36 research outputs found

### 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.Comment: 4 pages + references + supplementary information, 1 figur

### Two-dimensional spin liquids with Z2 topological order in an array of quantum wires

Insulating Z[subscript 2] spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground-state degeneracies on manifolds with nontrivial topology. We construct a time-reversal symmetric Z[subscript 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 Z[subscript 2] spin liquid to a Fermi liquid via a Kondo-like coupling.Gordon and Betty Moore Foundation (Postdoctoral Fellowship Grant GBMF-4303)National Science Foundation (U.S.) (Grant DMR-13001648

### 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 $z > 1$.Comment: 15 pages in two-column format, 7 figure

### 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.Comment: 21 pages + Appendices + References, 4 figure