Abstract:
We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, $V(\epsilon)\sim {A\over 2}\ln ^2(\epsilon)$. The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when $A<1$. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME with weak confinement. For $A_c\approx 0.4$ the distribution function of the energy-level spacings (LSDF) of this RME coincides in a large energy window with the LSDF of the three dimensional Anderson model at the metal-insulator transition. For the same $A_c$, the variance of the number of levels, $\langle n^2\rangle -\langle n\rangle^2$, in an interval containing $\langle n\rangle$ levels on average, grows linearly with $\langle n\rangle$, and its slope is equal to $0.32 \pm 0.02$, which is consistent with the value found for the Anderson model at the critical point.

Abstract:
We have investigated numerically the electron addition spectra in quantum dots containing a small number (N < 11) of interacting electrons, in presence of strong disorder. For a short-range Coulomb repulsion, we find regimes in which two successive electrons enter the dot at very close values of the chemical potential. In the strongly correlated regime these close additions, or pairing, are associated with electrons tunneling into distinct electron puddles within the dot. We discuss the tunneling rates at pairing, and we argue that our results are related to a phenomenon known as "bunching", recently observed experimentally.

Abstract:
We report on microscopic tight-binding modeling of surface states in Bi$_2$Se$_3$ three-dimensional topological insulator, based on a sp$^3$ Slater-Koster Hamiltonian, with parameters calculated from density functional theory. The effect of spin-orbit interaction on the electronic structure of the bulk and of a slab with finite thickness is investigated. In particular, a phenomenological criterion of band inversion is formulated for both bulk and slab, based on the calculated atomic- and orbital-projections of the wavefunctions, associated with valence and conduction band extrema at the center of the Brillouin zone. We carry out a thorough analysis of the calculated bandstructures of slabs with varying thickness, where surface states are identified using a quantitative criterion according to their spatial distribution. The thickness-dependent energy gap, attributed to inter-surface interaction, and the emergence of gapless surface states for slabs above a critical thickness are investigated. We map out the transition to the infinite-thickness limit by calculating explicitly the modifications in the spatial distribution and spin-character of the surface states wavefunction with increasing the slab thickness. Our numerical analysis shows that the system must be approximately forty quintuple-layers thick to exhibit completely decoupled surface states, localized on the opposite surfaces. These results have implications on the effect of external perturbations on the surface states near the Dirac point.

Abstract:
It is shown that the two-level correlation function $R(s,s')$ in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term ${\rm var}(n)=\eta n$ that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, $\eta$ playing the role of an order-parameter.

Abstract:
We present a computational study of individual and pairs of substitutional Mn impurities on the (110) surface of GaAs samples based on density functional theory. We focus on the anisotropy properties of these magnetic centers and their dependence on on-site correlations, spin-orbit interaction and surface-induced symmetry-breaking effects. For a Mn impurity on the surface, the associated acceptor-hole wavefunction tends to be more localized around the Mn than for an impurity in bulk GaAs. The magnetic anisotropy energy for isolated Mn impurities is of the order of 1 meV, and can be related to the anisotropy of the orbital magnetic moment of the Mn acceptor hole. Typically Mn pairs have their spin magnetic moments parallel aligned, with an exchange energy that strongly depends on the pair orientation on the surface. The spin magnetic moment and exchange energies for these magnetic entities are not significantly modified by the spin-orbit interaction, but are more sensitive to on-site correlations. Correlations in general reduce the magnetic anisotropy for most of the ferromagnetic Mn pairs.

Abstract:
We present a theory of the low-energy excitations of a ferromagnetic metal nanoparticle. In addition to the particle-hole excitations, which occur in a paramagnetic metal nanoparticle, we predict a branch of excitations involving the magnetization-orientation collective coordinate. Tunneling matrix elements are in general sizable for several different collective states associated with the same band configuration. We point out that the average change in ground state spin per added electron differs from non-interacting quasiparticle expectations, and that the change in the spin-polarization, due to Zeeman coupling, is strongly influenced by Coulomb blockade physics.

Abstract:
The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin $S =1/2$ doublets with opposite chirality. According to a group theory analysis [M. Trif \textit{et al.}, Phys. Rev. Lett. \textbf{101}, 217201 (2008)] an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, $d$, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by \textit{ab-initio} methods [M. F. Islam \textit{et al.}, Phys. Rev. B \textbf{82}, 155446 (2010)]. In this work we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a $d$-dependent splitting of the ground state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters $t$ and $U$, and the spin-electric coupling constant $d$. This allows us to predict the regime in which the coupling constant $d$ can be extracted from experiment.

Abstract:
Motivated by recent STM experiments, we present a theoretical study of the electronic and magnetic properties of the Mn-induced acceptor level obtained by substituting a single Ga atom in the (110) surface layer of GaAs or in one of the atoms layers below the surface. We employ a kinetic-exchange tight-binding model in which the relaxation of the (110) surface is taken into account. The acceptor wave function is strongly anisotropic in space and its detailed features depend on the depth of the sublayer in which the Mn atom is located. The local-density-of-states (LDOS) on the (110) surface associated with the acceptor level is more sensitive to the direction of the Mn magnetic moment when the Mn atom is located further below the surface. We show that the total magnetic anisotropy energy of the system is due almost entirely to the dependence of the acceptor level energy on Mn spin orientation, and that this quantity is strongly dependent on the depth of the Mn atom.

Abstract:
We present a theory of the elementary spin excitations in transition metal ferromagnet nanoparticles which achieves a unified and consistent quantum description of both collective and quasiparticle physics. The theory starts by recognizing the essential role played by spin-orbit interactions in determining the energies of ferromagnetic resonances in the collective excitation spectrum and the strength of their coupling to low-energy particle-hole excitations. We argue that a crossover between Landau-damped ferromagnetic resonance and pure-state collective magnetic excitations occurs as the number of atoms in typical transition metal ferromagnet nanoparticles drops below approximately $10^4$, approximately where the single-particle level spacing, $\delta$, becomes larger than, $\sqrt{\alpha} E_{\rm res}$, where $E_{\rm res}$ is the ferromagnetic resonance frequency and $\alpha$ is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semi-realistic model Hamiltonians, which we solve numerically for nanoparticles containing several hundred atoms. For small nanoparticles, we find one isolated ferromagnetic resonance collective mode below the lowest particle-hole excitation energy, at $E_{\rm res} \approx 0.1$ meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As $\delta$ approaches $\sqrt{\alpha} E_{\rm res}$, the ferromagnetic collective excitation is more likely to couple strongly with discrete particle-hole excitations. In this regime the distinction between the two types of excitations blurs. We discuss the significance of this picture for the interpretation of recent single-electron tunneling experiments.

Abstract:
Motivated in part by experiments performed by M.H. Pan et al. (nanoletters, v.5, p 83, 2005), we have undertaken a theoretical study of the the magnetic properties of two-monolayer thick Co nanoplatelets with an equilateral triangular shape. The analysis is carried out using a microscopic Slater-Koster tight-binding model with atomic exchange and spin-orbit interactions designed to realistically capture the salient magnetic features of large nanoclusters containing up to 350 atoms. Two different truncations of the FCC lattice are studied, in which the nanoplatelet surface is aligned parallel to the FCC (111) and (001)crystal planes respectively. We find that the higher coordination number in the (111) truncated crystal is more likely to reproduce the perpendicular easy direction found in experiment. Qualitatively, the most important parameter governing the anisotropy of the model is found to be the value of the intra-atomic exchange integral J. If we set the value of J near the bulk value in order to reproduce the experimentally observed magnitude of the magnetic moments, we find both quasi-easy-planes and perpendicular easy directions. At larger values of J we find that the easy-axis of magnetization is perpendicular to the surface, and the value of the magnetic anisotropy energy per atom is larger. The possible role of hybridization with substrate surface states in the experimental systems is discussed.