arXiv subjects

Subir Sachdev

Publications and source records attributed to Subir Sachdev.

At least 199 records · Page 11Linked to original sources

arXiv2015

Bekenstein-Hawking Entropy and Strange Metals

We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$, and a non-zero entropy density $\mathcal{S}$ at vanishing temperature. Real time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency $ω_{\mathcal{S}} = (q \, T/\hbar) (\partial \mathcal{S}/\partial{\mathcal{Q}})$ which determines a spectral asymmetry. We show that the correlators match precisely with those of the AdS$_2$ horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density, and the laws of black hole thermodynamics which relate $(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2 π)$ to the electric field strength in AdS$_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.

hep-th↗

arXiv2015

Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State

Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic 'pseudogap' phenomenon$^{1,2}$ and the more recently investigated density wave state$^{3-13}$. This state always exhibits wave vector $Q$ parallel to the planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a key objective$^{18-30}$ of this field. To accomplish this, one must identify the momentum-space ($k$-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization$^{14}$ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy $Δ_{1}$. Moreover, we demonstrate that the dFF-DW modulations at $E=-Δ_{1}$ (filled states) occur with relative phase $π$ compared to those at $E=Δ_{1}$ (empty states). Finally, we show that the dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier' regions of $k$-space beyond which Bogoliubov quasiparticles cease to exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in $k$-space where the pseudogap opens.

cond-mat.supr-con↗

arXiv2015

Probing excitations in insulators via injection of spin-currents

We propose a spin transport experiment to measure the low-energy excitations in insulators with spin degrees of freedom, with a focus on detecting ground states that lack magnetic order. A general formalism to compute the spin-current from a metal with a non-equilibrium distribution of spins to an insulator is developed. It is applied to insulating states with and without long range magnetic order, and salient features in the spin-conductance are noted.

cond-mat.str-el↗

arXiv2015

A quantum dimer model for the pseudogap metal

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, $p$. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin $S=1/2$, charge $+e$ fermionic dimers. The model realizes a `fractionalized Fermi liquid' with no symmetry-breaking and small hole pocket Fermi surfaces enclosing a total area determined by $p$. Exact diagonalization, on lattices of sizes up to $8 \times 8$, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

cond-mat.str-el↗

arXiv2015

Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations

We study charge ordered solutions for fermions on a square lattice interacting with dynamic antiferromagnetic fluctuations. Our approach is based on real space Eliashberg equations which are solved self-consistently. We first show that the antiferromagnetic fluctuations can induce arc features in the spectral functions, as spectral weight is suppressed at the hot spots; however, no real pseudogap is generated. At low temperature spontaneous charge order with a $d$-form factor can be stabilized for certain parameters. As long as the interacting Fermi surfaces possesses hot spots, the ordering wave vector corresponds to the diagonal connection of the hot spots, similar to the non-self-consistent case. Tendencies towards observed axial order only appear in situations without hot spots.

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

Memory matrix theory of magnetotransport in strange metals

We model strange metals as quantum liquids without quasiparticle excitations, but with slow momentum relaxation, and with slow diffusive dynamics of a conserved charge and energy. General expressions are obtained for electrical, thermal and thermoelectric transport in the presence of an applied magnetic field using the memory matrix formalism. In the appropriate limits, our expressions agree with previous hydrodynamic and holographic results. We discuss the relationship of such results to thermoelectric and Hall transport measurements in the strange metal phase of the hole-doped cuprates.

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↗

arXiv2015

Are non-Fermi-liquids stable to Cooper pairing?

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include: ${\it (i)}$ quantum critical points associated with the onset of order in metals; ${\it (ii)}$ spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator; ${\it (iii)}$ Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of a phase transition in a metal, and demonstrate that the attractive interaction mediated by the order parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between ${\it (i)}$ $U(1)$ and $Z_2$ spin-liquid states; ${\it (ii)}$ Halperin-Lee-Read and Moore-Read states.

cond-mat.str-el↗

arXiv2015

Charge ordering in three-band models of the cuprates

We examine trends in the wavevectors and form-factors of charge density wave instabilities of three-band models of the underdoped cuprates. For instabilities from a high temperature state with a large Fermi surface, we extend a study by Bulut et al. (arXiv:1305.3301) to include a direct antiferromagnetic exchange coupling between the Cu sites. As in previous work, we invariably find that the primary instability has a diagonal wavevector $(\pm Q_0, \pm Q_0)$ and a $d$-form factor. The experimentally observed wavevectors along the principal axes $(\pm Q_0,0)$, $(0, \pm Q_0)$ have higher energy, but they also have a predominantly $d$-form factor. Next, we gap out the Fermi surface in the anti-nodal regions of the Brillouin zone by including static, long-range antiferromagnetic order at the wavevector $(π, π)$: this is a simple model of the pseudogap in which we assume the antiferromagnetic order averages to zero by `renormalized classical' thermal fluctuations in its orientation, valid when the antiferromagnetic correlation length is large. The charge density wave instabilities of this pseudogap state are found to have the optimal wavevector $(\pm Q_0,0)$, $(0, \pm Q_0)$, with the magnitude of the $d$-form factor decreasing with increasing magnetic order.

cond-mat.str-el↗

arXiv2015

Conductivity of weakly disordered strange metals: from conformal to hyperscaling-violating regimes

We present a semi-analytic method for constructing holographic black holes that interpolate from anti-de Sitter space to hyperscaling-violating geometries. These are holographic duals of conformal field theories in the presence of an applied chemical potential, $μ$, at a non-zero temperature, $T$, and allow us to describe the crossover from `strange metal' physics at $T \ll μ$, to conformal physics at $T \gg μ$. Our holographic technique adds an extra gauge field and exploits structure of the Einstein-Maxwell system to manifestly find 1-parameter families of solutions of the Einstein-matter system in terms of a small family of functions, obeying a nested set of differential equations. Using these interpolating geometries, we re-consider holographically some recent questions of interest about hyperscaling-violating field theories. Our focus is a more detailed holographic computation of the conductivity of strange metals, weakly perturbed by disorder coupled to scalar operators, including both the average conductivity as well as sample-to-sample fluctuations. Our findings are consistent with previous scaling arguments, though we point out logarithmic corrections in some special (holographic) cases. We also discuss the nature of superconducting instabilities in hyperscaling-violating geometries with appropriate choices of scalar couplings.

hep-th↗

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

Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography

We compute the non-zero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 spacetime dimensions. At frequencies much greater than the temperature, $\hbarω>> k_B T$, the $ω$ dependence can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large $ω$ results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small $\hbar ω/(k_B T)$. Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large $ω$ behavior for a large class of CFTs. However, for the Wilson-Fisher CFT a relevant "thermal" operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value. We also establish sum rules obeyed by the conductivity of a wide class of CFTs.

cond-mat.str-el↗

arXiv2014

DC resistivity at the onset of spin density wave order in two-dimensional metals

The theory for the onset of spin density wave order in a metal in two dimensions flows to strong coupling, with strong interactions not only at the `hot spots', but on the entire Fermi surface. We advocate the computation of DC transport in a regime where there is rapid relaxation to local equilibrium around the Fermi surface by processes which conserve total momentum. The DC resistivity is then controlled by weaker perturbations which do not conserve momentum. We consider variations in the local position of the quantum critical point, induced by long-wavelength disorder, and find a contribution to the resistivity which is linear in temperature (up to logarithmic corrections) at low temperature. Scattering of fermions between hot spots, by short-wavelength disorder, leads to a residual resistivity and a correction which is linear in temperature.

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

Conserved current correlators of conformal field theories in 2+1 dimensions

We compute current correlators of the CP^{N-1} field theory in 2+1 dimensions, both at the critical point and in the phase with spontaneously broken SU(N) symmetry. Universal constants are obtained to next-to-leading order in the 1/N expansion. Implications are noted for quantum critical points of antiferromagnets, and their vicinity.

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↗