arXiv subjects

Philip W. Phillips

Publications and source records attributed to Philip W. Phillips.

At least 73 records · Page 4Linked to original sources

arXiv2017

Quasiparticle interference and resonant states in normal and superconducting line nodal semimetals

We study impurity scattering in the normal and d-wave superconducting states of line nodal semimetals and show that, due to additional scattering phase space available for impurities on the surface, the quasiparticle interference pattern acquires an extended character instead of a discrete collection of delta function peaks. Moreover, using the T-matrix formalism, we demonstrate that the conventional behavior of a scalar impurity in a d-wave superconductor breaks down on the surface of a line nodal semimetal in the quasi flat band limit.

cond-mat.supr-con↗

arXiv2017

Geodesically Complete Metrics Induce Boundary Non-locality in Holography: Consequences for the Entanglement Entropy

We show explicitly that the full structure of IIB string theory is needed to remove the non-localities that arise in boundary conformal theories that border hyperbolic spaces on AdS$_5$. Specifically, using the Caffarelli/Silvestri\cite{caffarelli}, Graham/Zworski\cite{graham}, and Chang/Gonzalez\cite{chang:2010} extension theorems, we prove that the boundary operator conjugate to bulk p-forms with negative mass in geodesically complete metrics is inherently a non-local operator, specifically the fractional conformal Laplacian. The non-locality, which arises even in compact spaces, applies to any degree p-form such as a gauge field. We show that the boundary theory contains fractional derivatives of the longitudinal components of the gauge field if the gauge field in the bulk along the holographic direction acquires a mass via the Higgs mechanism. The non-locality is shown to vanish once the metric becomes incomplete, for example, either 1) asymptotically by adding N transversely stacked Dd-branes or 2) exactly by giving the boundary a brane structure and including a single transverse Dd-brane in the bulk. The original Maldacena conjecture within IIB string theory corresponds to the former. In either of these proposals, the location of the Dd-branes places an upper bound on the entanglement entropy because the minimal bulk surface in the AdS reduction is ill-defined at a brane interface. Since the brane singularities can be circumvented in the full 10-dimensional spacetime, we conjecture that the true entanglement entropy must be computed from the minimal surface in 10-dimensions, which is of course not minimal in the AdS$_5$ reduction.

hep-th↗

arXiv2016

Violation of f-sum Rule with Generalized Kinetic Energy

Motivated by the normal state of the cuprates in which the f-sum rule increases faster than a linear function of the particle density, we derive a conductivity sum rule for a system in which the kinetic energy operator in the Hamiltonian is a general function of the momentum squared. Such a kinetic energy arises in scale invariant theories and can be derived within the context of holography. Our derivation of the f-sum rule is based on the gauge couplings of a non-local Lagrangian in which the kinetic operator is a fractional Laplacian of order $α$. We find that the f-sum rule in this case deviates from the standard linear dependence on the particle density. We find two regimes. At high temperatures and low densities, the sum rule is proportional to $nT^{\frac{α-1}α}$ where $T$ is the temperature. At low temperatures and high densities, the sum rule is proportional to $n^{1+\frac{2(α-1)}{d}}$ with $d$ being the number of spatial dimensions. The result in the low temperature and high density limit, when $α< 1$, can be used to qualitatively explain the behavior of the effective number of charge carriers in the cuprates at various doping concentrations.

cond-mat.str-el↗

arXiv2016

Absence of nematic ordering transition in a diamond lattice: Application to $FeSc_2S_4$

Recent neutron scattering observations by Plumb et al. [1] reveal that the ground state of $FeSc_2S_4$ is magnetic with two distinct Fe environments, instead of a quantum spin liquid as had been previously thought. Starting with the relevant O(N)-symmetric vector model of $FeSc_2S_4$, we study how the discrete ($Z_2$) and continuous rotational symmetries are successively broken, yielding nematic and ordered phases. At high temperatures, we find that the nematic order parameter falls as $T^{-γ}$ ($γ>0$), and therefore, $FeSc_2S_4$ lacks any distinct nematic ordering temperature. This feature indicates that the three-dimensional diamond lattice of $FeSc_2S_4$ is highly susceptible to the breaking of Ising symmetries, and explains the two distinct Fe environments that is present even at high temperatures, as seen by Mössbauer and far infrared optical spectroscopy.

cond-mat.str-el↗

arXiv2016

Realizing infrared power-law liquids in the cuprates from unparticle interactions

Recent photoemission experiments \cite{dessau} reveal that the excitations along the nodal region in the strange metal of the cuprates, rather than corresponding to poles in the single-particle Green function, exhibit power-law scaling as a function of frequency and temperature. Because such power-law scaling is indicative of a scale-invariant sector, as a first step, we perturbatively evaluate the electron self-energy due to interactions with scale-invariant unparticles. We focus on a $G_0W$ type diagram with an interaction $W$ mediated by a bosonic scalar unparticle. We find that, in the high-temperature limit, the imaginary part of the self-energy $\mathrm{Im}Σ$ is linear in temperature. In the low-temperature limit, $\mathrm{Im}Σ$ exhibits the same power law in both temperature and frequency, with an exponent that depends on the scaling dimension of an unparticle operator. Such behavior is qualitatively consistent with the experimental observations. We then expand the unparticle propagator into coherent and incoherent contributions, and study how the incoherent part violates the density of states (DOS) and density-density correlation function sum rules (f-sum rule). Such violations can, in principle, be observed experimentally. Our work indicates that the physical mechanism for the origin of the power-law scaling is the incoherent background, which is generated from the Mott-scale physics.

cond-mat.str-el↗

arXiv2016

Not Just a Phase: Bose Metal Unveiled

I analyze the recent observation of a Bose metal in NbSe$_2$ and place these results in the wider context of the first sighting of such a phase in amorphous Bi and MoGe thin films.

cond-mat.supr-con↗

arXiv2015

Study of non-Fermi Liquid behavior from partial nesting in multi-orbital superconductors

Partial nesting between two connected or disconnected regions of the Fermi surface leads to fractional powers of the Coulomb scattering lifetime as a function of temperature and frequency. This result is first demonstrated for a toy band structure where partial nesting occurs within a single band and between different regions of the Brillouin zone. A comparison is then made to a multiband scenario by studying the scattering rate of an effective two orbital model that was proposed in the context of multi-orbital superconductors. In the process, various model independent factors affecting the temperature exponent, n, are identified. The logarithmically divergent contributions of the lowest order vertex correction to the multi-orbital susceptibility, and the role played by nesting in suppressing these divergences is analyzed. The relevance of these results is discussed keeping the recently observed anomalous resistivity in the Co doped Iron superconductor LiFeAs as a backdrop.

cond-mat.supr-con↗

arXiv2015

Unparticles and Anomalous Dimensions in the Cuprates

Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and $T-$linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis\cite{ Hartnoll:2015sea}. We also predict that regardless of the bare dynamical exponent, $z$, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a $d+1$ gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.

cond-mat.str-el↗

arXiv2015

Exact Strongly Coupled Fixed Point in $gφ^4$ Theory

We show explicitly how a strongly coupled fixed point can be constructed in scalar $gφ^4$ theory from the solutions to a non-linear eigenvalue problem. The fixed point exists only for $d< 4$, is unstable and characterized by $ν=2/d$ (correlation length exponent), $η=1/2-d/8$ (anomalous dimension). For $d=2$, these exponents reproduce to those of the Ising model which can be understood from the codimension of the critical point. At this fixed point, $φ^{2i}$ terms with $i>2$ are all irrelevant. The testable prediction of this fixed point is that the specific heat exponent vanishes. 2d critical Mott systems are well described by this new fixed point.

cond-mat.str-el↗

arXiv2015

Absence of Power-Law Mid-Infrared Conductivity in Gravitational Crystals

We compute conductivities of strongly-interacting and non-uniform charge densities dual to inhomogeneous anti-de Sitter--black hole spacetimes. Backreacting bulk scalars with periodic boundary profiles, we construct generalizations of Reissner-Nordström-AdS that interpolate between those used in two previous studies --- one that reports power-law scaling for the boundary optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors.

cond-mat.str-el↗

arXiv2014

Beyond Particles: Unparticles in Strongly Correlated Electron Matter

I am concerned in these lectures with the breakdown of the particle concept in strongly correlated electron matter. I first show that the standard procedure for counting particles, namely Luttinger's theorem, breaks down anytime pole-like excitations are replaced by ones that have a divergent self-energy. Such a breakdown obtains in electronic systems whose pole-like excitations do not extend to the edge of the Brillouin zone, as in Fermi arcs in the cuprates. Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, unparticles are the natural candidate to explain the presence of charged degrees of freedom that have no particle content. The continuous mass formulation of unparticles is recast as an action in anti de Sitter space. Such an action serves as the generating functional for the propagator. This mapping fixes the scaling dimension of the unparticle to be $d_U=d/2+\sqrt{d^2+4}/2$ and ensures that the corresponding propagator has zeros with $d$ the spacetime dimension of the unparticle field. The general {\it dynamical} mechanism by which bulk operators, such as the Pauli term, couple to the scaling dimension of the boundary operator and thereby lead to a vanishing of the spectral weight at zero energy is reviewed in the context of unparticles and zeros. The analogue of the BCS gap equations with unparticles indicates that the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.

cond-mat.str-el↗

arXiv2014

Theory of Point Contact Spectroscopy in Correlated Materials

We develop a microscopic theory for the point-contact conductance between a metalic electrode and a strongly correlated material using the non-equilibrium Schwinger-Kadanoff-Baym-Keldysh formalism. We explicitly show that in the classical limit, contact size shorter than the scattering length of the system, the microscopic model can be reduced to an effective model with transfer matrix elements that conserve in-plane momentum. We find that the conductance $dI/dV$ is proportional to the {\it effective density of states}, that is, the integrated single-particle spectral function $A(ω=eV)$ over the whole Brillouin zone. From this conclusion, we are able to establish the conditions under which a non-Fermi liquid metal exhibits a zero-bias peak in the conductance. This finding is discussed in the context of recent point-contact spectroscopy on the iron pnictides and chalcogenides which has exhibited a zero-bias conductance peak.

cond-mat.str-el↗

arXiv2014

Minding the Gap in Holographic Models of Interacting Fermions

We study the holographic dual of fermions interacting in a Schwarzschild-AdS$_{d+1}$ background via a dipole (Pauli) coupling sourced by a probe gauge field. We find quite generally that a gap forms in the dual operator spectrum as the Pauli coupling is strengthened. Previous investigations have observed this behavior in analogous constructions with Reissner-Nordström-AdS (RN-AdS$_4$) backgrounds, but the emergence of log-oscillatory behavior in those models' spectra prevented identification of the underlying gapping mechanism. Our model obviates this issue through its modified geometry and traces the gapping mechanism back to the bulk dynamics. We show in general that there is a duality between zeros for large positive values of the coupling and poles in the spectrum for equivalent couplings but with opposite sign as seen recently in the RN-AdS$_4$ background\cite{alsup}. The duality arises from the two possible quantizations for computing the retarded propagator. Coupled with the earlier string results\cite{gauntlett,gubser2} that Fermi surfaces are generally absent from the spectral function, our finding that the Pauli term engineers the gap suggests that the model examined here offers a way of studying non-perturbative physics in fermionic matter at finite density typified by Mott insulating systems.

cond-mat.str-el↗

arXiv2014

Divergent Thermopower without a Quantum Phase Transition

A general principle of modern statistical physics is that divergences of either thermodynamic or transport properties are only possible if the correlation length diverges. We show by explicit calculation that the thermopower in the quantum XY model $d=1+1$ and the Kitaev model in $d=2+1$ can 1) diverge even when the correlation length is finite and 2) remain finite even when the correlation length diverges, thereby providing a counterexample to the standard paradigm.Two conditions are necessary: 1) the sign of the charge carriers and that of the group velocity must be uncorrelated and 2) the current operator defined formally as the derivative of the Hamiltonian with respect to the gauge field does not describe a set of excitations that have a particle interpretation, as in strongly correlated electron matter. The recent experimental\cite{2dtp} and theoretical\cite{kirkpatrick} findings on the divergent thermopower of a 2D electron gas are discussed in this context.

cond-mat.str-el↗

arXiv2013

Breakdown of self-averaging in the Bose glass

We study the square-lattice Bose-Hubbard model with bounded random on-site energies at zero temperature. Starting from a dual representation obtained from a strong-coupling expansion around the atomic limit, we employ a real-space block decimation scheme. This approach is non-perturbative in the disorder and enables us to study the renormalization-group flow of the induced random-mass distribution. In both insulating phases, the Mott insulator and the Bose glass, the average mass diverges, signaling short range superfluid correlations. The relative variance of the mass distribution distinguishes the two phases, renormalizing to zero in the Mott insulator and diverging in the Bose glass. Negative mass values in the tail of the distribution indicate the presence of rare superfluid regions in the Bose glass. The breakdown of self-averaging is evidenced by the divergent relative variance and increasingly non-Gaussian distributions. We determine an explicit phase boundary between the Mott insulator and Bose glass.

cond-mat.dis-nn↗

arXiv2013

Orbital Resonance Mode in Superconducting Iron Pnictides

We show that the fluctuations associated with ferro orbital order in the $d_{xz}$ and $d_{yz}$ orbitals can develop a sharp resonance mode in the superconducting state with a nodeless gap on the Fermi surface. This orbital resonance mode appears below the particle-hole continuum and is analogous to the magnetic resonance mode found in various unconventional superconductors. If the pairing symmetry is $s_{\pm}$, a dynamical coupling between the orbital ordering and the d-wave subdominant pairing channels is present by symmetry. Therefore the nature of the resonance mode depends on the relative strengths of the fluctuations in these two channels, which could vary significantly for different families of the iron based superconductors. The application of our theory to a recent observation of a new $δ$-function-like peak in the B$_{1g}$ Raman spectrum of Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ is discussed.

cond-mat.supr-con↗

arXiv2013

Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter

Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, we argue that the form of the single-particle propagator can be deduced simply by imposing scale invariance. As a consequence, the unparticle picture proposed by Georgi\cite{georgi} is the natural candidate to describe such dynamics. Unparticle stuff is scale-invariant matter with no particular mass. Scale invariance dictates that the propagator has an algebraic form which can admit zeros and hence is a candidate to explain the ubiquitous pseudogap state of the cuprates. The non-perturbative electronic state formed out of unparticles we refer to as an un-Fermi liquid. We show that the underlying action of the continuous mass formulation of unparticles can be recast exactly as an action in anti de Sitter space. We find that this mapping fixes the scaling dimension of the unparticle to be $d_U=d/2+\sqrt{d^2+4}/2$ and ensures that the corresponding propagator has zeros with $d$ the spacetime dimension of the unparticle field. Should $d=2+1$, unparticles acquire the non-trivial phase $2πd_U$ upon interchange. Because $d_U$ is non-integer and in general not half-integer, clockwise and counterclockwise interchange of unparticles do not lead to the same phase and time reversal symmetry is broken spontaneously as reported in numerous experiments in the pseudogap phase of the cuprates. The possible relevance of this mechanism to such experiments is discussed. We then formulate the analogous BCS gap using unparticles and find that in contrast to the Fermi liquid case, the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.

cond-mat.str-el↗

arXiv2013

Non-equilibrium Transport in the Strange Metal and Pseudogap phases of the Cuprates

We propose that the non-equilibrium current measured in the $a-b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively one expects the strange metal to be more different from a Fermi liquid than is the pseudogap. We compute the expected non-equilibrium transport signal with the three Green functions that are available in the literature: 1) marginal Fermi liquid theory, 2) the phenomenological ansatz for the pseudogap regime and 3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear IV curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi liquid approach. The key finding, however, is that IV curves for the strange metal/Fermi liquid contact that exceed that of the pseudogap/Fermi liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than is the pseudogap. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.

cond-mat.str-el↗