arXiv subjects

C. M. Varma

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

At least 19 recordsLinked to original sources

arXiv2024

Quantum-criticality and superconductivity in twisted transition metal di-chalcogenides

We analyze a model for electronic structure and interactions in twisted transition metal chalcogenide WSe$_2$ for superconductivity. In this material, spin-orbit scattering locks the z-components of spins of low-energy fermions near the Dirac ${\bf K}$ and ${\bf K}'$ points of the hexagonal Brillouin zone, reducing the symmetry of spin-spin interactions to that of an xy model. We show that a nominally repulsive 4-fermion interaction gives rise to an attraction for pairing in a two-component $E^{-}$ channel, which is a hexagonal lattice representation of the $\ell =1$ channel. The gap function is inversion-odd and a linear combination of spin singlet and spin triplet. At weak coupling superconductivity emerges via the Kohn-Luttinger mechanism; we compute $T_c$ for the Fermi-level lying close to the van Hove singularity. At strong coupling, the pairing is mediated by XY magnetic fluctuations peaked at momenta ${\bf K}-{\bf K}' = 2 {\bf K}$ and we estimate $T_c$ using the form of the quantum-critical XY fluctuations, displaying $ω/T$ scaling.

cond-mat.supr-con↗

arXiv2024

Dark Fermions in Fluctuating Valence Insulators

A fluctuating-valence impurity in a metal is quantum-critical unlike a Kondo impurity which has the properties of a local Fermi-liquid. A systematic theory for the fluctuating-valence lattice is constructed, based on the hybridization and pairing of itinerant d-orbitals with localized f-orbitals both of which are essential parts of the solution of the impurity problem. It also uses the fact that the single-particle excitations at the Fermi-surface in any dimension can be written as orthogonal Majoranas and those with linear departures from the Fermi-surface as linear combination of bare particles and holes with the same spin. The calculations on the lattice give four spin-degenerate one-particle excitations of fractionalized fermions; two sets disperse across the chemical potential and the other two have gaps. The former are shown to be dark to any linear electro-magnetic probes of their charge and spin and observable only through probes of their free-energy such as a Fermi-liquid specific heat and magneto-oscillations characteristic of a Fermi-surface but without a Zeeman splitting. The excitations with the gaps behave as in insulators but with renormalized amplitudes. The superfluid density is zero. A magnetic field $H$ turns the insulator to a metal with a singularity in magnetization proportional to $\sqrt{H - H_c}$, with $H_c$ related to the gap. Beyond $H_c$, the usual Zeeman splitting appears in the magneto-oscillations. The properties and predictions are compared to the momentous recent discoveries in fluctuating-valence insulators. Similar excitations may be expected in transition metal chalcogenide layers at fluctuating-valence, and quite likely for Kagome lattices, and twisted multi-layer graphene near specific fillings.

cond-mat.str-el↗

arXiv2023

Quantum-criticality in twisted bi-layer graphene

Transport experiments in twisted bilayer graphene (TBG) show a fan-like region near integer fillings with a resistivity linear in temperature down to the lowest temperature measured. This suggests quantum-critical points at the boundaries to long-range ordered phases. The particular order proposed by Blutinck et al. for twisted bi-layer graphene (TBG) is a loop-current order at the carbon length-scale together with modulations on the moiré length scale. This is shown to be the ground state of a xy model with translational symmetry and time-reversal broken. Here, this is extended to derive a model for quantum-critical properties. We derive the quantum xy model coupled to fermions in this situation. The kinetic energy operator for the model and the coupling of fermions to the fluctuations of the xy model are derived. The previously derived universal properties in the quantum-critical region of such a model, leading to a marginal Fermi-liquid, irrespective of the underlying microscopics is briefly reviewed. The properties include the resistivity and various other transport properties with and without applying a magnetic field and the instability of the quantum fluctuating state to superconductivity in d-wave symmetry.

cond-mat.str-el↗

arXiv2021

Violation of Onsager Reciprocity in Underdoped Cuprates ?

One of the canons of condensed matter physics is the Onsager Reciprocity principle in systems in which the Hamiltonian commutes with the time-reversal operator. Recent results of measurements of the Nernst coefficient in underdoped YBa_2Cu_30_{6+x}, together with the measurements of the anisotropy of conductivity and the inferred anisotropy of the thermopower, imply that this principle is violated. The probable violation and its temperature dependence are shown to be consistent with the Loop-current phase which has been directly observed in other experiments. The violation is related directly to the magneto-electric symmetry of such a phase in which an applied electric field generates an effective magnetic field at right angle to it and to the order parameter vector, and vice versa.

cond-mat.supr-con↗

arXiv2020

Majoranas in mixed-valence insulators

A physical model for a mixed-valence impurity in a metal must satisfy the Friedel screening theorem for both valences. Such a model is shown, following earlier work which showed low energy singularities in it, to be supersymmetric, leading to a free Majorana and a phase-shifted Majorana excitation. The theory extended approximately to a lattice of mixed-valence ions at appropriate filling gives, without fine-tuning the parameters, a protected gapless Majorana fermion band across the chemical potential, besides the mixed-valence particle and hole bands separated by gaps. In this situation the system is electrically neutral in linear response but has de Haas-van Alphen oscillations. This is used to explain the recently observed magneto-oscillations in mixed-valence insulators as well as their accompanying low energy thermodynamic and relaxation rate anomalies. Some predictions to test the validity of the theoretical results are provided, the most striking of which is that there should be extensive ground state entropy in such compounds.

cond-mat.str-el↗

arXiv2018

Chiral spin-order in some purported Kitaev spin-liquid compounds

We examine recent magnetic torque measurements in two compounds, $γ$-Li$_2$IrO$_3$ and RuCl$_3$, which have been discussed as possible realizations of the Kitaev model. The analysis of the reported discontinuity in torque, as an external magnetic field is rotated across the $c-$axis in both crystals, suggests that they have a translationally-invariant chiral spin-order of the from $<{\bf S}_i. ({\bf S}_j ~\times ~ {\bf S}_k)> \ne 0$ in the ground state and persisting over a very wide range of magnetic field and temperature. An extra-ordinary $|B|B^2$ dependence of the torque for small fields, beside the usual $B^2$ part, is predicted due to the chiral spin-order, and found to be consistent with experiments upon further analysis of the data. Other experiments such as inelastic scattering and thermal Hall effect and several questions raised by the discovery of chiral spin-order, including its topological consequences are discussed.

cond-mat.str-el↗

arXiv2015

Quantum Criticality in Quasi-Two Dimensional Itinerant Antiferromagnets

Quasi-two dimensional itinerant fermions in the Anti-Ferro-Magnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with temperature and a contribution to specific heat or thermopower proportional to $T \ln T$. It is shown here that a generic model of itinerant AFM can be canonically transformed such that its critical fluctuations around the AFM-vector $Q$ can be obtained from the fluctuations in the long wave-length limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently and in a large regime of parameters, they are determined, not by renormalized spin-fluctuations but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a dynamical critical exponent $z =\infty.$ The time dependence gives $ω/T$-scaling at criticality. The observed resistivity and entropy then follow directly. Several predictions to test the theory are also given.

cond-mat.str-el↗

arXiv2015

Quantum critical response function in quasi-two dimensional itinerant antiferromagnets

We re-examine the experimental results for the magnetic response function $χ''({\bf q}, E, T)$, for ${\bf q}$ around the anti-ferromagnetic vectors ${\bf Q}$, in the quantum-critical region, obtained by inelastic neutron scattering, on an Fe-based superconductor, and on a heavy Fermion compound. The motivation is to compare the results with a recent theory, which shows that the fluctuations in a generic anti-ferromagnetic model for itinerant fermions map to those in the universality class of the dissipative quantum-XY model. The quantum-critical fluctuations in this model, in a range of parameters, are given by the correlations of spatial and of temporal topological defects. The theory predicts a $χ''({\bf q}, E, T)$ (i) which is a separable function of $({\bf q -Q})$ and of ($E$,$T$), (ii) at crticality, the energy dependent part is $\propto \tanh (E/2T)$ below a cut-off energy, (iii) the correlation time departs from its infinite value at criticality on the disordered side by an essential singularity, and (iv) the correlation length depends logarithmically on the correlation time, so that the dynamical critical exponent $z$ is $\infty$ . The limited existing experimental results are found to be consistent with the first two unusual predictions from which the linear dependence of the resistivity on T and the $T \ln T$ dependence of the entropy also follow. More experiments are suggested, especially to test the theory of variations on the correlation time and length on the departure from criticality.

cond-mat.str-el↗

arXiv2015

Structure Factor of a Relaxor Ferroelectric

We study a minimal model for a relaxor ferroelectric including dipolar interactions, and short-range harmonic and anharmonic forces for the critical modes as in the theory of pure ferroelectrics together with quenched disorder coupled linearly to the critical modes. We present the simplest approximate solution of the model necessary to obtain the principal features of the correlation functions. Specifically, we calculate and compare the structure factor measured by neutron scattering in different characteristic regimes of temperature in the relaxor PbMg$_{1/3}$Nb$_{2/3}$O$_3$.

cond-mat.dis-nn↗

arXiv2015

Amplitude / Higgs Modes in Condensed Matter Physics

The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function $Ψ({\bf r}, t)$. These states include superfluids, superconductors, and a subclass of antiferromagnets and charge-density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of $Ψ({\bf r}, t)$. The phase oscillations are the {\it Goldstone} modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry as in particle physics, and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called {\it Higgs} modes in particle physics, whose prediction and discovery is very important for the standard model of particle physics. In this review, we discuss the theory and the possible observation of the amplitude or Higgs modes in condensed matter physics -- in superconductors, cold-atoms in periodic lattices, and in uniaxial antiferromagnets. We discuss the necessity for at least approximate particle-hole symmetry as well as the special conditions required to couple to such modes because, being scalars, they do not couple linearly to the usual condensed matter probes.

cond-mat.supr-con↗

arXiv2014

Pseudogap in Cuprates and other Metals or How to Almost Elude Bloch's Theorem

The loop-current state discovered in under-doped cuprates is characterized by a vector ${\bf Ω}$ which has four possible orientations which correspond to different domains of order in a perfect sample. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. For disorder coupling also to the direction of ${\bf Ω}$, there can only be a finite temperature dependent static correlation length for the loop-current state below the ordering temperature of the pure problem. It is shown that, in this situation, singular forward scattering of fermions for large correlation lengths induces an angle dependent pseudo-gap in the single-particle spectral function near the chemical potential. The peaks in the spectral function at the fermi-vectors are away from the chemical potential proportionally to the square of the average loop order parameter measurable by polarized neutron scattering. This result is tested. Due to the finite correlation length there always exist low frequency excitations at long wavelength at all temperatures in the "ordered" phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

cond-mat.str-el↗

arXiv2014

Landau Renormalizations of Superfluid density in Heavy Fermion Superconductor CeCoIn5

The formation of heavy fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid $^3$He that Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth~$Λ$ quite different from that in the BCS theory. Using Leggett's theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $Λ$ in high quality samples both Landau parameters $F_0^s$ and $F_1^s$; this has never been accomplished before. A modification of the temperature dependence of the specific heat $C_\mathrm{el}$, related to that of $Λ$, is also expected. We have carefully determined the magnitude and temperature dependence of $Λ$ in CeCoIn$_5$ by muon spin relaxation rate measurements to obtain $F_0^s = 36 \pm 1$ and $F_1^s = 1.2 \pm 0.3$, and find a consistent change in the temperature dependence of electronic specific heat $C_\mathrm{el}$. This, the first determination of $F_1^s$ with a value~$\ll F_0^s$ in a heavy fermion compound, tests the basic assumption of the theory of heavy fermions, that the frequency dependence of the self-energy is much more important than its momentum dependence.

cond-mat.str-el↗

arXiv2014

Intrinsic Anomalous Hall Effect in Magneto-Chiral States

We show that a finite Hall effect in zero applied magnetic field occurs for partially filled bands in certain time-reversal violating states with zero net flux per unit-cell. These states are the Magneto-chiral states with parameters in the effective one-particle Hamiltonian such that they do not satisfy the Haldane-type constraints for topological electronic states. The results extend an earlier discussion of the Kerr effect observed in the cuprates but may be applicable to other experimental situations.

cond-mat.str-el↗

arXiv2014

Zeeman Modulated Spin Echo in Orthorhombic Symmetry

The experimental study of the modulation of the envelope of spin-echo signals due to internal and external fields is an important spectroscopic tool to detect very small internal magnetic fields. We derive the free induction decay and the frequency spectrum and amplitude of spin-echo signals for arbitrary orientation of fields with respect to crystalline axis for nuclei in a crystal of orthorhombic symmetry. Results reproduce the results that no modulation should be observed in tetragonal crystals for fields either along the c-axis or any direction in the basal plane and give details of the signal as a function of the orthorhombicity parameter. They are used to discuss recent experimental results and provide guidelines for future experiments.

cond-mat.str-el↗

arXiv2013

Gyrotropic Birefringence in the Under-doped Cuprates

The optical effects due to the loop-current order parameter in under-doped cuprates are studied in order to understand the recent observation of unusual birefringence in electromagnetic propagation in under-doped cuprates. It is shown why birefringence occurs even in multiple domains of order with size of domains much smaller than the wave-length and in twinned samples. Not only is there a rotation of polarization of incident light but also a rotation of the principal optical axis from the crystalline axes. Both are calculated in relative agreement with experiments in terms of the same parameters. The magnitude of the effect is orders of magnitude larger than the unusual Kerr effect observed in under-doped cuprates earlier. The new observations, including their comparison with the Kerr effect, test the symmetry of the proposed order decisively and confirm the conclusions from polarized neutron scattering.

cond-mat.str-el↗

arXiv2013

Paraelectric and Ferroelectric States in a Model for Relaxor Ferroelectrics

We study the free energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature $T_c$. We calculate the phase diagram in the electric field-temperature plane and find a coexistence line of the polar and non-polar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and non-polar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and to gain physical understanding of various experimental results in typical relaxors.

cond-mat.dis-nn↗

arXiv2013

A variational method in the problem of screening an external charge in strongly correlated metals

We describe a variational calculation for the problem of screening of a point charge in a layered correlated metal for dopings close to the Mott transition where the screening is non-linear due to the proximity to the incompressible insulating state. We find that external charge can induce locally incompressible regions and that the non-linear dependence of the screening on density can induce overscreening in the nearest nearby layers while preserving overall charge neutrality.

cond-mat.str-el↗

arXiv2013

Superconducting Transition Temperatures for Spin-Fluctuation Promoted Superconductivity in Heavy Fermion Compounds

The quantum critical Antiferromagnetic (AFM) fluctuation spectra measured by inelastic neutron scattering recently in two heavy fermion superconductors are used together with their other measured properties to calculate their D-wave superconducting transition temperatures $T_{\rm c}$. To this end, the linearized Eliashberg equations for D-wave superconductivity induced by AFM fluctuations are solved in models of fermions with various levels of nesting. The results for the ratio of $T_{\rm c}$ to the characteristic spin-fluctuation energy are well parametrized by a dimensionless coupling constant and the AFM correlation length. Comparing the results with experiments suggests that one may reasonably conclude that superconductivity in these compounds is indeed caused by AFM fluctuations. This conclusion is strengthened by a calculation with the same parameters of the measured coefficient of the normal state quantum-critical resistivity $\propto T^{3/2}$ characteristic of {\it gaussian} AFM quantum-critical fluctuations. The calculations give details of the superconducting coupling as a function of the correlation length and the integrated fluctuation spectra useful in other compounds.

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