Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure

Why and when the Minkowski's stress tensor can be used in the problem of Casimir force acting on bodies embedded in media

It is shown that the criticism by Raabe and Welsch of the Dzyaloshinskii-Lifshitz-Pitaevskii theory of the van der Waals-Casimir forces inside a medium is based on misunderstandings. It is explained why and at which conditions one can use the ''Minkowski-like '' stress tensor for calculations of the forces. The reason, why approach of Raabe and Welsch is incorrect, is discussed.Comment: Comment, 2 pages. 2 misprints were correcte

RPAE versus RPA for the Tomonaga model with quadratic energy dispersion

Recently the damping of the collective charge (and spin) modes of interacting fermions in one spatial dimension was studied. It results from the nonlinear correction to the energy dispersion in the vicinity of the Fermi points. To investigate the damping one has to replace the random phase approximation (RPA) bare bubble by a sum of more complicated diagrams. It is shown here that a better starting point than the bare RPA is to use the (conserving) linearized time dependent Hartree-Fock equations, i.e. to perform a random phase approximation (with) exchange (RPAE) calculation. It is shown that the RPAE equation can be solved analytically for the special form of the two-body interaction often used in the Luttinger liquid framework. While (bare) RPA and RPAE agree for the case of a strictly linear disperson there are qualitative differences for the case of the usual nonrelativistic quadratic dispersion.Comment: 6 pages, 3 figures, misprints corrected; to appear in PRB7

Electrically driven magnetism on a Pd thin film

Using first-principles density functional calculations we demonstrate that ferromagnetism can be induced and modulated on an otherwise paramagnetic Pd metal thin-film surface through application of an external electric field. As free charges are either accumulated or depleted at the Pd surface to screen the applied electric field there is a corresponding change in the surface density of states. This change can be made sufficient for the Fermi-level density of states to satisfy the Stoner criterion, driving a transition locally at the surface from a paramagnetic state to an itinerant ferromagnetic state above a critical applied electric field, Ec. Furthermore, due to the second-order nature of this transition, the surface magnetization of the ferromagnetic state just above the transition exhibits a substantial dependence on electric field, as the result of an enhanced magnetoelectric susceptibility. Using a linearized Stoner model we explain the occurrence of the itinerant ferromagnetism and demonstrate that the magnetic moment on the Pd surface follows a square-root variation with electric field consistent with our first-principles calculations.Comment: 8 pages, 7 figure

Magnetoelectric effects in single crystals of the cubic ferrimagnetic helimagnet Cu2OSeO3

We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu$_2$OSeO$_3$. A magnetic field-induced electric polarization ($\vec{P}$) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state ($T_c = 59$ K). Both $\vec{P}$ and MC are explored in considerable detail as a function of temperature (T), applied field $\vec{H}_a$, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow to map out the phase diagram of the system in the $H_a$-T plane. Below the 3up-1down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyalozinskii-Moriya term D \vec{M} \cdot(\bs{\nabla}\times\vec{M}) that is present in this non-centrosymmetric compound. We also present a phenomenological Landau-Ginzburg theory for the ME$_H$ effect, which is in excellent agreement with experimental data, and shows three novel features: (i) the polarization $\vec{P}$ has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of $\vec{P}$ points along the vector $(H^yH^z, H^zH^x, H^xH^y)$, and (iii) its strength is proportional to $\eta_\parallel^2-\eta_\perp^2/2$, where $\eta_\parallel$ is the longitudinal and $\eta_\perp$ is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of P provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC

Deformation of anisotropic Fermi surfaces due to electron-electron interactions

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.Comment: 7 pages, 3 figure

Broken parity and a chiral ground state in the frustrated magnet CdCr2O4

We present a model describing the lattice distortion and incommensurate magnetic order in the spinel CdCr2O4, a good realization of the Heisenberg "pyrochlore" antiferromagnet. The magnetic frustration is relieved through the spin-Peierls distortion of the lattice involving a phonon doublet with odd parity. The distortion stablizes a collinear magnetic order with the propagation wavevector q=2\pi(0,0,1). The lack of inversion symmetry makes the crystal structure chiral. The handedness is transferred to magnetic order by the relativistic spin-orbit coupling: the collinear state is twisted into a long spiral with the spins in the ac plane and q shifted to 2\pi(0,\delta,1).Comment: Incremental changes in response to referee report

Functional renormalization group for Luttinger liquids with impurities

We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow-equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral properties of single-particle excitations, and the oscillations in the density profile induced by impurities or boundaries for chains with up to 1000000 lattice sites. The expected asymptotic power-laws at low energy or long distance are fully captured by the fRG. Results on the relevant energy scales and crossover phenomena at intermediate scales are also obtained. A comparison with numerical density matrix renormalization results for systems with up to 1000 sites shows that the fRG with the inclusion of vertex renormalization is remarkably accurate even for intermediate interaction strengths.Comment: 35 pages, 16 figures, revised version as publishe

Anisotropic Fermi surfaces and Kohn-Luttinger superconductivity in two dimensions

The instabilities induced on a two-dimensional system of correlated electrons by the anisotropies of its Fermi line are analyzed on general grounds. Simple scaling arguments allow to predict the opening of a superconducting gap with a well-defined symmetry prescribed by the geometry of the Fermi line. The same arguments predict a critical dimension of 3/2 for the transition of the two-dimensional system to non-Fermi liquid behavior. The methods are applied to the t-t' Hubbard model in a wide range of dopings.Comment: 25 pages, 13 postscript figure

Kinematics of electrons near a Van Hove singularity

A two dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities, and it is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of the electron scattering in this model. The similitudes, and differences, between a standard Renormalization Group approach and previous work based on parquet summations of log$^2$ divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.Comment: 5 pages, 3 postscript figure