arXiv subjects

Chandra M. Varma

Publications and source records attributed to Chandra M. Varma.

At least 19 recordsLinked to original sources

arXiv2026

${\bf \frac{h}{e}}$ flux quantization in metals due to Berry phase coherence

Berry curvature does not show itself in the relative phase correlation of wave-functions at different spatial points in a metal unless the fermions have closed trajectories in momentum space, for example those around isolated impurities. But these, just as the Bloch phase correlations, disappear at lengths larger than the diffusion length. If a quasi-two dimensional metal with Berry curvature has a set of domains, their boundaries necessarily carry chiral currents precluding back-ward scattering. The Berry induced phase coherence then persists over length scales of order the scale at which the chiral one-dimensional states scatter into the bulk states, which can be macroscopic. The conditions for their occurrence and the lengths and the orientation of such states are derived. These calculations are used to understand the remarkable aspects of a recent experiment in an anisotropic metal, reported to have loop-current order, with mean-free path of about 0.01 $μ$m which exhibits flux quantization in some transport properties over lengths of several $μ$m. %It is also shown that generating the appropriately oriented channels in the plane by the field applied is plausible.

cond-mat.str-el↗

arXiv2026

Quantum-critical transport in marginal Fermi liquids

We use the Kubo response functions to calculate the electrical and thermal conductivity and Seebeck coefficient at low temperatures and frequencies in the quantum-critical region for fermions on a lattice. The theory uses scattering of the fermions with the previously derived collective fluctuations due to topological defects of the quantum XY model coupled to fermions. The microscopic model is applicable to the fluctuations of the loop-current order in cuprates as well as to a class of quasi-two-dimensional heavy-fermion and other metallic antiferromagnets, and proposed recently also for the possible loop-current order in Moiré twisted bi-layer graphene and bilayer WSe$_2$. All these metals have a linear-in-temperature electrical resistivity in the quantum-critical region of their phase diagrams, often termed ``Planckian" resistivity. The solution of the Kubo equation for transport shows that vertex renormalizations to the external fields, beside those caused by Aslamazov-Larkin (A-L) processes, are absent. A-L appears as an Umklapp scattering matrix, which gives a temperature-independent multiplicative factor for the electrical resistivity but does not affect the thermal conductivity. We also show that the mass renormalization which gives a logarithmic enhancement of the marginal Fermi-liquid specific heat does not appear in the electrical resistivity and, more remarkably, in the thermal conductivity. On the other hand the mass renormalization $\propto \ln ω_c/T$ appears in the Seebeck coefficient. We also discuss in detail the conservation laws which play a crucial role in all transport properties. We calculate exactly, the numerical coefficients of the transport properties for a circular Fermi surface. The leading temperature dependences is shown to remain the same for a general Fermi surface, but it is too messy to calculate the numerical coefficient.

cond-mat.str-el↗

arXiv2025

Time-dependent correlations of the Edwards-Anderson order parameter above the spin-glass transition

In 1975 Edwards and Anderson introduced a new paradigm that interacting quenched systems, such as a spin-glass, have a phase transition in which long time memory of spatial patterns is realized without spatial correlations. We show here that the information about the time-dependent correlations above the spin-glass transition are embedded in the four spin correlations of the intensity of speckle pattern. This encodes the spin-orientation memory and can be measured by the technique of resonant magnetic x-ray photon correlation spectroscopy (RM- XPCS). We have implemented this method to observe and accurately characterize the critical slowing down of the spin orientation fluctuations in the classic metallic spin glass alloy $Cu_{1-x}{Mn}_x$ over time scales of ${2}$ sec. to $2 \times 10^{\mathbf{4}}$ secs. Remarkably the divergence of the correlation time as a function of temperature is consistent with the Vogel-Vulcher law, universally used to characterize the viscous relaxation time in structural glasses. Our method also opens the way for studying phase transitions in systems such as spin ices, quantum spin liquids, the structural glass transition, as well as possibly provide new perspectives on the multifarious problems in which spin-glass concepts have found applications.

cond-mat.dis-nn↗

arXiv2025

Anti-symmetric Chiral currents at zero magnetic field in some two-dimensional superconductors

Non-reciprocal critical currents without applying an external magnetic field have been observed recently in several superconductors, in various forms of Graphene, a Kagome compound and in an under-doped cuprate. A necessary requirement for this is that the usual supercurrent be accompanied by an anti-symmetric chiral super-current, i.e. with the symmetry of a hall current; equivalently that the superfluid density tensor have an anti-symmetric chiral component. It also requires inversion breaking. The conditions for this phenomena are derived to find that their normal states must break time-reversal and chirality and that the superconducting states must in addition be non-unitary. Each of the superconductors where spontaneous non-reciprocal critical currents are observed have shown some evidence for such broken symmetries in the normal state. The superconducting state of such materials have topological edge currents, but their projected electro-magnetic part is in general not an integer. The edge states are protected in the superconductor due to a gap. The normal state should show a Kerr effect and, under ideal conditions, an anomalous Hall effect.

cond-mat.str-el↗

arXiv2025

Universality and Crossovers for Quantum-Criticality in 2d metals

A simple generalization of the theory of crossovers in classical-criticality to quantum-criticality gives that, a Heisenberg model with a small anisotropy favoring planar order has a cross-over towards the fixed point of the xy model in the temperature direction which is very rapid compared to those in the orthogonal directions, if the temporal correlation length is much larger than the spatial correlation length, i.e. for a large dynamic exponent $z$. At the other end of the flow, the stability of the fixed point of the quantum xy model coupled to fermions is exponentially enhanced in the temperature direction. This is used to explain why the quantum-critical fluctuations of all measured 2d anti-ferromagnetic compounds - cuprates, heavy-fermion and Fe-based metals shows the characteristic fluctuations of the quantum xy model, and have the same anomalous transport and thermodynamic properties as the cuprates and twisted WSe$_2$ and Graphene. We segue briefly to the range of extended quantum-criticality due to disorder by generalizing the Harris criteria as well, using the properties of the quantum xy model. The observed $T \ln T$ specific heat at criticality is derived quite simply using the same methods which derive the cross-overs. This paper is written for the commemoration volume for Jan Zaanen whom I knew very well, starting from his days as a post-doc at Bell labs to his career as a distinguished Professor at Leiden.

cond-mat.str-el↗

arXiv2024

Shot Noise near Quantum-Criticality

Shot-noise measures the correlations of fluctuations of current for a voltage applied much larger than the temperature and reveals aspects of correlations in fermions beyond those revealed in the conductivity. Recent measurements of shot-noise in the quantum-critical region of the heavy-fermion compound YbRh$_2$Si$_2$ (YRS) have presented a conceptual challenge to old theory and those devised following the experiments. Since the measured resistivity and the specific heat in YRS follow the predictions of marginal Fermi liquid (MFL) theory, we use it to calculate noise using the method developed by Nagaev. We get fair agreement with the magnitude and temperature dependence in the experiments using parameters from resistivity measurements. To achieve this, we find it necessary that the collisions between fermions by exchanging the MFL fluctuations conserve energy but lose momentum through Umklapp scattering and that the fermions and their fluctuations are locally in mutual equilibrium. %and that the self-energy rides the local chemical potential. At low temperatures, impurity scattering determines the noise and at high temperatures the MFL scattering. We show that the noise for MFL scattering for high T alone is the same as the Johnson-Nyquist noise, which in this case is temperature independent. Therefore the Fano factor crosses over to $0$ at high temperatures independent of the voltage applied.

cond-mat.str-el↗

arXiv2024

Extended superconducting fluctuation region and 6e and 4e flux-quantization in a Kagome compound with a normal state of 3Q-order

The superconducting state with the usual 2e-flux quantization formed from a normal state with 3Q charge density or loop-current order is a linear combination of 3 different paired states with an overall gauge invariant phase and two internal phases such that the phases in equilibrium are at $2π/3$ with respect to each other. In the fluctuation regime of such a 3-component superconductor, internal phase fluctuations are of the same class as for frustrated classical xy-spins on a triangular lattice. The fluctuation region is known therefore to be abnormally extended below the mean-field or the Kosterlitz-Thouless transition temperature. A 6e-flux and a 4e-flux quantized states can be constructed which are also eigenstates of the BCS Hamiltonian and stationary points of the Ginzburg-Landau free-energy with a transition temperature above that of the renormalized 2e-flux quantized state. Such states have no internal phases and so no frustrating internal phase fluctuations. These state however cannot acquire long-range order because their free-energy is higher than the co-existing fluctuating state of 2e flux-quantization. 6e- as well as 4e- flux-quantized Little-Parks oscillations however occur in which the resistivity increases periodically with field above that of the 2e-fluctuating state in its extended fluctuation regime, as are observed, followed at low temperatures to a condensation of the time-reversal odd 2e-quantized state

cond-mat.supr-con↗

arXiv2022

Local magnetic moments due to loop currents in metals

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop-currents $L_o$ and spin-loop currents $L_s$ and compare them to the conditions of formation of local spin-moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$ respectively, and inter-site kinetic energy, hybridizing with conduction electrons with a parameter $Δ$ is investigated. $L_o$ and $L_s$ are promoted by large $V/Δ$ and their magnitude is relatively unaffected by $U/Δ$. Spin-magnetic moments $M$ promoted by large $U/Δ$ on the other hand are adversely affected by $V/Δ$. In this model, $L_o$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson's local model for $M$. $L_o$ and $L_s$ are degenerate if exchange interactions and Hund's rule are neglected but $L_o$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small $L_o, L_s$ and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. We also briefly discuss the connection and differences of the interaction generated orbital currents and spin-currents discussed here and generalized to a lattice with the topological states in metals and semi-conductors.

cond-mat.str-el↗

arXiv2022

Theory of melting of glasses

Glassy matter like crystals resists change in shape. Therefore a theory for their continuous melting should show how the shear elastic constant $μ$ goes to zero. Since viscosity is the long wave-length low frequency limit of shear correlations, the same theory should give phenomena like the Volger-Fulcher dependence of the viscosity on temperature near the transition. A continuum model interrupted randomly by asymmetric rigid defects with orientational degrees of freedom is considered. Such defects are orthogonal to the continuum excitations, and are required to be imprisoned by rotational motion of the nearby atoms of the continuum. The defects interact with an angle dependent $μ/r^3$ potential. A renormalization group for the elastic constants, and the fugacity of the defects in 3D is constructed. The principal results are that there is a scale-invariant reduction of $μ$ as a function of length at any temperature $T < T_0$, above which it is 0 macrosopically but has a finite correlation length $ξ(T)$ which diverges as $T \to T_0$. Viscosity is shown to be proportional to $ξ^2(T)$ and has the Vogel-Fulcher form. The specific heat is $\propto ξ^{-3}(T)$. As $T \to T_0$, the Kauzman temperature from above, the configuration entropy of the liquid is exhausted. The theory also gives the ``fragility" of glasses in terms of their $T_0/μ$.

cond-mat.dis-nn↗

arXiv2022

Intrinsic new properties of a quantum spin liquid

Quantum fluctuations are expected to lead to highly entangled spin-liquid states in certain two-dimensional spin-1/2 compounds. We have synthesized and measured thermodynamic properties and muon spin relaxation rates in the copper-based two-dimensional triangular-lattice spin liquids Lu$_3$Cu$_2$Sb$_3$O$_{14}$ and Lu$_3$CuZnSb$_3$O$_{14}$. The former is the least disordered of this kind discovered to date. Magnetic entropy generation at high temperatures has been ruled out after carefully correcting for the lattice specific heat. Surprisingly, roughly half of the magnetic entropy is missing down to temperatures of O(10$^{-3}$) the exchange energy, independent of magnetic field up to $gμ_B H \gtrsim k_BΘ_W$, where $Θ_W$ is the Weiss temperature. The magnetic specific heat divided by temperature $C_M(T)/T$ and muon spin relaxation rate $λ(T)$ are both temperature-independent at low temperatures, followed by logarithmic decreases with increasing temperature. This behavior can be simply characterized by scale-invariant time-dependent fluctuations with a single parameter. Since no cooperative effects due to impurities are observed, the measured properties are intrinsic. They are evidence that in Lu$_3$Cu$_2$Sb$_3$O$_{14}$ massive quantum fluctuations lead to either a gigantic specific heat peak from singlet excitations at very low temperatures or, perhaps less likely, an extensively degenerate possibly topological singlet ground state.

cond-mat.str-el↗

arXiv2022

Quantum-critical resistivity of strange metals in a magnetic field

Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy-fermions, Fe-chalogenides and pnictides, twisted bi-layer graphene and WSe$_2$, is linear in temperature $T$ as well as in a magnetic field $H$. Scattering of fermions by the excitations of a time-reversal odd polar vector field ${\bf Ω}$ characterizing loop-current fluctuations has been shown to give a linear in T resistivity and other anomalous properties in the cuprates. An extension of this theory to an applied magnetic field is presented. Magnetic field is shown to generate vortices in the field ${\bf Ω}$ proportional to $H_z$, the component orthogonal to the conducting planes. The elastic scattering of fermions from the vortices gives a resistivity linear in $H_z$. The coefficient of the linear in $H_z$ resistivity is predicted to vary as the marginal fermi-liquid susceptibility $\propto \ln(\frac{ω_c}{T})$ at criticality. Quantitative comparison with experiments is presented.

cond-mat.str-el↗

arXiv2020

Observation of broken inversion and chiral symmetries in the pseudogap phase in single and double layer bismuth-based cuprates

We deduce the symmetry of the pseudogap state in the single and double layer bismuth-based cuprate superconductors by measuring and analyzing their circular and linear photogalvanic responses, which are related linearly to the chirality and inversion breaking respectively of the order parameter. After separating out the trivial contribution arising from the surface where inversion symmetry is already broken, we show that both responses start below the pseudogap temperature $T^*$ and grow below it to a sizable magnitude, revealing the broken symmetries in the bulk of the crystal. Through a detailed analysis of the dependence of the signals on the angle of incidence, the polarization of the light, and the orientation of the crystal, we are able to discover that the point group symmetry below $T^*$ is limited to $mm2$ or $mm2\underline{1}$ groups. Taking into account formation of domains and previous measurements, our results narrow down the possible symmetries of the microscopic origin of the phase transition(s) at $T^*$.

cond-mat.str-el↗

arXiv2020

Thermal Hall effect in the pseudogap phase of cuprates

The conjecture made recently by the group at Sherbrooke, that their observed anomalous thermal Hall effect in the pseudo-gap phase in the cuprates is due to phonons, is supported on the basis of an earlier result that the observed loop-current order in this phase must induce lattice distortions which are linear in the order parameter and an applied magnetic field. The lowered symmetry of the crystal depends on the direction of the field. A consequence is that the elastic constants change proportional to the field and are shown to induce axial thermal transport with the same symmetries as the Lorentz force enforces for the normal electronic Hall effect. Direct measurements of elastic constants in a magnetic field are suggested to verify the quantitative aspects of the results.

cond-mat.str-el↗

arXiv2020

Direct measurement of temporal correlations above the spin-glass transition by coherent resonant magnetic x-ray spectroscopy

In the 1970s a new paradigm was introduced that interacting quenched systems, such as a spin-glass, have a phase transition in which long time memory of spatial patterns is realized without spatial correlations. The principal methods to study the spin-glass transition, besides some elaborate and elegant theoretical constructions, have been numerical computer simulations and neutron spin echo measurements . We show here that the dynamical correlations of the spin-glass transition are embedded in measurements of the four-spin correlations at very long times. This information is directly available in the temporal correlations of the intensity, which encode the spin-orientation memory, obtained by the technique of resonant magnetic x-ray photon correlation spectroscopy (RM- XPCS). We have implemented this method to observe and accurately characterize the critical slowing down of the spin orientation fluctuations in the classic metallic spin glass alloy Cu(Mn) over time scales of 1 to 1000 secs. Our method opens the way for studying phase transitions in systems such as spin ices, and quantum spin liquids, as well as the structural glass transition.

cond-mat.str-el↗

arXiv2020

Linear in Temperature Resistivity and Associated Mysteries

Recent experimental results: (i) the measurement of the $T \ln T$ specific heat in cuprates and the earlier such results in some heavy fermion compounds, (ii) the measurement of the single-particle scattering rates, (iii) the density fluctuation spectrum in cuprates and (iv) the long standing results on the linear temperature dependence of the resistivity, show that a theory of the quantum-criticality in these compounds based on the solution of the dissipative 2D - XY model gives the temperature and frequency dependence of each of them, and the magnitudes of all four with one dimensionless coupling parameter. These low frequency or temperature dependences persist to an upper cut-off which is measured to be about the same from the singularity in the specific heat or the saturation of the single-particle self-energy. The same two parameters are deduced in the analysis of results of photoemission experiments to give d-wave superconductivity and its transition temperature. The coupling parameter and the cut-off had been estimated in the microscopic theory to within a factor of 2. The simplicity of the results depends on the discovery that orthogonal topological excitations in space and in time determine the fluctuations near criticality such that the space and time metrics are free of each other. The interacting fermions then form a marginal Fermi-liquid.

cond-mat.str-el↗

arXiv2019

Pseudogap and Fermi-arcs in underdoped cuprates

The proposed loop-current order in cuprates cannot give the observed pseudogap and the Fermi-arcs because it preserves translation symmetry. A modification to a periodic arrangement of the four possible orientations of the order parameter with a large period of between about 12 to 30 lattice constants is proposed and shown in a simple and controlled calculation to give one-particle spectra with every feature as in the ARPES experiments. The results follow from (1) the currents at the boundaries of the periodic domains with similar topology as the Affleck-Marston flux phase, and (2) the mixing introduced by the boundary currents between the states near the erstwhile Fermi-surface and the ghost Fermi-surfaces which are displaced from it by mini-reciprocal vectors. The proposed idea can be ruled out or verified by high resolution diffraction or imaging experiments. It does not run afoul of the variety of different experiments consistent with the loop-current order as well as the theory of the marginal Fermi-liquid and d-wave superconductivity based on quantum-critical fluctuations of the loop current order.

cond-mat.str-el↗

arXiv2018

Renormalizations in unconventional superconducting states born of normal and singular Fermi-liquids

The density of low energy particle-hole excitations is non-analytic in a singular Fermi-liquid, but it is altered on entering a superconducting state in which, in the pure limit, it vanishes asymptotically at the chemical potential and in general is analytic. The single-particle excitations in the superconducting states are then quasi-particles so that a form of Landau theory may be constructed for thermodynamic and transport properties in the superconducting state. In this theory, the renormalization of measurable properties due to quasi-particle interactions, such as specific heat, compressibility, magnetic susceptibility, superfluid density, etc. changes in a temperature dependent fashion from the non-interacting theory. This is illustrated by showing the renormalization of these quantities and the relation between the parameters introduced to account for their temperature dependence. When the renormalizations in the normal state are large or singular, temperature dependence of properties in the superconducting states are then in general not useful for identifying the nodal character or symmetry of the superconducting state except for measurements at very low temperatures, upper limits of which are specified. The results obtained are expected to be useful in interpreting the experimental results for the temperature dependence of various properties in the superconducting state born of singular Fermi liquids.

cond-mat.str-el↗

arXiv2018

Crossovers due to anisotropy and disorder in quantum critical fluctuations

Scaling relations are used to study cross-overs, due to anisotropic spin interactions or single ion anisotropy, and due to disorder, in the thermodynamics and correlation functions near quantum-critical transitions. The principal results are simple with a wide range of applications. The region of attraction to the stable anisotropic fixed point in the quantum-critical region is exponentially enhanced by the dynamical critical exponent $z$ compared to the region of attraction to the fixed point in the quantum disordered region. The result implies that, even for small anisotropy, the region of attraction to the stable incommensurate Ising or planar metallic anti-ferromagnetic critical points, which belong to the universality class of the XY model with $z \to \infty$, covers the entire quantum-critical region. In crossovers due to disorder, the instability of the pure fixed point in the quantum disordered region is exponentially enhanced by $z$ compared to that in the quantum-critical region. This result suggests that for some classes of disorder and for large enough $z$, one may find singularities in the correlations as a function of frequency and temperature down to very low temperatures even though the correlation length in space remains short range.

cond-mat.str-el↗