## Small nanoclusters

My most recent research in area of nanoscience with my colleagues Dr. G. Fernando and K. Palandage from University of Connecticut and Dr. J. Davenport in Brookhaven Natioonal Laboratory is on electron pairing and formation of various types of magnetic correlations for ensembles of small clusters of different geometries are studied with emphasis on tetrahedrons and square pyramids under variation of interaction strength, electron doping and temperature. These exact calculations of charge and spin collective excitations and pseudogaps yield intriguing insights into level crossing degeneracies, phase separation and condensation. Obtained coherent and incoherent pairings provide a route for possible superconductivity different from the conventional BCS theory. Criteria for spin-charge separation, reconciliation and recombination driven by interaction strength, next-nearest coupling and temperature are found. Resulting phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen recently in high-Tc cuprates, manganites and colossal magnetoresistive (CMR) nanomaterials, assembled magnetic molecules. Small clusters display pseudogap behavior recently visualized in scanning tunelling microscopy (STM) measurements in high Tc cuprates at atomic scale.
A very basic bottom-line summary of this work is that by STM in spectroscopy mode – measuring tunneling current as a function of applied voltage for a specific site, one can probe electronic properties – for example superconducting or pseudo-gap with essentially atomic resolution. The information is similar to ARPES, but spatially resolved, rather than momentum resolved. The most fascinating discovery is that in BSCCO, which is the favorite compound for ARPES/STS and other surface-sensitive probes, the gap is not uniformly distributed, but rather shows some nanoscopic “patches”, as shown on the figure above. By using STM one could go several steps further and correlate dopants with the patchy gap distribution – for example gap is increased where dopant oxygen atoms are located. More recently they correlated gap with periodic “supermodulations” – distortions of the lattice. The implication here is that by changing the length of Cu-O bond (intersite coupling) in octahedron clusters of perovskite structure, one could conceivably increase the superconducting gap (and therefore Tc) to higher temperatures. The most intriguing (unpublished) results, in my opinion, are the measurements of d^{2}I/dV^{2} spectra (combined with O^{16 }and O^{18} isotope effect measurements) that indicate that the bosonic “glue” mediating the superconductivity at rather low temperatures may indeed be some sort of the BCS-like opposite spin pairing local in nature. However, in contrast to the BCS coherent pairing with a unique critical temperature the spin gap vanishes at superconducting temperature Tc, while electron charge pairing instability can exist above Tc. Indeed, the STM measurements give most definitive spectroscopic evidence that the material is a superconductor, even above the transition temperature, but one without the quantum phase coherence required for current to flow with no resistance.

These studies have also immediate application to the quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold fermionic atoms. For example, gaseous spinor Bose–Einstein condensates (whose atoms have non-zero internal angular momentum) are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. Here we explore spontaneous symmetry breaking on the ensemble of nanoclusters. For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here at cluster level we observe such a quantum phase transition in a Bose–Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase from a superfluid to a Mott insulator in a gas of coherence.. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum.