arXiv subjects

C. M. Varma

Publications and source records attributed to C. M. Varma.

At least 37 records · Page 2Linked to original sources

arXiv2012

Collective modes in singlet superconductors

A brief summary of collective mode excitations that can exist in singlet superconductors with irreducible representation $L$ is given. Such excitations may be classified as the coupled excitations of the charge density $ρ$ and the phase $ϕ$ of the order parameter, or of the amplitude $Δ$ of order parameter. Each of these classes may be further characterized in the long wavelength limit by the irreducible representation $\ell$ of the excitation, which may or may not be the same as the ground state $L$.

cond-mat.supr-con↗

arXiv2012

Coexistence of Two Sharp-Mode Couplings and Their Unusual Momentum Dependence in the Superconducting State of Bi2Sr2CaCu2O8+d Superconductor Revealed by Laser-Based Angle-Resolved Photoemission

Super-high resolution laser-based angle-resolved photoemission measurements have been carried out on Bi2Sr2CaCu2O8+d (Bi2212) superconductors to investigate momentum dependence of electron coupling with collective excitations (modes). Two coexisting energy scales are clearly revealed over a large momentum space for the first time in the superconducting state of an overdoped Bi2212 superconductor. These two energy scales exhibit distinct momentum dependence: one keeps its energy near 78 meV over a large momentum space while the other changes its energy from $\sim$40 meV near the antinodal region to $\sim$70 meV near the nodal region. These observations provide a new picture on momentum evolution of electron-boson coupling in Bi2212 that electrons are coupled with two sharp modes simultaneously over a large momentum space in the superconducting states. Their unusual momentum dependence poses a challenge to our current understanding of electron-mode-coupling and its role for high temperature superconductivity in cuprate superconductors.

cond-mat.supr-con↗

arXiv2012

Fermi pockets in a d-wave superconductor with coexisting loop-current order

A d-wave superconducting phase with coexisting intra-unit-cell orbital current order has the remarkable property that it supports finite size Fermi pockets of Bougoliubov quasiparticles. Experimentally detectable consequences of this include a residual $T$-linear term in the specific heat in the absence of disorder and residual features in the thermal and microwave conductivity in the low disorder limit.

cond-mat.str-el↗

arXiv2012

Topological Excitations near the Local Critical Point in the Dissipative 2D XY model

The dissipative XY model in two spatial dimensions belongs to a new universality class of quantum critical phenomena with the remarkable property of the decoupling of the critical fluctuations in space and time. We have shown earlier that the quantum critical point is driven by proliferation in time of topological configurations that we termed warps. We show here that a warp may be regarded as a configuration of a monopoles surrounded symmetrically by anti-monopoles so that the total charge of the configuration is zero. Therefore the interaction with other warps is local in space. They however interact with other warps at the same spatial point logarithmically in time. As a function of dissipation warps unbind leading to a quantum phase transition. The critical fluctuations are momentum independent but have power law correlations in time.

cond-mat.str-el↗

arXiv2012

Higgs Bosons in D-wave Superconductors

The concept of "broken symmetry", that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics whose long awaited discovery is imminent. An equivalent mode in superconductors is implicit in the early theories of their collective fluctuations. Spurred by some mysterious experimental results, the theory of the oscillation of the amplitude of superconductivity order parameter, which is the equivalent to the Higgs modes in s-wave superconductors and its identification in the experiments, was explicitly provided. It was also shown that a necessary condition for this to occur is the emergent Lorentz invariance in the superconducting state while the metallic state and the region just below $T_c$ is manifestly non-Lorentz invariant. Here we show that d-wave superconductors, such as the high temperature Cuprate superconductors, should have a rich assortment of Higgs bosons, each in a different irreducible representation of the point-group symmetries of the lattice. We also show that these modes have a characteristic singular spectral structure which can be discovered in Raman scattering experiments.

cond-mat.supr-con↗

arXiv2012

Theory of Polarized Neutron Scattering in the Loop Ordered Phase of Cuprates

The collective modes observed in the loop-current ordered state in under-doped cuprates by polarized neutron scattering require that the ground state is a linear combination in each unit-cell of the four basis states which are the possible classical magnetic moment configurations in each unit-cell. The direction of such moments is in the c-axis of the crystals. The basis states are connected by both time-reversal as well as spatial rotations about the center of the unit-cells. Several new features arise in the theory of polarized neutron scattering cross-section in this situation which appear not to have been encountered before. An important consequence of these is that a finite component transverse to the classical magnetic moment directions is detected in the experiments. We show that this transverse component is of purely quantum-mechanical origin and that its direction in the plane normal to the c-axis is not detectable, even in principle, in experiments, at least in the quantum-mechanical model we have adopted. We estimate the direction of the "tilt" in the moment, i.e. the ratio of the transverse component to the c-axis component, using parameters of the ground state obtained by fitting to the observed dispersion of the collective modes in the ordered state. We can obtain reasonable agreement with experiments but only by introducing a parameter for which only an approximate magnitude can be estimated. Approximate calculations of the form-factors are also provided.

cond-mat.str-el↗

arXiv2012

Collective Modes in the Loop Current Ordered Phase of Cuprates

Recently two branches of weakly dispersive collective modes have been discovered in under-doped cuprates by inelastic neutron scattering. Polarization analysis reveals that the modes are magnetic excitations. They are only visible for temperatures below the transition temperature to a broken symmetry phase which was discovered earlier and their intensity increases as temperature is further decreased. The broken symmetry phase itself has symmetries consistent with ordering of orbital current loops within a unit-cell without breaking translational symmetry. In order to calculate the collective modes of such a state we add quantum terms to the Ashkin-Teller (AT) model with which the classical loop current order has been described. We derive that the mean field ground state of the quantum model is a product over all unit-cells of linear combination of the four possible classical configurations of the loop current order in each unit-cell. The collective modes are calculated by using a generalized Holstein-Primakoff boson representation of orbital moment operators and lead to three branches of gapped weakly dispersive collective modes. The experimental results are consistent with the two lower energy branches; the third mode is at a higher energy than looked for by present neutron scattering experiments and might also be over-damped. Implications of the discovery of the collective modes are discussed.

cond-mat.str-el↗

arXiv2012

Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian

We consider the Anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific we consider a model appropriate for the Copper-Oxide lattice to highlight the necessary conditions for time-reversal breaking states which are AH states and which are not. We compare the singularities of the wave-functions of the three-orbital model, which are related to the nonzero Berry curvature, and their variation with a change of gauge to those in the two-orbital model introduced in a seminal paper by Haldane. Explicit derivation using wave-functions rather than the more powerful abstract methods may provide additional physical understanding of the phenomena.

cond-mat.str-el↗

arXiv2011

Superconductivity in the Cuprates: Deduction of Mechanism for D-Wave Pairing Through Analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions $(α^2 F)_n(ω, θ)$ and $(α^2 F)_{p,d}(ω)$ determine, respectively, the "normal" and the "pairing" self-energies. We present a quantitative analysis of the high-resolution laser based ARPES data on the compound Bi-2212 to deduce the function$(α^2 F)_n(ω, θ)$. Besides its detailed $ω$ dependence, we find the remarkable result that this function is nearly independent of $θ$ between the ($π,π$)-direction and 25 degrees from it. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function $(α^2 F)_{p,d}(ω)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(α^2 F)_n(θ, ω)$. We show that the deduced $(α^2 F)_n(θ, ω)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(α^2 F)_{p,d}(ω)$ consistent with such a correlation length and the symmetry of matrix-elements scattering fermions off AFM fluctuations, we calculate $T_c$ an show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantum-critical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the $θ$ and $ω$ dependence of the deduced $(α^2 F)_n(ω, θ)$. The pairing kernel $(α^2 F)_{p,d}(ω)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.

cond-mat.supr-con↗

arXiv2011

A comprehensive study of electric, thermoelectric and thermal conductivities of Graphene with short range unitary and charged impurities

Motivated by the experimental measurement of electrical and hall conductivity, thermopower and Nernst effect, we calculate the longitudinal and transverse electrical and heat transport in graphene in the presence of unitary scatterers as well as charged impurities. The temperature and carrier density dependence in this system display a number of anomalous features that arise due to the relativistic nature of the low energy fermionic degrees of freedom. We derive the properties in detail including the effect of unitary and charged impurities self-consistently, and present tables giving the analytic expressions for all the transport properties in the limit of small and large temperature compared to the chemical potential and the scattering rates. We compare our results with the available experimental data. While the qualitative variations with temperature and density of carriers or chemical potential of all transport properties can be reproduced, we find that a given set of parameters of the impurities fits the Hall conductivity, Thermopower and the Nernst effect quantitatively but cannot fit the conductivity quantitatively. On the other hand a single set of parameters for scattering from Coulomb impurities fits conductivity, hall resistance and thermopower but not Nernst.

cond-mat.mtrl-sci↗

arXiv2011

Extraction of Electron Self-Energy and Gap Function in the Superconducting State of Bi_2Sr_2CaCu_2O_8 Superconductor via Laser-Based Angle-Resolved Photoemission

Super-high resolution laser-based angle-resolved photoemission measurements have been performed on a high temperature superconductor Bi_2Sr_2CaCu_2O_8. The band back-bending characteristic of the Bogoliubov-like quasiparticle dispersion is clearly revealed at low temperature in the superconducting state. This makes it possible for the first time to experimentally extract the complex electron self-energy and the complex gap function in the superconducting state. The resultant electron self-energy and gap function exhibit features at ~54 meV and ~40 meV, in addition to the superconducting gap-induced structure at lower binding energy and a broad featureless structure at higher binding energy. These information will provide key insight and constraints on the origin of electron pairing in high temperature superconductors.

cond-mat.supr-con↗

arXiv2011

Considerations on the symmetry of loop order in cuprates

The loop-current state discovered in the pseudogap phase of cuprates breaks time reversal symmetry and lowers the point group symmetry of the crystal. The order parameter and the magnetic structure within each unit cell which is associated with it can be described by a toroidal moment parallel to the copper-oxide planes. We discuss lattice point group symmetry of the magnetic structure. As an application, we discuss a few effects that necessarily accompany order parameter in the pseudogap phase. The magnitude estimated for these specific effects makes them hard to observe because they rely on the small magnetic fields associated with the order parameter. Effects, associated with the electronic energies are much larger. Some of them have already been discussed.

cond-mat.supr-con↗

arXiv2010

Collective Modes in the Loop Ordered Phase of Cuprates

We show that the two branches of collective modes discovered recently in under-doped Cuprates with huge spectral weight are a necessary consequence of the loop-current state. Such a state has been shown in earlier experiments to be consistent with the symmetry of the order parameter competing with superconductivity in four families of Cuprates. We also predict a third branch of excitations and suggest techniques to discover it. Using parameters to fit the observed modes, we show that the direction of the effective moments in the ground state lies in a cone at an angle to the c-axis as observed in experiments.

cond-mat.str-el↗

arXiv2010

Negative Thermal Expansion and Some Elastic properties of a Class of Solids

We consider the thermal expansion, change of sound velocity with pressure and temperature, and the Poisson ratio of lattices which have rigid units (polyhedra very large stiffness to change in bond-length and to bond-angle variations) connected to other such units through relatively compressible polyhedra. We show that in such a model, the potential energy for rotations of the rigid units can occur only as a function of the combination ${\boldsymbol Θ}_i \equiv ({\boldsymbol θ}_i - (\nabla \times {\bf u}_i)/2)$, where ${\boldsymbol θ_i} $ are the orthogonal rotation angles of the rigid unit $i$ and ${\bf u}_i$ is its displacement. Given such new invariants in the theory of elasticity and the hierarchy of force constants of the model, a negative thermal expansion coefficient as well as a decrease in the elastic constants of the solid with temperature and pressure is shown to follow. These are consistent with the observations.

cond-mat.mtrl-sci↗

arXiv2010

Considerations on the Mechanisms and Transition Temperatures of Superconductors

An overview of the momentum and frequency dependence of effective electron-electron interactions which favor electronic instability to a superconducting state in the angular-momentum channel $\ell$ and the properties of the interactions which determine $T_c$ is provided. Both interactions induced through exchange of phonons as well as purely electronic fluctuations of spin density, charge density or current density are considered. Special attention is paid to the role of quantum critical fluctuations including pairing due to their virtual exchange as well as de-pairing due to inelastic scattering. In light of the above, empirical data and theory specific to phonon induced superconductivity, in cold atoms, superfluidity in liquid $He^3$, superconductivity in some of the heavy fermion compounds, in Cuprates, in pncitides and the valence skipping compound, is reviewed. The physical basis for the following observation is provided: The universal ratio of s-wave $T_c$ to Fermi-energy for fermions at the unitarity limit with attractive interactions is about 0.15, the ratio of the maximum $T_c$ to the typical phonon frequency in phonon induced s-wave superconductivity is of the same order; the ratio of p-wave $T_c$ to the renormalized Fermi-energy in liquid $He^3$, a very strongly correlated Fermi-liquid near its melting pressure, is only $O(10^{-3})$; in the Cuprates and the heavy-fermions where d-wave superconductivity occurs in a region governed by a special class of quantum-critical fluctuations, this ratio rises to $O(10^{-2})$. These discussions also suggest factors important for obtaining higher $T_c$.

cond-mat.supr-con↗

arXiv2009

Magnetically tunable dielectric materials

The coupling between localized spins and phonons can lead to shifts in the dielectric constant of insulating materials at magnetic ordering transitions. Studies on isostructural SeCuO3 (ferromagnetic) and TeCuO3 (antiferromagnetic) illustrate how the q-dependent spin-spin correlation function couples to phonon frequencies leading to a shift in the dielectric constant. A model is discussed for this spin-phonon coupling. The magnetodielectric coupling in multiferroic materials can be very large at a ferroelectric transition temperature. This coupling is investigated in the recently identified multiferroic Ni3V2O8.

cond-mat.mtrl-sci↗

arXiv2009

Thermodynamic Properties near the onset of Loop-Current Order in high-$T_c$ superconducting cuprates

We have performed large-scale Monte Carlo simulations on a two-dimensional generalized Ashkin-Teller model to calculate the thermodynamic properties in the critical region near its transitions. The Ashkin-Teller model has a pair of Ising spins at each site which interact with neighboring spins through pair-wise and 4-spin interactions. The model represents the interactions between orbital current loops in $Cu O_2$-plaquettes of high-$T_c$ cuprates, which order with a staggered magnetization $\Mso$ inside each unit-cell in the underdoped region of the phase diagram below a temperature $T^*(x)$ which depends on doping. The pair of Ising spins per unit-cell represent the directions of the currents in the links of the current loops. The generalizations are the inclusion of anisotropy in the pair-wise nearest neighbor current-current couplings consistent with the symmetries of a square lattice and the next nearest neighbor pair-wise couplings. We use the Binder cumulant to estimate the correlation length exponent $ν$ and the order parameter exponent $β$. Our principal results are that in a range of parameters, the Ashkin-Teller model as well as its generalization has an order parameter susceptibility which diverges as $T \to T^*$ and an order parameter below $T^*$. Importantly, however, there is no divergence in the specific heat. This puts the properties of the model in accord with the experimental results in the underdoped cuprates. We also calculate the magnitude of the "bump" in the specific heat in the critical region to put limits on its observability. Finally, we show that the staggered magnetization couples to the uniform magnetization $M_0$ such that the latter has a weak singularity at $T^*$ and also displays a wide critical region, also in accord with recent experiments.

cond-mat.str-el↗

arXiv2009

Long Wavelength Correlations and Transport in a Marginal Fermi Liquid

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi-surface is proportional to the energy measured from the chemical potential, $τ_i^{-1}\proptoε$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi-liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.

cond-mat.str-el↗