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Cal State L.A.


Dr. Armen Kocharian


"Relativity applies to physics, not ethics"

Nanoscience - Bottom up approach

Pairing instabilities found from exact diagonalization of Hubbard nanoclusters in different bipartite and non-bipartite topologies provide novel insights into the several mysterious many body problems in condensed matter physics. Exact solution displays the mechanism of spontaneous phase separation, pairing instabilities and inhomogeneities in Hubbard nanoclusters. Rigorous Nagaoka type criteria in finite size small clusters reveal also spin charge separation and recombination driven by interaction strength, inter-site couplings, electron concentration, magnetic flux and temperature. The calculated phase diagrams in the ground state and finite temperatures display level crossing and a number of inhomogeneous paired phases, superconductivity, ferromagnetism and ferroelectricity, found in ultra small vanadium, niobium, cobalt and other nanoparticles, which provide further support for possible role of local on-site electron correlations in the origin of electron pairing, spin charge separation, inhomogeneities in assembled clusters and nanoparticles. Moreover, the thermodynamic phase diagrams also are remarkably similar to the properties of inhomogeneous bulk (perovskite) concentrated materials such as high temperature superconductors, manganites, magnetoelectric, multiferroic and heterostructured nanomaterials probed by scanning tunneling spectroscopy. Away from half filling in low and high spin regions we found superconductivity, ferromagnetism, phase separation, coherent and incoherent pairings and local inhomogeneities, surprisingly similar to pair modulation and phases in the family of doped HTSC cuprates, manganites, mulltiferroics, various nanomaterials and ultracold fermionic atoms.

Small nanoclusters

Entry photo exampleMy 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 d2I/dV2 spectra (combined with O16 and O18 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.


Electronic Structure


Our main interest has been the electronic structure calculations and physical properties of solids, surfaces and interfaces that provide us information pertaining to the ground state electronic and magnetic structures, surface and interface induced changes etc. We use to study the bewildering variety of phases in condensed-matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several examples. We discuss elementary excitations and incommensurate phases to find out analogy between the mean field Hamiltonians with attractive and repulsive electron-electron interactions. We have employed these basis approaches in the past for studies of the electronic or electron-hole instabilities and phase transitions of the first and second order in different anomalous rare-earth and transition metal compounds from classical critical phenomena to quantum phase transitions driven by pressure, temperature and composition of material. Also, there are fundamental problems that have to be addressed and made computationally efficient. As an example, although the mean field (MF) approach has been quite successful with respect to the ground state properties, improvements beyond MF such as better treatments of correlations and computationally efficient ways of handling the single electron spectrum and electronic structure problem are necessary, especially when studying correlated electron systems at finite temperatures, magnetic field or (real) materials with non local interactions. These calculations use a basis set to expand a one electron wave function and are based on the unrestricted mean field calculations and local (spin) density approximation (L(S)DA) by including the effects of random phase approximation.

Exact and Self-consistent studies

Exact and self

We explore the question whether the self-consistent field approach, which commonly applied to higher dimensions, can properly describe the single particle spectrum and ground state properties of 1d system, such as a Luttinger or Fermi liquid. We test the developed generalized self-consistent field (GSCF) approach for attractive and repulsive Hubbard model by comparison of its predictions with the Bethe-ansatz. We also analyze the GSCF spectrum and the relation between the incommensurate parameter q and corresponding exact momentum within the Luttinger theorem and asymptotic of the correlation function. Our studies show that there is no principle differences for the self-consistent treatment of both U>0 and U<0 models with electron-electron and electron-hole instabilities as a signature for the presence or absence of a normal Fermi liquid behavior. It is difficult to assess the reliability of the resulting approximations in the perturbation theory for general interaction strength. However in the GSCF approach for all n in the extreme cases of small and large U/t limits becomes exact (results coincide with the Bethe-ansatz one) and therefore corresponding fluctuations around the GSCF solution are small. The calculated second order perturbation correction to the ground state energy near the GSCF solution converges to the exact solution everywhere. We developed dynamical self-consistent perturbation theory around the self-consistent solution is similar to that derived within the free Fermi gas approach in the weak interaction limit. Obtained results in entire range of U/t, n and h show significant improvements over the standard perturbation theory and the GSCF results. This approach gives also insight into a single-particle picture within 1d Hubbard model.

Problems Addressed

Problems Addressed

Research is dedicated to a wide range of subjects in the general area of strongly correlated electron systems, quantum fluids and solids. Characteristics of materials been investigated in extreme conditions of high temperature, pressure and strong magnetic field. Systems currently being explored include high temperature superconductors, various unusual magnetic materials, strongly correlated f-electron materials, materials in confined geometric configurations such as one and quasi-one-dimensional systems, the two dimensional planar surfaces and nanocrystals, interplay of quantum disorder and thermal fluctuations, classical and quantum magnetism, superfluity. Some basic problems in condensed matter physics that we have addressed using the above mentioned techniques include; chemisorption on transition metals, surface magnetism, phase stabilities and related energetics of (3d, 4d, 5d) transition metals and their compounds, diffusion in simple metals from the simple models of the bulk and surfaces electronic structure of transition metals, rare-earth and actinides, spin and orbital magnetism, electronic phase transitions, mixed valence states on surfaces and interfaces, and related issues in hard magnets.

Spin and Orbital Exchange

spin and Orbital

We consider the superexchange in european monochalcogenides EuO, EuS, EuSe, EuTe, transition metal oxides. We have explored spin, charge, and orbitally ordered states in generalized Hubbard-like two component models using model Hartree-Fock calculations on d-p-type lattice models. We also discuss why in some cases these materials may still behave as an orbital quantum liquid in anisotropic Heisenberg-like model, while in other there is a classical behavior based on limiting Ising model. Several charge and orbitally modulated states are found to be stable and almost degenerate in energy with a homogeneous and spatially ordered orbital magnetism consistent with the experiment observation of mixed valence states inCeAl2O3, SmS, SmSe. We also have studied the magnetic saturation of iron in metallic environments.

Finite-size systems

Finit Size

One way of making the transition between the quasi-long range order in a chain of S=1/2 spins coupled antiferromagnetically and the true long range order that occurs in a plane, is by assembling chains to make ladders of increasing width. Surprisingly this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this novel ground state for the strongly correlated electrons in finite size lattices have now been verified for the finite size closed chains with even and odd numbers of atoms placed in strong magnetic field. The research integrates understanding the physics of the novel phenomena being studied and the materials exhibiting the phenomena of superconductivity, discovery and characterization of several novel Kondo materials, observation of superconducting and magnetic crossover from the itinerant BCS behavior into the localized Bose condensation regime in 1D and 2D metals, giant magnetoresistance in several types of ferromagnetic materials, and studies of magnetization reversal in individual sub-micron particles. My research interest ranges from materials science to low-dimensional physics, mainly on nanoscale materials and composites. My current research efforts are focused on gaining atomic-scale understanding and control of the surface-adsorbate and adsorbate-adsorbate interactions in terms of bonding, electronic structure, and dynamics.

BCS -- Bose condensation crossover


I am interested in the qualitative and quantitative understanding of the macroscopic and collective properties of condensed matter systems, and on the relation between macro and the microscopic physics at the single-electron level. I have been particularly interested in exploring the spectacular consequences of strong correlation effects in electronic materials where the low energy properties are qualitatively different from those of a non-interacting electron gas. Prime examples of this on which I have focused my attentions are the one and two dimensional electron on a lattice placed in a strong magnetic field, which exhibits phenomena associated with the induced ferromagnetic effect and on the amazing electronic properties of the cuprate perovskites, including high temperature superconductivity, quantum anti-ferromagnetism, BCS--Bose condensation crossover and a delicate interplay between superconducting, charge-density-wave, and spin-density wave ordering. Recently, I have also developed an approach to understanding of the magnetic crossover from itinerant into localized magnetism. It is my feeling that understanding of these physically important problems is vital to obtain exact, and well controlled approximate solutions of simplified model problems which properly caricature the important physics, and this has dictated the use of more accurate self-consistent methods based on incorporation of the second order perturbation term into this scheme. These techniques have been applied to the Hubbard model in order to successfully predict the ground state properties by comparison with the exact solution in 1d case without using significant experimental input. In my opinion, the LDA has worked better than it should have, even in describing certain ground state properties of materials. However, there are clear problems in the existing mean field that have to be addressed in order to have better self-consistent predictions of complex materials.

Nucleon on a lattices

Nuclen on a lattices

Thermal properties of nucleon matter are investigated assuming a simple form of the nucleon-nucleon interaction. The nucleons are dynamically interacting through a spin-dependent force on a three-dimensional lattice in a way similar to the extended attractive Hubbard model with the intersite interaction. A mean field calculation suggests that the super-fluid ground state generated by strong nucleon parings undergoes a second-order phase transition to a normal state at a higher temperature.

Current Work

Current Work

There are several projects currently underway. Magnetic interactions in rare-earth/transition metal compounds are being studied in order to understand various phase diagrams and observed enhancements in magnetic properties of these materials. Fundamental aspects of electronic structure are being examined in order to go beyond various approximations necessary in the self-consistent studies. Currently, we are also interested in studying the coexistence of the magnetism and superconductivity. Exact calculations in small cluster of atoms would be able to guide engineers and materials scientists towards designing assembled clusters in the verge of electron instabilities by exhibiting phase transitions and crossovers under small variation of external parameters. Our studies are also important for improving the critical parameters of high temperature superconducting materials. Based on present calculations of the phase diagrams there is also the exciting possibility of designing completely new materials with desirable properties. These are few example of how advances in computational and materials physics can be applied to very practical problems.


We have access to several IBM and SUN work stations and powerful PCs in US, Armenia and Taiwan. Most of the projects mentioned above have been collaborative efforts, with the condensed matter theory group at the Connecticut University, Brookhaven National Laboratory, other groups at Tamkang University in Taiwan, Yerevan Physics Institute in Armenia and other universities. These collaborations have been very fruitful, and we intend to continue these during the years ahead.

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Last Update: 09/14/2009