arXiv subjects

Rahul Nandkishore

Publications and source records attributed to Rahul Nandkishore.

At least 73 records · Page 4Linked to original sources

arXiv2014

A mean-field theory of nearly many-body localized metals

We develop a mean-field theory of the metallic phase near the many-body localization (MBL) transition, using the observation that a system near the MBL transition should become an increasingly slow heat bath for its constituent parts. As a first step, we consider the properties of a many-body localized system coupled to a generic ergodic bath whose characteristic dynamical timescales are much slower than those of the system. As we discuss, a wide range of experimentally relevant systems fall into this class; we argue that relaxation in these systems is dominated by collective many-particle rearrangements, and compute the associated timescales and spectral broadening. We then use the observation that the self-consistent environment of any region in a nearly localized metal can itself be modeled as a slowly fluctuating bath to outline a self-consistent mean-field description of the nearly localized metal and the localization transition. In the nearly localized regime, the spectra of local operators are highly inhomogeneous and the typical local spectral linewidth is narrow. The local spectral linewidth is proportional to the DC conductivity, which is small in the nearly localized regime. This typical linewidth and the DC conductivity go to zero as the localized phase is approached, with a scaling that we calculate, and which appears to be in good agreement with recent experimental results.

cond-mat.dis-nn↗

arXiv2014

Polar Kerr effect from chiral-nematic charge order

We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral-nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in $x$ and $y$ directions, and $C_4$ lattice rotation symmetry. The Kerr angle $θ_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $σ_{xy}-σ_{yx}$. We show that this result holds when $C_4$ symmetry is broken. We show that in order for $σ_{xy}$ and $σ_{yx}$ to be non-zero the mirror symmetries in $x$ and $y$ directions have to be broken, and that for $σ_{xy}-σ_{yx}$ to be non-zero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a non-zero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a non-zero $θ_K$ in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from $(π,π)$ and has to include particle-hole asymmetry. Alternatively, in the presence of disorder one can get a non-zero $θ_K$ from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. The impurity analysis in our case is similar to that in earlier works on Kerr effect in $p_x+ip_y$ superconductor, however in our case the magnitude of $θ_K$ is enhanced by the flattening of the Fermi surface in the "hot" regions which mostly contribute to charge order.

cond-mat.str-el↗

arXiv2014

Non-local Adiabatic Response of a Localized System to Local Manipulations

We examine the response of a system localized by disorder to a time dependent local perturbation which varies smoothly with a characteristic timescale $τ$. We find that such a perturbation induces a non-local response, involving a rearrangement of conserved quantities over a length scale $\sim \ln τ$. This effect lies beyond linear response, is absent in undisordered insulators and highlights the remarkable subtlety of localized phases. The effect is common to both single particle and many body localized phases. Our results have implications for numerous fields, including topological quantum computation in quantum Hall systems, quantum control in disordered environments, and time dependent localized systems. For example, they indicate that attempts to braid quasiparticles in quantum Hall systems or Majorana nanowires will surely fail if the manipulations are performed asymptotically slowly, and thus using such platforms for topological quantum computation will require considerable engineering. They also establish that disorder localized insulators suffer from a statistical orthogonality catastrophe.

cond-mat.dis-nn↗

arXiv2014

Numerical Study of a Many-Body Localized System Coupled to a Bath

We use exact diagonalization to study the breakdown of many-body localization in a strongly disordered and interacting system coupled to a thermalizing environment. We show that the many-body level statistics cross over from Poisson to GOE, and the localized eigenstates thermalize, with the crossover coupling decreasing with the size of the bath in a manner consistent with the hypothesis that an infinitesimally small coupling to a thermodynamic bath should destroy localization of the eigenstates. However, signatures of incomplete localization survive in spectral functions of local operators even when the coupling to the environment is non-zero. These include a discrete spectrum and a gap at zero frequency. Both features are washed out by line broadening as one increases the coupling to the bath.

cond-mat.dis-nn↗

arXiv2014

Disorder-tuned selection of order in bilayer graphene

The nature of the interaction-driven spontaneously broken-symmetry state in charge neutral bilayer graphene (BLG) has attracted a lot of interest. Theoretical studies predict various ordered states as the candidates for the ground state of BLG in the absence of external fields. Several experiments have been performed by different groups to identify the nature of the collective ground state in BLG. However, so far, there is no consensus: some experiments show evidence that suggests the establishment of a nematic gapless state, while others present results that are more consistent with the establishment of a fully gapped state. Moreover, even among the experiments that appear to see a bulk gap, some of the samples are found to be conducting (suggesting existence of gapless edge states), while others are insulating. Here we explore the hypothesis that disorder might explain the discrepancy between experiments. We find that the pair breaking effect due to non-magnetic short-range disorder varies among the candidate ground states, giving rise to different amounts of suppression of their mean-field transition temperatures. Our results indicate that BLG can undergo a transition between different ordered states as a function of the disorder strength providing a possible scenario to resolve the discrepancy between experimental observations.

cond-mat.mes-hall↗

arXiv2014

Many body localization and delocalization in the two dimensional continuum

I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions. I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T < T_c$, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave. Meanwhile, for $T > T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization. I calculate the boundary of the region of perturbative stability of localization in the interaction strength - temperature plane. I also discuss the behavior in a speckle disorder (relevant for cold atoms experiments) and conclude that perturbation theory about the non-interacting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many body localization in the two dimensional continuum cannot survive away from the impurity limit.

cond-mat.stat-mech↗

arXiv2014

Spectral features of a many-body localized system weakly coupled to a heat bath

We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. We argue that these spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a "soft gap" at zero frequency in the spatially-averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and find that characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for all experiments on many-body localization.

cond-mat.stat-mech↗

arXiv2014

Superconductivity of disordered Dirac fermions in graphene

We numerically study the interplay between superconductivity and disorder on the graphene honeycomb lattice with on-site Hubbard attractive interactions U using a spatially inhomogeneous self-consistent Bogoliubov-de Gennes (BdG) approach. In the absence of disorder there are two phases at charge neutrality. Below a critical value Uc for attractive interactions there is a Dirac semimetal phase and above it there is a superconducting phase. We add scalar potential disorder to the system, while remaining at charge neutrality on average. Numerical solution of the BdG equations suggests that while in the strong attraction regime (U > Uc) disorder has the usual effect of suppressing superconductivity, in the weak attraction regime (U < Uc) weak disorder enhances superconductivity. In the weak attraction regime, disorder that is too strong eventually suppresses superconductivity, i.e., there is an optimal disorder strength that maximizes the critical temperature Tc. Our numerical results also suggest that in the weakly disordered regime, mesoscopic inhomogeneities enhance superconductivity significantly more than what is predicted by a spatially uniform mean-field theory a` la Abrikosov-Gorkov. In this regime, superconductivity consists of rare phase-coherent superconducting islands. We also study the enhancement of the superconducting proximity effect by disorder and mesoscopic inhomogeneities, and obtain typical spatial plots of the tunneling density of states and the superfluid susceptibility that can be directly compared to scanning tunneling miscroscopy (STM) experiments on proximity-induced superconductivity in graphene.

cond-mat.supr-con↗

arXiv2014

Weyl semimetals with short-range interactions

We construct a low-energy effective field theory of electrons interacting via short-range interactions in a Weyl semimetal and investigate possible broken-symmetry ground states through an unbiased one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Weyl semimetal to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to determine the most likely broken-symmetry ground state, we calculate susceptibilities in the particle-hole and particle-particle channels along this trajectory and find that the leading instability is towards a fully gapped spin-density wave (SDW) ground state. The sliding mode of this SDW couples to the external electromagnetic fields like the Peccei-Quinn axion field of particle physics. We also study a maximally symmetric toy model of an interacting Weyl semimetal with a single independent coupling constant. The most likely ground states in this case are either gapless ferromagnetic states where the spin waves couple to the Weyl fermions like the spatial components of a (possibly chiral) gauge field, or a fully gapped spin-singlet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state.

cond-mat.str-el↗

arXiv2014

Many body localization and thermalization in quantum statistical mechanics

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the `Eigenstate Thermalization Hypothesis' (ETH), and the resulting `single-eigenstate statistical mechanics'. We then focus on a class of systems which fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can locally remember forever information about their local initial conditions, and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL), and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveals dynamically-stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality where equilibrium ordering is forbidden.

cond-mat.stat-mech↗

arXiv2014

Marginal Anderson localization and many body delocalization

We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short range interactions trigger delocalization for partially filled bands at non-zero energy density if ν\ge 1/d. We use the Harris/Chayes bound ν\ge 2/d, to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at non-zero energy density.

cond-mat.stat-mech↗

arXiv2014

Superconductivity from weak repulsion in hexagonal lattice systems

We analyze the pairing instabilities for fermions on hexagonal lattices (both honeycomb and triangular ones) in a wide range of fermionic densities. We argue that for a generic doping in this range, superconductivity at weak coupling is of Kohn-Luttinger type, and, due to the presence of electronic interactions beyond on-site repulsion, is a threshold phenomenon, with superconductivity emerging only if the attraction generated by the Kohn-Luttinger mechanism exceeds the bare repulsion in some channel. For disconnected Fermi pockets, we predict that Kohn-Luttinger superconductivity, if it occurs, is likely to be $f$-wave. While the Kohn-Luttinger analysis is adequate over most of the doping range, a more sophisticated analysis is needed near Van Hove doping. We treat Van Hove doping using a parquet renormalization group, the equations for which we derive and analyze. Near this doping level, superconductivity is a universal phenomenon, arising from any choice of bare repulsive interactions. The strongest pairing instability is into a chiral $d-$wave state ($d+id$). At a truly weak coupling, the strongest competitor is a spin-density-wave instability, however, $d-$wave superconductivity still wins. Moreover, the feedback of the spin density fluctuations into the Cooper channel significantly enhances the critical temperature over the estimates of the Kohn Luttinger theory. We analyze renormalization group equations at stronger couplings and find that the main competitor to $d-$wave supoerconductivity away from weak coupling is actually ferromagnetism. We also discuss the effect of the edge fermions and show that they are unimportant in the asymptotic weak coupling limit, but may give rise to, e.g., a charge-density-wave order at moderate coupling strengths.

cond-mat.supr-con↗

arXiv2013

Dirty Weyl fermions: rare region effects near 3D Dirac points

We study three-dimensional Dirac fermions with weak finite-range scalar potential disorder. We show that even though disorder is perturbatively irrelevant at 3D Dirac points, nonperturbative effects from rare regions give rise to a nonzero density of states and a finite mean free path, with the transport at the Dirac point being dominated by hopping between rare regions. As one moves in chemical potential away from the Dirac point, there are interesting intermediate-energy regimes where the rare regions produce scattering resonances that determine the DC conductivity. We also discuss the interplay of disorder with interactions at the Dirac point. Attractive interactions drive a transition into a granular superconductor, with a critical temperature that depends strongly on the disorder distribution. In the presence of Coulomb repulsion and weak retarded attraction, the system can be a Bose glass. Our results apply to all 3D systems with Dirac points, including Weyl semimetals, and overturn a thirty year old consensus regarding the irrelevance of weak disorder at 3D Dirac points.

cond-mat.str-el↗

arXiv2013

A phenomenology of certain many-body-localized systems

We consider isolated quantum systems with all of their many-body eigenstates localized. We define a sense in which such systems are integrable, and discuss a method for finding their localized conserved quantum numbers ("constants of motion"). These localized operators are interacting pseudospins and are subject to dephasing but not to dissipation, so any quantum states of these pseudospins can in principle be recovered via (spin) echo procedures. We also discuss the spreading of entanglement in many-body localized systems, which is another aspect of the dephasing due to interactions between these localized conserved operators.

cond-mat.dis-nn↗

arXiv2013

Superconductivity of disordered Dirac fermions

We study the effect of disorder on massless, spinful Dirac fermions in two spatial dimensions with attractive interactions, and show that the combination of disorder and attractive interactions is deadly to the Dirac semimetal phase. First, we derive the zero temperature phase diagram of a clean Dirac fermion system with tunable doping level (μ) and attraction strength (g). We show that it contains two phases: a superconductor and a Dirac semimetal. Then, we show that arbitrarily weak disorder destroys the Dirac semimetal, turning it into a superconductor. We discuss the strength of the superconductivity for both long range and short range disorder. For long range disorder, the superconductivity is exponentially weak in the disorder strength. For short range disorder, a uniform mean field analysis predicts that superconductivity should be doubly exponentially weak in the disorder strength. However, a more careful treatment of mesoscopic fluctuations suggests that locally superconducting puddles should form at a much higher temperature, and should establish global phase coherence at a temperature that is only exponentially small in weak disorder. We also discuss the effect of disorder on the quantum critical point of the clean system, building in the effect of disorder through a replica field theory. We show that disorder is a relevant perturbation to the supersymmetric quantum critical point. We expect that in the presence of attractive interactions, the flow away from the critical point ends up in the superconducting phase, although firm conclusions cannot be drawn since the renormalization group analysis flows to strong coupling. We argue that although we expect the quantum critical point to get buried under a superconducting phase, signatures of the critical point may be visible in the finite temperature quantum critical regime.

cond-mat.str-el↗

arXiv2013

Flat bands with local Berry curvature in multilayer graphene

We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N. For N = 7 the bands become nearly flat, with a small bandwidth of 3.6 meV. The two nearly flat bands coming from the K and K' valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the local Berry curvature of the bands endows the system with a nontrivial quantum geometry. The quantum geometry effects manifest themselves through the quantum distance (Fubini-Study) metric, rather than the more conventional Chern number. Multilayer graphene on BN thus provides a platform for investigating the effect of interactions in a system with a non-trivial quantum distance metric, without the complication of non-zero Chern numbers. We note in passing that flat bands with non-zero Chern number can also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry.

cond-mat.mes-hall↗

arXiv2013

Localization protected quantum order

Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order in that individual many-body eigenstates can break symmetries or display topological order in the infinite volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e.: localization protects order. In addition, localized systems can move between ordered and disordered localized phases via non-thermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a `spectral transition' involving a sharp change in the spectral statistics of the many-body Hamiltonian.

cond-mat.stat-mech↗

arXiv2013

Common path interference in Zener tunneling is a universal phenomenon

We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first `Zener oscillation' occurs at a transmission probability which is exponentially small when the co-efficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of $p$ in the low energy dispersion relation. Since odd powers of $p$ are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the $p^4$ term makes the leading contribution.

cond-mat.mes-hall↗