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arXiv2009

One-dimensional quantum wires: A pedestrian approach to bosonization

In these lecture notes we will consider systems in which the motion of electrons is confined to one dimension (1D). In these so-called quantum wires electron-electron interaction effects play an important role because the restricted dimensions enhance the scattering between the electrons and completely destroy the quasi-particle picture. New density wave excitations appear that are described by bosonic operators. Here, we will develop this bosonic description, following a pedestrian approach which does not require any previous knowledge in field theory methods. These notes therefore serve as a detailed introduction into bosonization by carefully deriving the most fundamental formulas.

cond-mat.str-el↗
arXiv2008

Kondo effect in an Antiferromagnetic metal

We study the fate of a spin-1/2 impurity in the itinerant antiferromagnetic metallic phase via a renormalization group analysis and a variational calculation. The local moment - conduction electron interaction hamiltonian in an antiferromagnetic metal is spin non-conserving. We show that for a general location of the impurity, the Kondo singularities still occur, but the ground state has a partially unscreened moment. We calculate the magnitude of this residual moment and the variation of the spin polarization with energy for a substitutional impurity as a function of the staggered magnetization. The usual Kondo effect only occurs if the impurity is placed at points where the magnetization is zero.

cond-mat.str-el↗
arXiv2007

Fractionally Quantized Hall Effect: Liquid-Crystal Ground-State and it Excitations

It is shown that the ground-state and the lowest excited-states of two-dimensional electron system (2DES), with ion jellium background, correspond to partial crystal-like (with the period $L_{x}^{\square}=\sqrt{2 m π} \ell_{0}$) correlation order among $N$ electrons of the main region (MR; $L_{x} \times L_{y}$). Many-body variational ground-state wave function of 2DES is presented at the fractional and the integral filling factors $ν=1/m$; $m=2\ell+1$ and $\ell=0, 1, 2,...$. The ground-state manifests the broken symmetry liquid-crystal state with 2DES density that is periodic along the $y-$ direction, with the period $L_{x}^{\square}/m$, and independent of $x$. At $m=3, 5$, the ground-state has essentially lower energy per electron than the Laughlin, uniform liquid, ground-state; the same holds at $m=1$. At $m \geq 3$, the compound form of the many-body ground-state wave function leads to the compound structure of each electron within the main strip (MS; $L_{x}^{\square} \times L_{y}$). Obtained compound exciton and compound spin-exciton states show finite excitation gaps. The excited compound electron (hole) is composed, within MS, from $m$ strongly correlated quasielectrons (quasiholes) of the total charge $e/m$ ($-e/m$) each. The activation gap is obtained: it is given by the excitation gap of relevant compound exciton, at $m \geq 3$, and by the gap of pertinent compound spin-exciton, at $m=1$. Quantized Hall conductance $σ_{H}=e^{2}/(2 m π\hbar)$ is obtained. The theory is in good agreement with experiments.

cond-mat.mes-hall↗
arXiv2007

Probing the doping in metallic and semiconducting carbon nanotubes by Raman and transport measurements

In-situ Raman experiments together with transport measurements have been carried out on carbon nanotubes as a function of gate voltage. In metallic tubes, a large increase in the Raman frequency of the $G^-$ band, accompanied by a substantial decrease of its line-width, is observed with electron or hole doping. In addition, we see an increase in Raman frequency of the $G^+$ band in semiconducting tubes. These results are quantitatively explained using ab-initio calculations that take into account effects beyond the adiabatic approximation. Our results imply that Raman spectroscopy can be used as an accurate measure of the doping of both metallic and semiconducting nanotubes.

cond-mat.mes-hall↗
arXiv2007

Computing quantum phase transitions

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.

cond-mat.stat-mech↗
arXiv2007

Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions

We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions - for 1/2 filling such ground states have roughly 166 million states. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found strong evidence of the very effective screening of the charge homogeneities due to the Hubbard interaction. We have successfully modelled these local charge densities using a non-interacting model with a static screening of the impurity potentials. In addition, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are remarkably successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions.

cond-mat.str-el↗
arXiv2007

Gap excitations in a four-leg Heisenberg spin tube antiferromagnet

Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu2Cl4 D8C4SO2. Contrary to previously conjectured models that relied on bond-alternating nearest neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S = 1/2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.

cond-mat.str-el↗
arXiv2007

From spin and orbital SU(4) to spin SU(2) Kondo effect in double quantum dot

We consider spin and orbital Kondo effect in a parallel arrangement of two strongly electrostatically coupled quantum dots. Increasing the exchange of electrons between the dots through the attached leads induces a smooth crossover between SU(4) spin- and orbital Kondo effect and SU(2) spin Kondo effect. Being the same for the SU(4) and SU(2) symmetry points, the Kondo temperature drops slightly in the intermediate regime. Experimentally, two kinds of Kondo effect can be discriminated by the sensitivity to the suppression of the spin Kondo effect by Zeeman field. The dependence of the Kondo temperature and of the differential conductance on the strength of electronic exchange through the leads and Zeeman field is analyzed in detail.

cond-mat.mes-hall↗
arXiv2008

Fermion pair production in planar Coulomb and Aharonov--Bohm potentials

Exact analytic solutions are found for the Dirac equation in 2+1 dimensions for a spin-one-half particle in a combination of the Lorentz 3-vector and scalar Coulomb as well as Aharonov--Bohm potentials. We employ the two-component Dirac equation which contains a new parameter introduced by Hagen to describe the spin of the spin-1/2 particle. We derive a transcendental equations that implicitly determine the energy spectrum of an electron near the negative-energy continuum boundary and the critical charges for some electron states. Fermion pair production from a vacuum by a strong Coulomb field in the presence of the magnetic flux tube of zero radius is considered. It is shown that the presence of the Ahanorov--Bohm flux tends to stabilize the system.

hep-th↗
arXiv2008

A mechanism for Fermi-surface-topology tuned superconductivity in the cuprates

Based on recent magnetic-quantum-oscillation, ARPES, neutron-scattering and other data, we propose that superconductivity in the cuprates occurs via a convenient matching of the spatial distribution of incommensurate spin fluctuations to the amplitude and phase of the $d_{x^2-y^2}$ Cooper-pair wavefunction; this establishes a robust causal relationship between the lengthscale of the fluctuations and the superconducting coherence length. It is suggested that the spin fluctuations are driven by the Fermi surface, which is prone to nesting; they couple to the itinerant holes via the on-site Coulomb correlation energy, which inhibits double occupancy of spins or holes. The maximum energy of the fluctuations gives an appropriate energy scale for the superconducting $T_{\rm c}$. Based on this model, one can specify the design of solids that will exhibit ``high $T_{\rm c}$'' superconductivity.

cond-mat.supr-con↗
arXiv2007

Depressed Surface Magnetization in Thin La0.8MnO3 Films

A systematic study the magnetization in La0.8.MnO3 films of thickness varying from ultra-thin to bulk-like has been conducted. The study reveals suppression of the bulk magnetization for films up to at least 1600 A. In addition, the surface (top 50 A) of all films exhibits depressed magnetization as observed by x-ray magnetic circular dichroism (XMCD). The reduced surface magnetization is attributed to the coexistence of magnetic and nonmagnetic components of the same chemical composition.

cond-mat.str-el↗
arXiv2007

Inhomogeneous charge ordering of a spinless fermionic system on the Bethe lattice

We show that a system of spinless Fermi particles, localized on the sites of the Bethe lattice with coordination number z and interacting through a repulsive nearest-neighbor interaction, exhibits a phase transition to a charge-ordered state. The phase diagram in the n-T plane is derived. Relevant thermodynamic quantities, such as the free energy, the specific heat, the entropy and the compressibility are analyzed in detail.

cond-mat.str-el↗
arXiv2007

Theoretical study of interacting electrons in one dimension - ground states and experimental signatures

This dissertation focuses on a theoretical study of interacting electrons in one dimension. The research elucidates the ground state (zero temperature) electronic phase diagram of an aluminum arsenide quantum wire which is an example of an interacting one dimensional electron liquid. Using one dimensional field theoretic methods involving abelian bosonization and the renormalization group we show the existence of a spin gapped quantum wire with electronic ground states such as charge density wave and singlet superconductivity. The superconducting state arises due to the unique umklapp interaction present in the aluminum arsenide quantum wire bandstructure discussed in this dissertation. It is characterized by Cooper pairs carrying a finite pairing momentum. This is a realization of the Fulde-Ferrell-Larkin- Ovchinnikov state which is known to lead to inhomogeneous superconductivity. The dissertation also presents a theoretical analysis of the finite temperature single hole spectral function of the one dimensional electron liquid with gapless spin and charge modes (Luttinger liquid). The hole spectral function is measured in angle resolved photoemission spectroscopy experiments. The results predict a kink in the effective electronic dispersion of the Luttinger liquid. A systematic study of the temperature and interaction dependence of the kink provides an alternative way to detect spincharge separation in one dimensional systems where the peak due to the spin part of the spectral function is suppressed.

cond-mat.str-el↗
arXiv2007

Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice

We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already observed in the equivalent spin-1 Ising model on the Bethe lattice.

cond-mat.str-el↗
arXiv2007

On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions

We analyze the original proof by Luttinger and Ward of the Luttinger theorem, according to which for uniform ground states of systems of (interacting) fermions, which may be metallic or insulating, the number of k points corresponding to non-negative values of G_s(k;mu) is equal to the total number of particles with spin index s in these ground states. Here G_s(k;mu) is the single-particle Green function of particles with spin index s at the chemical potential mu. For the cases where the two-body interaction potential is short-range, and in particular for lattice models, we explicitly demonstrate that this theorem is unconditionally valid, irrespective of the strength of the bare interaction potential. We arrive at this conclusion by amongst other things demonstrating that the perturbation series expansion for self-energy in terms of skeleton diagrams, as encountered in the proof of the Luttinger-Ward identity, is uniformly convergent for almost all momenta and energies. We further investigate the mechanisms underlying some reported instances of failure of the Luttinger theorem. With one exception, for all the cases considered in this paper, we show that the apparent failures of the Luttinger theorem can be attributed either to shortcomings of the employed single-particle Green functions or to misapplication of this theorem. The one exceptional case brings to light the possibility of a genuine failure of the Luttinger theorem for insulating ground states, which we show to be brought about by a false limit that in principle can be reached on taking the zero-temperature limit without the value of mu coinciding with the zero-temperature limit of the chemical potential satisfying the equation of state at finite temperatures; no such ambiguity can arise for metallic states.

cond-mat.str-el↗
arXiv2014

Electronic structures and lattice dynamics of BaTiO3 and BiFeO3 : a comparative first-principles study

First-principles calculations were performed to investigate the ferroelectric properties of barium titanate and bismuth ferrite, as well as phonon dispersion of BaTiO3, using density functional theory and density functional perturbation theory. Results show that the strong hybridization of Ti-O and Bi-O lead to the corresponding mechanisms for stabilizing the distorted structure. The spontaneous polarization of 59.4 μC/cm2 and 27.6 μC/cm2 were calculated for BiFeO3 and BaTiO3 respectively, using berry phase method within the modern theory of polarization. The stereochemical activity of Bi-6s long-pair, which was the driven mechanism for ferroelectricity in BiFeO3, was able to produce greater polarization than the Ti off-centring displacement in BaTiO3. New multiferroic perovskite type materials combined with these two ferroelectric instabilities were predicted to have a better ferromagnetic ordering in comparison with BiFeO3.

cond-mat.mtrl-sci↗