrated that
quantum interference of electronic waves can be uti-
lized for “custom-designing” exciting new quantum
phenomena. Further examples of nanostructures
which exhibit a variety of intriguingquantum effects
include triangular [49] and ferromagnetic [50, 51]
quantum corrals, optical quantum corrals [54–56],
and interacting Kondo impurities [57–59].
In this chapter, we discuss a series of exciting
quantum phenomena at the intersection of the three
fields discussed above by studying the effects of or-
dered nanoscale impurity structures and molecules
on the local electronic structure of superconductors.
It is the interplay between quantum interference and
the nature of the superconducting correlations that
is responsible for the emergence of novel quantum
effects ranging from unconventional quantum imag-
ing,“optical” selection rules and the reversal of pair-
breaking effects to a zero-bias conductance peak,the
screening of impurity states, quantum interference
induced quantum phase transitions, and new pos-
sibilities for manipulating a superconductor’s local
electronic structure. Conventional and unconven-
tional superconductors each possess unique prop-
erties that are essential for the emergence of these
effects. For example, the formation of a fermionic
boundstatearounda magnetic impurity in an s-wave
superconductor provides a new “quantum candle”
(i.e.,a characteristic signature in the LDOS viz.peaks
inside the superconducting gap) for quantum imag-
ing. In addition, the qualitatively different effect of
magnetic and non-magnetic impurities on the local
electronic structure permits the study of quantum
interference effects separately from the formation of
fermionic impurity states. Furthermore, the possi-
bility to tune an s-wave superconductors through a
first order phase transition in which its ground state
spin polarization changes [11, 14, 24, 60] opens the
possibility to study quantum interference induced
phase transitions [61,62]. On the other hand, uncon-
ventional superconductors give rise to novel types
of quantum interference effects due to the momen-
tum dependence of their order parameter. The in-
terplay between this momentum dependence and
the geometry and orientation of a nanoscale im-
purity structure leads to destructive or construc-
tive quantum interference and the possibility to
screen impurity states and to identify the sym-
metry of unconventional superconductors in gen-
eral.
The first observation of quantum interference
effects in the high-temperature superconductor
YBa
2
Cu
3
O
6+x
was recently reported in STM exper-
iments by Derro et al. [63] who studied the LDOS
of the CuO chains. They observed two important
results below T
c
: first, a gap exists in the LDOS of
the CuO chains, and second, several fermionic reso-
nances exist inside the gap. Specifically, they found
two hole-likeandtwo particle-likepeaksintheLDOS
at symmetric energies, ±6meVand±13 meV. Since
a singleimpurity ingeneral gives rise toone particle-
like and one hole-like peak in the LDOS only, it was
suggested [61] that the observed two pairs of peaks
arise from quantum interference between two oxy-
gen defect sites in the chains. This simple (two im-
purity) nanostructure gives rise to a hybridization
of the impurity states and the formation of bond-
ing and antibonding resonance with a resulting four
peak structure in the LDOS. Quantum interference
effects were also recently investigated by McElroy et
al. [64], Howald et al. [65] and Vershinin et al. [66]
who studied Friedel-like oscillations in the LDOS of
the cuprate superconductor Bi
2
Sr
2
CaCuO
8+ı
. These
oscillations arise from quantum interference due to
spatially random and weakly scattering impurities.
It was shown that the combined momentum and fre-
quency dependence of these oscillations in the super-
conducting state provides insight into the electronic
structure of this complex material, and in particular,
into the form of its normal state Fermi surface [64]