Quantum impurities in twodimensional antiferromagnets and dwave
superconductors
A very large number of recent experiments have studied the consequences
of replacing the magnetic Cu ions in various correlated electron systems
by nonmagnetic Zn or Li ions. Unlike the Cu ions they replace, the nonmagnetic
impurity ions have no active unpaired d electron with a fluctuating
spin, and so each impurity effectively creates a static hole in a background
of fluctuating spins: this turns out to be an exquisitely sensitive probe
of the spin wavefunction of the original system and an important playground
for the confrontation of theory and experiment. In the high temperature
superconductors, there is very strong evidence that each nonmagnetic impurity
ion actually binds a net S=1/2 moment of Cu spins in its vicinity:
this is most directly evident from sitespecific NMR experiments which
have now been carried out at very low temperatures within the superconducting
phase (J. Bobroff et al condmat/0010234).
We have argued that this moment formation implies that
the high temperature superconductors are best understood as doped Mott
insulators with confinement of S=1/2 excitations in the Mott
insulating state . Such confining Mott insulators are discussed under a separate category, and we can use similar cartoon pictures to understand the confinement of a S=1/2 near each nonmagnetic impurity.
Confinement of a moment near a nonmagnetic impurity in a confining Mott insulator. The X's represent the nonmagnetic ion. In the top picture, we sketch a trial wavefunction for the ground state within the subspace of shortrange singlet bonds: there is a line of defect bonds which costs additional energy per unit length. Eventually the system will prefer to break a singlet bond and create free S=1/2 spins near each impurity, as in the lower picture. See also the cartoon pictures of states without impurities .
The Mott insulator above has a broken translational symmetry associated with bond order.
This order is expected to survive for a finite range of doping, and experimental evidence for such
ordering is discussed under a separate category. The quantum transition where translational symmetry is restored need not coincide with the transition where the moment is eventually screened by the S=1/2
fermionic quasiparticles.
These ideas have been reviewed in a nontechnical manner in paper 6.
This picture has also allowed us to develop quantitative theories
of neutron scattering (H.F. Fong et al, Physical Review Letters 82,
1939 (1999) and Y. Sidis et al, Physical Review Letters 84, 5900
(2000)) and Scanning Tunneling Microscopy (E.W. Hudson et al, Science
285,
88 (1999), S.H. Pan et al, Nature 403, 746 (2000)) experiments
of Zn/Li/Ni impurities, and the results are in good accord with the experiments.
PAPERS

Quantum impurity in a nearlycritical two dimensional
antiferromagnet, S. Sachdev, C. Buragohain, and M. Vojta, Science 286,
2479 (1999); condmat/0004156.

Quantum impurity dynamics in twodimensional antiferromagnets
and superconductors, M. Vojta, C. Buragohain, and S. Sachdev, Physical
Review B 61, 15152 (2000); condmat/9912020.

Impurity spin dynamics in 2D antiferromagnets and superconductors,
M. Vojta, C. Buragohain. and S. Sachdev, Proceedings of the M2SHTSCVI
conference, Physica C 341348, 327 (2000); condmat/0002316.

Damping
of collective modes and quasiparticles in dwave superconductors, S.
Sachdev and M. Vojta, New Theoretical Approaches to Strongly Correlated
Systems, NATO ASI Series, Kluwer Academic, Dordrecht (2000);
condmat/0005250.

Static hole in a critical antiferromagnet:
fieldtheoretic renormalization group,
S. Sachdev, Physica C 357, 78
(2001);
condmat/0011233.

Impurity in a dwave superconductor: Kondo effect
and STM spectra, A. Polkovnikov, S. Sachdev, and M. Vojta, Physical Review Letters 86, 296 (2001);
condmat/0007431.

Nonmagnetic impurities as probes of insulating and
doped Mott insulators in two dimensions, S. Sachdev and M. Vojta,
Proceedings of the XIII International Congress on Mathematical Physics,
July 2000, London, A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski eds, International Press, Boston (2001); condmat/0009202.

Spin and charge order in Mott insulators and dwave
superconductors, S. Sachdev, Journal of Physics and Chemistry of Solids 63, 2269 (2002); condmat/0108238.

Quantum impurity in an antiferromagnet: nonlinear sigma model theory, S. Sachdev, and M. Vojta, Physical Review B 68, 064419 (2003);
condmat/0303001.

Quantum impurity in a magnetic environment, S. Sachdev, Proceedings
of the conference on Field Theory and Statistical Mechanics, Rome, June 2002 in honor of G. JonaLasinio, Journal of Statistical Physics 115, 47 (2004); condmat/0304171.
 Theory of quantum impurities in spin liquids, A. Kolezhuk, S. Sachdev, R. R. Biswas, and P. Chen, Physical Review B 74, 165114 (2006); condmat/0606385.
 Impurity induced spin texture in quantum critical 2D antiferromagnets,
K. H. Hoglund, A. W. Sandvik, and S. Sachdev, Physical Review Letters 98, 087203 (2007); condmat/0611418.
 Impurity spin textures across conventional and deconfined quantum critical points of
twodimensional antiferromagnets, M. A. Metlitski and S. Sachdev, Physical Review B 76, 064423 (2007); condmat/0703790.
 Valence bond solid order near impurities in twodimensional quantum antiferromagnets, M. A. Metlitski and S. Sachdev,
Physical Review B 77, 054411 (2008); arXiv:0710.0626.
 Imaging bond order near nonmagnetic impurities in square lattice antiferromagnets, R. K. Kaul, R. G. Melko, M. A. Metlitski, and
S. Sachdev, Physical Review Letters 101, 187206 (2008);
arXiv:0808.0495.
 Edge and impurity response in twodimensional quantum antiferromagnets, M. A. Metlitski, and
S. Sachdev, Physical Review B 78, 174410 (2008);
arXiv:0808.0496.
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