arXiv subjects

Chandra M. Varma

Publications and source records attributed to Chandra M. Varma.

33 records · Page 2Linked to original sources

arXiv2018

Quantum critical singularities in two-dimensional metallic XY ferromagnets

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe$_2$Al$_{10}$, which is a realization of the DQXY model in 2D. The frequency, temperature and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model, and its applications in understanding quantum-critical properties of diverse systems.

cond-mat.str-el↗

arXiv2017

Dynamic structure function of some singular Fermi-liquids

The density correlations of some singular Fermi liquids with anomalous properties such as resistivity varying linearly with T at low temperatures, a $T \log T$ contribution to the entropy and thermopower, etc., are expected to be quite different from that in Landau Fermi liquids. A possible statistical mechanical model for the quantum critical fluctuations in diverse systems with such properties is the 2D dissipative quantum XY model. Exact relations between the density correlations and singular irreducible vertices due to coupling of Fermions to the topological excitations of the 2D dissipative quantum XY model are used to derive results which were proposed phenomenologically long ago but are measurable only recently due to advances in experimental techniques. The density correlations are unusual at all momenta ${\bf q}$ and energy $ν$, from the hydrodynamic limit to that for large momenta and energy. The hydrodynamic limit together with the continuity equation gives the linear in T resistivity. The density correlations are almost independent of frequency up to a high frequency cut-off for $q_{ZB} \gtrsim q >> ν/v_F$; $q_{ZB}$ is the Brillouin zone boundary and $v_F$ is the Fermi-velocity. The results should be applicable to loop-current quantum criticality in cuprates, and to 2D Fe based compounds near their antiferromagnetic quantum-criticality. The relation of the results to the temperature and frequency dependent conductivity and to Raman response is also discussed.

cond-mat.str-el↗

arXiv2017

Quantum criticality in the two-dimensional dissipative quantum XY model-II

Earlier Monte-Carlo calculations on the dissipative two-dimensional XY model are extended in several directions. We study the phase diagram and the correlation functions when dissipation is very small, where it has properties of the classical 3D-XY transition, i.e. one with a dynamical critical exponent $z=1$. The transition changes from $z=1$ to the class of criticality with $z \to \infty$ driven by topological defects, discovered earlier, beyond a critical dissipation. We also find that the critical correlations have power-law singularities as a function of tuning the ratio of the kinetic energy to the potential energy for fixed large dissipation, as opposed to essential singularities on tuning dissipation keeping the former fixed. A phase with temporal disorder but spatial order of the Kosterlitz-Thouless form is also further investigated. We also present results for the transition when the allowed Caldeira-Leggett form of dissipation and the allowed form of dissipation coupling to the compact rotor variables are both included. The nature of the transition is then determined by the Caldeira-Leggett form.

cond-mat.str-el↗

arXiv2016

Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates

The anomalous transport and thermodynamic properties in the quantum-critical region, in the cuprates, and in the quasi-two dimensional Fe-based superconductors and heavy-fermion compounds, have the same temperature dependences. This can occur only if, despite their vast microscopic differences, a common statistical mechanical model describes their phase transitions. The antiferromagnetic (AFM)-ic models for the latter two, just as the loop-current model for the cuprates, map to the dissipative XY model. The solution of this model in 2+1 D reveals that the critical fluctuations are determined by topological excitations, vortices and a variety of instantons, and not by renormalized spin-wave theories of the Landau-Ginzburg-Wilson type, adapted by Moriya, Hertz and others for quantum-criticality. The absorptive part of the fluctuations is a separable function of momentum ${\bf q}$, measured from the ordering vector, and of the frequency $ω$ and the temperature $T$ which scale as $\tanh(ω/2T)$ at criticality. Direct measurements of the fluctuations by neutron scattering in the quasi-two-dimensional heavy fermion and Fe-based compounds, near their antiferromagnetic quantum critical point, are consistent with this form. Such fluctuations, together with the vertex coupling them to fermions, lead to a marginal fermi-liquid, with the imaginary part of the self-energy $\propto max(ω, T)$ for all momenta, a resistivity $\propto T$, a $T \ln T$ contribution to the specific heat, and other singular fermi-liquid properties common to these diverse compounds, as well as to d-wave superconductivity. This is explicitly verified, in the cuprates, by analysis of the pairing and the normal self-energy directly extracted from the recent high resolution angle resolved photoemission measurements.

cond-mat.str-el↗

arXiv2016

Phase diagram and quantum-criticality of the two dimensional dissipative quantum XY model

The two-dimensional dissipative quantum XY model is applicable to the quantum-critical properties of diverse experimental systems, ranging from the superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in the cuprates. We solve the re-expression of this model in terms of topological excitations: vortices and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte-Carlo calculations: the separability of the quantum critical fluctuations (QCF) in space and time, the spatial correlation length proportional to logarithm of the temporal correlation length near the transition from disordered to the fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e. of the dynamical critical exponent $z$. These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high temperature superconductivity.

cond-mat.str-el↗

arXiv2016

Quantitative Determination of the Pairing Interactions for High Temperature Superconductivity in Cuprates

A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated strange metal state. Here we report the quantitative determination of the normal and pairing self-energies, made possible by laser-based angle-resolved photoemission measurements with unprecedented accuracy and stability. Through a precise inversion procedure, both the effective interactions in the attractive d-wave symmetry and the repulsive part in the full symmetry are determined. The latter are nearly angle independent. Near Tc both interactions are nearly independent of frequency, and have almost the same magnitude, over the complete energy range of up to about 0.4 eV except for a low energy feature around 50 meV present only in the repulsive part which has less than 10% of the total spectral weight. Well below Tc, they both change similarly by superconductivity induced features at low energies. Besides finding the pairing self-energy and the attractive interactions for the first time, these results expose a central paradox of the high Tc problem: how the same frequency independent fluctuations can dominantly scatter at angles +-pi/2 in the attractive channel as well as lead to angle-independent repulsive scattering. The experimental results are compared with the available theoretical calculations based on antiferromagnetic fluctuations, Hubbard model and the quantum-critical fluctuations of loop-current order.

cond-mat.str-el↗

arXiv2015

Local Quantum Criticality in the Two-dimensional Dissipative Quantum XY Model

We use quantum Monte-Carlo simulations to calculate the phase diagram and the correlation functions for the quantum phase transitions in the two-dimensional dissipative XY model with and without four-fold anisotropy. Without anisotropy, the model describes the superconductor to insulator transition in two-dimensional dirty superconductors. With anisotropy, the model represents the loop-current order observed in the under-doped cuprates and its fluctuations, as well as the fluctuations near the ordering vector in simple models of itinerant antiferromagnets. These calculations test an analytic solution of the model which re-expressed it in terms of topological excitations - the vortices with interactions only in space but none in time, and warps with leading interactions only in time but none in space, as well as sub-leading interactions which are both space and time-dependent. For parameters for which the proliferation of warps dominates the phase transition, the critical fluctuations as a function of the deviation of the dissipation parameter $α$ from its critical value $α_c$ are scale-invariant in imaginary time $τ$ as the correlation length in time $ξ_τ = τ_c e^{|α_c/(α_c-α)|^{1/2}}$ diverges. On the other hand, the spatial correlations develop with a correlation length $ξ_x \approx ξ_0 \log{(ξ_τ)}$, with $ξ_0$ of the order of a lattice constant. The dynamic correlation exponent $z$ is therefore $\infty$. These results are consistent with the phenomenology proposed for the strange metal properties of the cuprates. The Monte-Carlo calculations also directly show warps and vortices. Their density and correlations across the various transitions in the model are calculated and related to those of the order parameter in the original model.

cond-mat.str-el↗

arXiv2014

Sharp low energy feature in single-particle spectra due to forward scattering in $d$-wave cuprate superconductors

There is an enormous interest in renormalization of quasi-particle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature $T_c$ because it enables determination of the fluctuation spectrum to which the qps are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to $T_c$ and its intensity increasing sharply below $T_c$. This unexpected feature needs to be reconciled with $d$-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below $T_c$ and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.

cond-mat.supr-con↗

arXiv2014

Specific Heat and Sound Velocity Distinguish the Relevant Competing Phase in the Pseudogap Region of High Temperature Superconductors

A great step forward towards the understanding of high temperature superconductors are the variety of experimental results which have led to the wide-spread acceptance of the idea that a phase with a broken symmetry competes with superconductivity in the under-doped region, often called the pseudo-gap region. There are a plethora of suggested phases. The idea, that a broken symmetry phase competes with superconductivity makes thermodynamic sense only if the energy gained due to it is comparable to that gained through the superconducting transition in their co-existence region. Extraordinarily, however, no specific heat signature of a phase transition has been identified at the pseudo-gap temperature $T^*$. We use the recent highly accurate sound-velocity measurements and the best available specific heat measurements in YBa$_2$Cu$_3$O$_{6+δ}$ to show that phase transitions to the universality class of the loop-current ordered state with free-energy reduction similar to the measured superconducting condensation are consistent with the sound velocity and with lack of identifiable observation in the specific heat. We also compare the measured specific heat with some more usual transitions and show that transitions with such symmetry classes can easily be shown by existing specific heat measurements to have energy reduction due to them less than 1/20 the superconducting condensation energy.

cond-mat.supr-con↗

arXiv2013

Phase Diagram of a Three Orbital Model for the high-T$_c$ cuprates

We study the phase diagram of an effective three orbital model of the cuprates using Variational Monte-Carlo calculations (VMC) on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant Anti-ferromagnetism (AFM), d-wave superconductivity (SC), and the Fermi-liquid (FL) are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and inter-site correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductors provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by O.K. Andersen. The results of the calculations are that this phase gives way at lower dopings to an AFM phase and at larger copings to a SC phase followed by a FL phase.

cond-mat.str-el↗

arXiv2013

Ordered Loop Current States in Bilayer Graphene

While single-layer graphene shows extraordinary phenomena which are stable against electronic interactions, the non-interacting state of bilayer graphene is unstable to infinitesimal interactions leading to one of many possible exotic states. Indeed a gapped state is found in experiments but none of the states proposed so far can provide full accounts of its properties. Here we show that a magnetoelectric (ME) state is consistent with the experimental observations. This state breaks time-reversal symmetry through a pair of spontaneously generated current loops in each layer, and has odd-parity with respect to the two layers. We also suggest further experiments to check whether the ME state is indeed the gapped state found in experiments.

cond-mat.mes-hall↗

arXiv2011

Analysis of Laser ARPES from Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in superconductive state: angle resolved self-energy and fluctuation spectrum

We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy $\w$ employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $θ$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $ω$ is directly obtained from the fitting. The obtained angle resolved self-energy is then used to deduce the Eliashberg function $α^2 F^{(+)}(þ,\w)$ in the diagonal channel by inverting the d-wave Eliashberg equation using the maximum entropy method. Besides a broad featureless spectrum up to the cutoff energy $ω_c$, the deduced $α^2 F$ exhibits two peaks around 0.05 eV and 0.015 eV. The former and the broad feature are already present in the normal state, while the latter emerges only below $T_c$. Both peaks become enhanced as $T$ is lowered or the angle $þ$ moves away from the nodal direction. The implication of these findings are discussed.

cond-mat.supr-con↗

arXiv2010

Momentum Dependence of the Single-Particle Self-Energy and Fluctuation Spectrum of Slightly Underdoped Bi_2 Sr_2 CaCu_2 O_{8+δ} from High Resolution Laser ARPES

We deduce the normal state angle-resolved single-particle self-energy $Σ(θ, ω)$ and the Eliashberg function (i.e., the product of the fluctuation spectrum and its coupling to fermions) $α^2 F(θ,ω)$ for the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ from the ultra high resolution laser angle-resolved photoemission spectroscopy (ARPES). The self-energy $Σ(θ, ω)$ at energy $ω$ along several cuts normal to the Fermi surface at the tilt angles $θ$ with respect to the nodal direction in a slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ were extracted by fitting the ARPES momentum distribution curves. Then, using the extracted self-energy as the experimental input, the $α^2 F(θ,ω)$ is deduced by inverting the Eliashberg equation employing the adaptive maximum entropy method. Our principal new result is that the Eliashberg function $α^2F(θ,ω)$ collapse for all $θ$ onto a single function of $ω$ up to the upper cut-off energy despite the $θ$ dependence of the self-energy. The in-plane momentum anisotropy is therefore predominantly due to the anisotropic band dispersion effects. The obtained Eliashberg function has a small peak at $ω\approx0.05$ eV and flattens out above 0.1 eV up to the angle-dependent cut-off. It takes the intrinsic cut-off of about 0.4 eV or the energy of the bottom of the band with respect to the Fermi energy in the direction $θ$, whichever is lower. The angle independence of the $α^2 F(θ,ω)$ is consistent only with the fluctuation spectra which have the short correlation length on the scale the lattice constant. This implies among others that the antiferromagnetic fluctuations may not be underlying physics of the deduced fluctuation spectrum.

cond-mat.supr-con↗

arXiv2001

Sweeping of Lattice Disorder and Associated Phenomena in Colossal Magnetoresistance Compounds

We show through a variational calculation that in a large range of parameters the paramagnetic to ferromagnetic transition in colossal magnetoresistance compounds is accompanied by a collapse of polaronic lattice disorder in addition to that of spin disorder. The spin-lattice disordered state is shown to be localized and the ordered state itinerant as observed. The observed dramatic change in the diffuse scattering at the transition as well as the isotope effect are also explained.

cond-mat.str-el↗

arXiv1999

Theory of Doped Excitonic Insulators

The theory of doped excitonic insulators is reinvestigated in light of recent experiments on hexaborides. For the appropriate valley-degenerate X_3,X_3' band structure, ``intra-valley'' condensation is energetically favored. Ferromagnetism occurs upon doping due to the quenching of kinetic energy at the otherwise direct first-order excitonic insulator-metal transition. The phase diagram includes states of spatially inhomogeneous density and magnetization at low temperatures.

cond-mat.str-el↗