arXiv subjects

Debanjan Chowdhury

Publications and source records attributed to Debanjan Chowdhury.

At least 91 records · Page 5Linked to original sources

arXiv2016

Two dimensional spin liquids with $\mathbb{Z}_2$ topological order in an array of quantum wires

Insulating $\mathbb{Z}_2$ spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground state degeneracies on manifolds with non-trivial topology. In this paper, we construct a time-reversal symmetric $\mathbb{Z}_2$ spin liquid in two spatial dimensions using an array of quantum wires. We identify the anyons as kinks in the appropriate Luttinger-liquid description, compute their mutual statistics and construct local operators that transport these quasiparticles. We also present a construction of a fractionalized Fermi-liquid (FL*) by coupling the spin sector of the $\mathbb{Z}_2$ spin-liquid to a Fermi-liquid via a Kondo-like coupling.

cond-mat.str-el↗

arXiv2016

Slow scrambling in disordered quantum systems

Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of commutators in a variety of contexts. We find generically that disorder slows the onset of scrambling, and, in the case of a many-body localized state, partially halts it. We access the many-body localized state using a standard fixed point Hamiltonian, and we show that operators exhibit slow logarithmic growth under time evolution. We compare the result with the expected growth of commutators in both localized and delocalized non-interacting disordered models. Finally, based on a scaling argument, we state a conjecture about the effect of weak interactions on the growth of commutators in an interacting diffusive metal.

cond-mat.str-el↗

arXiv2016

Confinement transition to density wave order in metallic doped spin liquids

Insulating quantum spin liquids can undergo a confinement transition to a valence bond solid state via the condensation of topological excitations of the associated gauge theory. We extend the theory of such transitions to fractionalized Fermi liquids (FL*): these are metallic doped spin liquids in which the Fermi surfaces only have gauge neutral quasiparticles. Using insights from a duality transform on a doped quantum dimer model for the U(1)-FL* state, we show that projective symmetry group of the theory of the topological excitations remains unmodified, but the Fermi surfaces can lead to additional frustrating interactions. We propose a theory for the confinement transition of $\mathbb{Z}_2$-FL* states via the condensation of visons. A variety of confining, incommensurate density wave states are possible, including some that are similar to the incommensurate $d$-form factor density wave order observed in several recent experiments on the cuprate superconductors.

cond-mat.str-el↗

arXiv2015

Fluctuating charge order in the cuprates: spatial anisotropy and feedback from superconductivity

We analyze the form of static charge susceptibility $χ(q)$ in underdoped cuprates near axial momenta $(Q,0)$ and $(0,Q)$ at which short-range static charge order has been observed. We show that the momentum dependence of $χ(q)$ is anisotropic, and the correlation length in the longitudinal direction is larger than in the transverse direction. We show that correlation lengths in both directions decrease once the system evolves into a superconductor, as a result of the competition between superconductivity and charge order. These results are in agreement with resonant x-ray scattering data [R. Comin et al., Science 347, 1335 (2015)]. We also argue that density and current components of the charge order parameter are affected differently by superconductivity --- the charge-density component is reduced less than the current component and hence extends deeper into the superconducting state. This gives rise to two distinct charge order transitions at zero temperature.

cond-mat.str-el↗

arXiv2015

Phase transition beneath the superconducting dome in BaFe$_2$(As$_{1-x}$P$_x$)$_2$

We present a theory for the large suppression of the superfluid-density, $ρ_s$, in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ in the vicinity of a putative spin-density wave quantum critical point at a P-doping, $x=x_{c}$. We argue that the transition becomes weakly first-order in the vicinity of $x_{c}$, and disorder induces puddles of superconducting and antiferromagnetic regions at short length-scales; thus the system becomes an electronic micro-emulsion. We propose that frustrated Josephson couplings between the superconducting grains suppress $ρ_s$. In addition, the presence of `normal' quasiparticles at the interface of the frustrated Josephson junctions will give rise to a highly non-trivial feature in the low frequency response in a narrow vicinity around $x_c$. We propose a number of experiments to test our theory.

cond-mat.str-el↗

arXiv2015

Higgs criticality in a two-dimensional metal

We analyze a candidate theory for the strange metal near optimal hole-doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the local antiferromagnetic correlations in a "rotating reference frame". We propose a global phase diagram around this Higgs transition, and describe its relationship to a variety of recent experiments on the cuprate superconductors.

cond-mat.str-el↗

arXiv2014

The enigma of the pseudogap phase of the cuprate superconductors

The last few years have seen significant experimental progress in characterizing the copper-based hole-doped high temperature superconductors in the regime of low hole density, p. Quantum oscillations, NMR, X-ray, and STM experiments have shed much light on the nature of the ordering at low temperatures. We review evidence that the order parameter in the non-Lanthanum-based cuprates is a d-form factor density-wave. This novel order acts as an unexpected window into the electronic structure of the pseudogap phase at higher temperatures in zero field: we argue in favor of a `fractionalized Fermi liquid' (FL*) with 4 pockets of spin S=1/2, charge +e fermions enclosing an area specified by p.

cond-mat.str-el↗

arXiv2014

Density-wave instabilities of fractionalized Fermi liquids

Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic correlations, where the electronic excitations are coupled to the fractionalized excitations of a quantum fluctuating antiferromagnet on the square lattice. The resulting charge density wave state emerging out of such a fractionalized Fermi-liquid (FL*) has wavevectors of the form $(\pm Q_0,0), (0,\pm Q_0)$, with a predominantly $d$-form factor, in agreement with experiments on a number of different families of the cuprates. In contrast, as previously shown, the charge density wave instability of a nearly antiferromagnetic metal with a large Fermi surface, interacting via short-range interactions, has wavevectors of the type $(\pm Q_0,\pm Q_0)$. Our results show that the observed charge density wave appears as a low-energy instability of a fractionalized metallic state linked to the proximity to an antiferromagnetic insulator, and the pseudogap regime can be described by such a metal at least over intermediate length and energy scales.

cond-mat.str-el↗

arXiv2014

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

The central puzzle of the cuprate superconductors at low hole density is the nature of the pseudogap regime. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge density wave order at intermediate temperatures, and quantum oscillations at high magnetic fields and low temperatures. We show that a model of competing charge density wave and superconducting orders provides a unified description of the intermediate and low temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge density and superconducting orders. Our results are compatible with experimental trends.

cond-mat.str-el↗

arXiv2014

Feedback of superconducting fluctuations on charge order in the underdoped cuprates

Metals interacting via short-range antiferromagnetic fluctuations are unstable to sign-changing superconductivity at low temperatures. For the cuprates, this leading instability leads to the well known $d-$wave superconducting state. However, there is also a secondary instability to an incommensurate charge density wave, with a predominantly $d-$wave form factor, arising from the same antiferromagnetic fluctuations. Recent experiments in the pseudogap regime of the hole-doped cuprates have found strong evidence for such a charge density wave order and, in particular, the predicted $d-$wave form factor. However, the observed wavevector of the charge order differs from the leading instability in Hartree-Fock theory, and is that of a subleading instability. In this paper, we examine the feedback of superconducting fluctuations on these different charge-density wave states, and find that over at least a small temperature window, they prefer the experimentally observed wavevector.

cond-mat.str-el↗

arXiv2014

Multipoint correlators of conformal field theories: implications for quantum critical transport

We compute three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an effective action on 3+1 dimensional anti-de Sitter space (AdS_4) proposed by Myers et al., and depend upon the co-efficient, γ, of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of γ. The CFTs of free fermions and bosons take the values γ=1/12,-1/12 respectively, and so saturate the bound |γ| <= 1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of γ. The value of γalso controls the frequency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of γlead to an appealing physical interpretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics.This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

cond-mat.str-el↗

arXiv2013

Singularity of the London penetration depth at quantum critical points in superconductors

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents, and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with $\mathbb{Z}_2$ fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ (Hashimoto et al., Science 336, 1554 (2012)).

cond-mat.str-el↗

arXiv2013

Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice

Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of spin liquids, the measured dynamic structure factor reveals an excitation continuum which is remarkably flat as a function of frequency and has almost no momentum dependence along several high-symmetry directions. Here we show that many experimentally observed features can be explained by the presence of topological vison excitations in a Z2 spin liquid. These visons form flat bands on the kagome lattice, and thus act as a momentum sink for spin-carrying excitations which are probed by neutron scattering. We compute the dynamic structure factor for two different Z2 spin liquids and find that one of them describes Herbertsmithite well above a very low energy cutoff.

cond-mat.str-el↗

arXiv2013

A signature of quantum spin liquids in superconductors with topological order

This paper has been withdrawn and superseded by a new version entitled "Singularity of the London penetration depth at quantum critical points in superconductors" by Debanjan Chowdhury, Brian Swingle, Erez Berg and Subir Sachdev, posted in arXiv:1305.2918. The more recent paper has a number of new interesting results and includes a comprehensive analysis of 3 different classes of QCPs, including the one that was originally considered.

cond-mat.str-el↗

arXiv2012

High sensitivity differential Magneto-Optical Imaging with a compact Faradaymodulator

We present here the design of a sensitive Compact Faraday-modulator (CFM) based optical magnetometer for imaging the distribution of weak local magnetic fields inside hysteretic magnetic materials. The system developed has a root mean square (rms) noise level of 50 mG.Hz-1/2 at a full frame rate of 1 frame per second with each frame being of size 512 x 512 pixels. By measuring the local magnetic field distribution in different superconducting samples we show that our magnetometer provides an order of magnitude improvement in the signal to noise (S/N) ratio at low fields as compared to ordinary magneto-optical imaging technique. Moreover, it provides the required sensitivity for imaging the weak magnetization response near a superconducting transition where a number of other imaging techniques are practically unviable. An advantage of our CFM design is that it can be scaled in size to fit into situations with tight space constraints.

cond-mat.supr-con↗

arXiv2012

Breakdown of Fermi liquid behavior at the (π,π)=2k_F spin-density wave quantum-critical point: the case of electron-doped cuprates

Many correlated materials display a quantum critical point between a paramagnetic and a SDW state. The SDW wave vector connects points (hot spots) on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here we consider the case where pairs of hot spots coalesce, and the wave vector (π,π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility and the self-energy at the hot spots are found using the Two-Particle-Self-Consistent theory and specific numerical examples worked out for parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudo-nesting conditions lead to drastic modifications to the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξscales like 1/T, i.e. z=1 instead of the naive z=2, the (π,π) static spin susceptibility χlike $1/\sqrt T$, and the imaginary part of the self-energy at the hot spots like $T^{3/2}$. The correction $T_1^{-1}\sim T^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless SDW fluctuations interacting with fermions. The imaginary part of the fermionic self-energy close to the hot spots scales as $-ω^{3/2}\logω$. This is less singular than earlier predictions of the form $-ω\logω$. The difference arises from the effects of umklapp terms that were not included in previous studies.

cond-mat.str-el↗

arXiv2011

Nematic order in the vicinity of a vortex in superconducting FeSe

We present a phenomenological theory of the interplay between nematic order and superconductivity in the vicinity of a vortex induced by an applied magnetic field. Nematic order can be strongly enhanced in the vortex core. As a result, the vortex cores become elliptical in shape. For the case where there is weak bulk nematic order at zero magnetic field, the field-induced eccentricity of the vortex core has a slow power-law decay away from the core. Conversely, if the nematic order is field-induced, then the eccentricity is confined to the vortex core. We discuss the relevance of our results to recent scanning tunnelling microscopy experiments on FeSe (Song et al., Science 332, 1410 (2011)).

cond-mat.supr-con↗

arXiv2010

Synchronization of oscillators with long range power law interactions

We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law exponent $α_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find $α_c=3/2$. Frequency entrainment and phase ordering are discussed as a function of $α\geq 1$. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the {\it d}-dimensional problem.

cond-mat.stat-mech↗