arXiv subjects

Aavishkar A. Patel

Publications and source records attributed to Aavishkar A. Patel.

At least 37 records · Page 2Linked to original sources

arXiv2021

Strange Metals from Melting Correlated Insulators in Twisted Bilayer Graphene

Even as the understanding of the mechanism behind correlated insulating states in magic-angle twisted bilayer graphene converges towards various kinds of spontaneous symmetry breaking, the metallic "normal state" above the insulating transition temperature remains mysterious, with its excessively high entropy and linear-in-temperature resistivity. In this work, we focus on the effects of fluctuations of the order-parameters describing correlated insulating states at integer fillings of the low-energy flat bands on charge transport. Motivated by the observation of heterogeneity in the order-parameter landscape at zero magnetic field in certain samples, we conjecture the existence of frustrating extended range interactions in an effective Ising model of the order-parameters on a triangular lattice. The competition between short-distance ferromagnetic interactions and frustrating extended range antiferromagnetic interactions leads to an emergent length scale that forms stripe-like mesoscale domains above the ordering transition. The gapless fluctuations of these heterogeneous configurations are found to be responsible for the linear-in-temperature resistivity as well as the enhanced low temperature entropy. Our insights link experimentally observed linear-in-temperature resistivity and enhanced entropy to the strength of frustration, or equivalently, to the emergence of mesoscopic length scales characterizing order-parameter domains.

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arXiv2021

Large $N$ theory of critical Fermi surfaces

We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions. The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces. We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$Σ$ path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large $N$ saddle-point equations, and the results agree with the critical behavior obtained analytically. Following analyses of Sachdev-Ye-Kitaev models, we describe scaling operators which descend from fermion bilinears around the Fermi surface. This leads to a systematic consideration of the role of time reparameterization symmetry, and the scaling of the Cooper pairing and $2k_F$ operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparameterizations. We also consider the same model but with spatially random couplings: this provides a systematic large $N$ theory of a marginal Fermi liquid with Planckian transport.

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arXiv2020

$T$-linear resistivity in models with local self-energy

A theoretical understanding of the enigmatic linear-in-temperature ($T$) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust $T$-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub "slope invariance". Recently, several solvable models with $T$-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate $T$-linearity: a lattice of coupled Sachdev-Ye-Kitaev (SYK) models and the Hubbard model in single-site dynamical mean-field theory (DMFT). We find that the two models achieve $T$-linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit "slope invariance" across the two temperature regimes. We thus not only reveal some of the diversity in the theoretical inner workings that can lead to $T$-linear resistivity, but we also establish that different mechanisms can result in "slope invarance".

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arXiv2019

Many-body chaos in the antiferromagnetic quantum critical metal

We compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory of Phys. Rev. X $\boldsymbol{7}$, 021010 (2017). At this strongly coupled fixed point, there is an emergent control parameter $w \ll 1$ that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. We find that the scrambling rates act as a measure of the "degree of integrability" of each sector of the theory: the Lyapunov exponent for the boson $λ_L^{(B)} \sim \mathcal O(\sqrt{w}) \,k_B T/\hbar$ is significantly larger than the fermion one $λ_L^{(F)} \sim \mathcal O(w^2) \,k_B T/\hbar$, where $T$ is the temperature. Although the interaction strength in the theory is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound of $λ_L=2πk_B T/\hbar$. We also compute the spatial spread of chaos by the boson operator, whose low-energy propagator is highly non-local. We find that this non-locality leads to a scrambled region that grows exponentially fast, giving an infinite "butterfly velocity" of the chaos front, a result that has also been found in lattice models with long-range interactions.

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arXiv2019

Theory of a Planckian metal

We present a lattice model of fermions with $N$ flavors and random interactions which describes a Planckian metal at low temperatures, $T \rightarrow 0$, in the solvable limit of large $N$. We begin with quasiparticles around a Fermi surface with effective mass $m^\ast$, and then include random interactions which lead to fermion spectral functions with frequency scaling with $k_B T/\hbar$. The resistivity, $ρ$, obeys the Drude formula $ρ= m^\ast/(n e^2 τ_{\textrm{tr}})$, where $n$ is the density of fermions, and the transport scattering rate is $1/τ_{\textrm{tr}} = f \, k_B T/\hbar$; we find $f$ of order unity, and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes non-resonant in the bare quasiparticle energies only renormalize $m^\ast$, while resonant processes are shown to produce the Planckian behavior.

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arXiv2018

A critical strange metal from fluctuating gauge fields in a solvable random model

Building upon techniques employed in the construction of the Sachdev-Ye-Kitaev (SYK) model, which is a solvable $0+1$ dimensional model of a non-Fermi liquid, we develop a solvable, infinite-ranged random-hopping model of fermions coupled to fluctuating U(1) gauge fields. In a specific large-$N$ limit, our model realizes a gapless non-Fermi liquid phase, which combines the effects of hopping and interaction terms. We derive the thermodynamic properties of the non-Fermi liquid phase realized by this model, and the charge transport properties of an infinite-dimensional version with spatial structure.

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arXiv2018

Coherent superconductivity with large gap ratio from incoherent metals

A mysterious incoherent metallic (IM) normal state with $T$-linear resistivity is ubiquitous among strongly correlated superconductors. Recent progress with microscopic models exhibiting IM transport has presented the opportunity for us to study new models that exhibit direct transitions into a superconducting state out of IM states within the framework of connected Sachdev-Ye-Kitaev (SYK) "quantum dots". Here local SYK interactions within a dot produce IM transport in the normal state, while local attractive interactions drive superconductivity. Through explicit calculations, we find two features of superconductivity arising from an IM normal state: First, despite the absence of quasiparticles in the normal state, the superconducting state still exhibits coherent superfluid transport. Second, the non-quasiparticle nature of the IM Green's functions produces a large enhancement in the ratio of the zero-temperature superconducting gap $Δ$ and transition temperature $T_{sc}$, $2Δ/T_{sc}$, with respect to its BCS value of $3.53$.

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arXiv2018

Magnetotransport in a model of a disordered strange metal

Despite much theoretical effort, there is no complete theory of the 'strange' metal state of the high temperature superconductors, and its linear-in-temperature, $T$, resistivity. Recent experiments showing an unexpected linear-in-field, $B$, magnetoresistivity have deepened the puzzle. We propose a simple model of itinerant electrons, interacting via random couplings with electrons localized on a lattice of quantum 'dots' or 'islands'. This model is solvable in a large-$N$ limit, and can reproduce observed behavior. The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations. For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-$T$ resistivity and a $T \ln T$ specific heat as $T\rightarrow 0$. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-$T$ crossover to a fully incoherent regime that also has a linear-in-$T$ resistivity. We show that the MFL regime has conductivities which scale as a function of $B/T$; however, its magnetoresistance saturates at large $B$. We then consider a macroscopically disordered sample with domains of MFLs with varying densities of electrons. Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field $B$ applied perpendicular to the plane of the sample, at large $B$. The resistance also scales linearly in $T$ at small $B$, and as $T f(B/T)$ at intermediate $B$. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

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arXiv2017

Hydrodynamic flows of non-Fermi liquids: magnetotransport and bilayer drag

We consider a hydrodynamic description of transport for generic two dimensional electron systems that lack Galilean invariance and do not fall into the category of Fermi liquids. We study magnetoresistance and show that it is governed only by the electronic viscosity provided that the wavelength of the underlying disorder potential is large compared to the microscopic equilibration length. We also derive the Coulomb drag transresistance for double-layer non-Fermi liquid systems in the hydrodynamic regime. As an example, we consider frictional drag between two quantum Hall states with half-filled lowest Landau levels, each described by a Fermi surface of composite fermions coupled to a $U(1)$ gauge field. We contrast our results to prior calculations of drag of Chern-Simons composite particles and place our findings in the context of available experimental data.

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arXiv2017

Quantum butterfly effect in weakly interacting diffusive metals

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron field operators inherits a light-cone like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information, that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent $z > 1$.

cond-mat.str-el↗

arXiv2017

Quantum chaos on a critical Fermi surface

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.

cond-mat.str-el↗

arXiv2017

Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals

In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\, η/s$, where $η$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $η$ scales in the same manner as a chiral conductivity, and the ratio $η/s$ diverges at low temperature ($T$) as $T^{-2/z}$, where $z$ is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.

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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.

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arXiv2016

Light induced enhancement of superconductivity via melting of competing bond-density wave order in underdoped cuprates

We develop a theory for light-induced superconductivity in underdoped cuprates in which the competing bond-density wave order is suppressed by driving phonons with light. Close to a bond-density wave instability in a system with a small Fermi surface, such as a fractionalized Fermi liquid, we show that the coupling of electrons to phonons is strongly enhanced at the bond-density wave ordering wavevectors, leading to a strong softening of phonons at these wavevectors. For a model of classical phonons with anharmonic couplings, we show that the combination of strong softening and driving can lead to large phonon oscillations. When coupled to a phenomenological model describing the competition between bond-density wave order and superconductivity, these phonon oscillations melt bond-density wave order, thereby enhancing pairing correlations.

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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.

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arXiv2015

Hyperscaling at the spin density wave quantum critical point in two dimensional metals

The hyperscaling property implies that spatially isotropic critical quantum states in $d$ spatial dimensions have a specific heat which scales with temperature as $T^{d/z}$, and an optical conductivity which scales with frequency as $ω^{(d-2)/z}$ for $ω\gg T$, where $z$ is the dynamic critical exponent. We examine the spin-density-wave critical fixed point of metals in $d=2$ found by Sur and Lee (Phys. Rev. B 91, 125136 (2015)) in an expansion in $ε= 3-d$. We find that the contributions of the "hot spots" on the Fermi surface to the optical conductivity and specific heat obey hyperscaling (up to logarithms), and agree with the results of the large $N$ analysis of the optical conductivity by Hartnoll et al. (Phys. Rev. B 84, 125115 (2011)). With a small bare velocity of the boson associated with the spin density wave order, there is an intermediate energy regime where hyperscaling is violated with $d \rightarrow d_t$, where $d_t = 1$ is the number of dimensions transverse to the Fermi surface. We also present a Boltzmann equation analysis which indicates that the hot spot contribution to the DC conductivity has the same scaling as the optical conductivity, with $T$ replacing $ω$.

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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↗

arXiv2013

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the z-direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to +1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

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