Free at Last: Bose Metal Uncaged
A Bose metallic phase disrupts the classic two-state superconductor-insulator picture.
cond-mat.supr-con↗
arXiv subjects
Philip W. Phillips
Publications and source records attributed to Philip W. Phillips.
Nöther's Second Theorem as an Obstruction to Charge Quantization
While it is a standard result in field theory that the scaling dimension of conserved currents and their associated gauge fields are determined strictly by dimensional analysis and hence cannot change under any amount of renormalization, it is also the case that the standard conservation laws for currents, $dJ=0$, remain unchanged in form if any differential operator that commutes with the total exterior derivative, $[d,\hat Y]=0$, multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther's second theorem. We review here our recent work on one particular instance of this theorem, namely fractional electromagnetism and highlight the holographic dilaton models that exhibit such behavior and the physical consequences this theory has for charge quantization. Namely, the standard electromagnetic gauge and the fractional counterpart cannot both yield integer values of Planck's constant when they are integrated around a closed loop, thereby leading to a breakdown of charge quantization.
hep-th↗
Fractional Electromagnetism in Quantum Matter and High-Energy Physics
We present here a theory of fractional electro-magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models. The starting point for our analysis is the observation that the standard current conservation equations remain unchanged if any differential operator that commutes with the total exterior derivative multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther's second theorem. Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian. We show that the resultant theories all allow for anomalous (non-traditional) scaling dimensions of the gauge field and the associated current. Using well known extension theorems and the membrane paradigm, we show that either the boundary (UV) or horizon (IR) theory of holographic dilatonic models are both described by such fractional electromagnetism. We also show that the non-local Pippard kernel introduced to solve the problem of the Meissner effect in elemental superconductors can also be formulated as a special case of fractional electromagnetism. We show that the standard charge quantization rules fail when the gauge field acquires an anomalous dimension. The breakdown of charge quantization is discussed extensively in terms of the experimentally measurable modified Aharonov-Bohm effect in the strange metal phase of the cuprate superconductors.
hep-th↗
Detecting isotropic density and nematic fluctuations using ultrafast coherent phonon spectroscopy
We propose a theoretical framework for the detection of order parameter fluctuations in three dimensions using ultrafast coherent phonon spectroscopy. We focus our attention on long wavelength charge density fluctuations (plasmons), and charged nematic fluctuations where the direction of the propagation vector is fixed perpendicular to the plane of anisotropy. By treating phonons and light classically and decoupling interactions to integrate out the fermionic degrees of freedom, we arrive at an effective theory of order parameter fluctuations about the spatially uniform saddle-point solution. We find that, due to the $(k_x^2-k_y^2) (B_{1g})$ symmetry of the form factor appearing in the vertex, nematic fluctuations couple to light only at fourth order, unlike isotropic density fluctuations which couple at second order. Hence, to lowest order, the interaction between electrons and the electromagnetic field contributes a driving force for plasmon oscillations while it provides a frequency shift for nematic fluctuations. From the resulting coupled harmonic oscillator equations of motion, we argue that ultrafast coherent phonon spectroscopy could be a useful tool to extract and analyze various electronic properties of interest such as the frequency of the collective mode and the coupling between electrons and phonons. Specific experiments are proposed on the normal state of FeSe to observe the frequency shift predicted here resulting directly from orbital ordering (nematic) fluctuations. Our paper presents a new mechanism for generating coherent phonons from long-range interactions (coherent long-range interaction induced phonons) that does not require the existence of multiple bands to act as intermediary states for quasiparticles.
cond-mat.str-el↗
Single-parameter scaling in the magnetoresistance of optimally doped La$_{2-x}$Sr$_{x}$CuO$_4$
We show that the recent magnetoresistance data on thin-film La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) in strong magnetic fields ($B$) obeys a single-parameter scaling of the form MR$(B,T)=f(μ_H(T)B)$, where $μ_H^{-1}(T)\sim T^α$ ($1\leα\le2$), from $T=180$K until $T\sim20$K, at which point the single-parameter scaling breaks down. The functional form of the MR is distinct from the simple quadratic-to-linear quadrature combination of temperature and magnetic field found in the optimally doped iron superconductor BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$. Further, low-temperature departure of the MR in LSCO from its high-temperature scaling law leads us to conclude that the MR curve collapse is not the result of quantum critical scaling. We examine the classical effective medium theory (EMT) previously used to obtain the quadrature resistivity dependence on field and temperature for metals with a $T$-linear zero-field resistivity. It appears that this scaling form results only for a binary, random distribution of metallic components. More generally, we find a low-temperature, high-field region where the resistivity is simultaneously $T$ and $B$ linear when multiple metallic components are present. Our findings indicate that if mesoscopic disorder is relevant to the magnetoresistance in strange metal materials, the binary-distribution model which seems to be relevant to the iron pnictides is distinct from the more broad-continuous distributions relevant to the cuprates. Using the latter, we examine the applicability of classical effective medium theory to the MR in LSCO and compare calculated MR curves with the experimental data.
cond-mat.str-el↗
Local Entropies across the Mott Transition in an Exactly Solvable Model
We study entanglement in the Hatsugai-Kohmoto model, which exhibits a continuous interaction-driven Mott transition. By virtue of the all-to-all nature of its center-of-mass conserving interactions, the model lacks dynamical spectral weight transfer, which is the key to intractability of the Hubbard model for $d>1$. In order to maintain a non-trivial Mott-like electron propagator, SU(2) symmetry is preserved in the Hamiltonian, leading to a ground state that is mixed on both sides of the phase transition. Because of this mixture, even the metal in this model is unentangled between any pair of sites, unlike free fermions whose ground state carries a filling-dependent site-site entanglement. We focus on the scaling behavior of the one- and two-site entropies $s_1$ and $s_2$, as well as the entropy density $s$, of the ground state near the Mott transition. At low temperatures in the two-dimensional Hubbard model, it was observed numerically (Walsh et al., 2018, arXiv:1807.10409) that $s_1$ and $s$ increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model, $s_1$ acquires the constant value $\ln4$ even at the Mott transition. The ground state's non-trivial entanglement structure is manifest in $s_2$ and $s$ which decrease into the metal, and thereby act as sharp signals of the Mott transition in any dimension. Specifically, we find that in one dimension, $s_2$ and $s$ exhibit kinks at the transition while in $d=2$, only $s$ exhibits a kink.
cond-mat.str-el↗
Scale-invariance as the cause of the superconducting dome in the cuprates
Recent photoemission spectroscopy measurements (T. J. Reber et al., arXiv:1509.01611) of cuprate superconductors have inferred that the self-energy exhibits critical scaling over an extended doping regime, thereby calling into question the conventional wisdom that critical scaling exists only at isolated points. In particular, this new state of matter, dubbed a power-law liquid, has a self-energy whose imaginary part scales as $Σ^{\prime\prime}\sim(ω^{2}+π^{2}T^{2})^α$, with $α=1$ in the overdoped Fermi-liquid state and $α\leq0.5$ in the optimal to underdoped regime. Previously, we showed that this self-energy can arise from interactions between electrons and unparticles, a scale-invariant sector that naturally emerges from strong correlations. Here, taking the self-energy as a given, we first reconstruct the real part of the self-energy. We find that the resultant quasiparticle weight vanishes for any doping level less than optimal, implying an absence of particle-like excitations in the underdoped regime. Consequently, the Fermi velocity vanishes and the effective mass diverges for $α\leq\frac{1}{2}$, in agreement with earlier experimental observations. We then use the self-energy to reconstruct the spectral function and compute the superconducting $T_c$ within the BCS formalism. We find that the $T_c$ has a dome-like structure, implying that broad scale invariance manifested in the form of a power-law liquid is the likely cause of the superconducting dome in the cuprates.
cond-mat.str-el↗
Low energy inelastic response in the superconducting phases of $PrOs_4Sb_{12}$
Recent AC susceptibility and polar Kerr effect measurements in the skutterudite superconductor PrOs4Sb12 (POS) uncovered the nature of the superconducting double transition from a high temperature, high field, time reversal symmetric phase (or the A phase) to a low temperature, low field, time reversal symmetry broken phase (or the B phase). Starting from a microscopic model, we derive a Ginzburg-Landau expansion relevant to POS that describes this entrance into the time reversal symmetry broken phase along the temperature axis. We also provide a study of the low energy inelastic (Raman) response in both the A and B phases of POS, and seek additional signatures which could help reveal the exact form of the gap functions previously proposed in these phases. By appropriately manipulating the incoming and scattered light geometries, along with additional subtraction procedures and suitable assumptions, we show that one can access the various irreducible representations contained in the point group describing POS. We demonstrate how to use this technique on example order parameters proposed in POS. Depending on whether there exist nodes along the c-axis, we find additional low energy spectral weight within the superconducting gap in the Eg geometry, a feature that could pin point the location of nodes on the Fermi surface.
cond-mat.supr-con↗
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
We devise a model to explain why twisted bi-layer graphene (TBLG) exhibits insulating behavior when $ν=2,3$ charges occupy a unit moiré cell, a feature attributed to Mottness, but not for $ν=1$, clearly inconsistent with Mott insulation. We compute $r_s=E_U/E_K$, where $E_U$ and $E_K$ are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density $10^4$ higher than in the experiments and (ii) a transition to a series of Wigner crystalline states exists as a function of $ν$. We find, for $ν=1$, $r_s$ fails to cross the threshold ($r_s = 37$) for the triangular lattice and metallic transport ensues. However, for $ν=2$ and $ν=3$, the thresholds, $r_s=22$, and $r_s=17$, respectively are satisfied for a transition to Wigner crystals (WCs) with a honeycomb ($ν=2$) and kagome ($ν=3$) structure. We believe, such crystalline states form the correct starting point for analyzing superconductivity.
cond-mat.str-el↗
Absence of Luttinger's theorem for fermions with power-law Green functions
We investigate the validity of Luttinger's theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger's theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. \cite{Blagoev1997,Yamanaka1997} showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger's theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and $\mathrm{Im} G(ω=0,-\infty)=0$. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.
cond-mat.str-el↗
Conjecture on the Butterfly Velocity across a Quantum Phase Transition
We study an anisotropic holographic bottom-up model displaying a quantum phase transition (QPT) between a topologically trivial insulator and a non-trivial Weyl semimetal phase. We analyze the properties of quantum chaos in the quantum critical region. We do not find any universal property of the Butterfly velocity across the QPT. In particular it turns out to be either maximized or minimized at the quantum critical point depending on the direction of propagation. We observe that instead of the butterfly velocity, it is the dimensionless information screening length that is always maximized at a quantum critical point. We argue that the null-energy condition (NEC) is the underlying reason for the upper bound, which now is just a simple combination of the number of spatial dimensions and the anisotropic scaling parameter.
hep-th↗
Inequivalence of the zero-momentum Limits of Transverse and Longitudinal Dielectric Response in the Cuprates
We address the question of the mismatch between the zero momentum limits of the transverse and longitudinal dielectric functions for a fixed direction of the driving field observed in the cuprates. This question translates to whether or not the order in which the longitudinal and transverse momentum transfers are taken to zero commute. While the two limits commute for both isotropic and anisotropic Drude metals, we argue that a scaleless vertex interaction that depends solely on the angle between scattered electron momenta is sufficient to achieve non-commutativity of the two limits even for a system that is inherently isotropic. We demonstrate this claim for a simple case of the Drude conductivity modified by electron-boson interactions through appropriate vertex corrections, and outline possible consequences of our result to optical and electron energy loss spectroscopy (EELS) measurements close to zero momentum transfer
cond-mat.str-el↗
Evolution of Holographic Fermi Arcs from a Mott Insulator
We study fermions in an electrically-probed and asymptotically anti-de Sitter Schwarzschild spacetime which interact via novel chiral symmetry-preserving interactions. Computing the dual fermion two-point correlator, we show that these bulk interactions anisotropically gap Fermi surfaces of the boundary spectrum. Consequently, the interactions we devise provide holographic models for Fermi arcs seen ubiquitously in the pseudogap regime of the cuprates. Our interactions are modifications of the chiral symmetry-breaking Pauli coupling, which has previously been proposed as the holographic realization of Mott physics. The onset of Mott insulation and pseudogap physics are respectively discussed in the context of bulk chiral and boundary parity symmetry breaking, and the Mott transition is interpreted as a deconfinement transition of non-Fermi liquid excitations.
cond-mat.str-el↗
Log-rise of the Resistivity in the Holographic Kondo Model
We study a single-channel Kondo effect using a recently developed holographic large-$N$ technique. In order to obtain resistivity of this model, we introduce a probe field. The gravity dual of a localized fermionic impurity in 1+1-dimensional host matter is constructed by embedding a localized 2-dimensional Anti-de Sitter (\ads{2})-brane in the bulk of \ads{3}. This helps us construct an impurity charge density which acts as a source to the bulk equation of motion of the probe gauge field. The functional form of the charge density is obtained independently by solving the equations of motion for the fields confined to the \ads{2}-brane. The asymptotic solution of the probe field is dictated by the impurity charge density, which in turn, affects the current-current correlation functions, and hence the resistivity. Our choice of parameters tunes the near-boundary impurity current to be marginal, resulting in a $\log T$ behavior in the UV resistivity, as is expected for the Kondo problem. The resistivity at the IR fixed point turns out to be zero, signaling a complete screening of the impurity.
hep-th↗
Bose Metal as a Disruption of the Berezinskii-Kosterlitz-Thouless Transition in 2D Superconductors
Destruction of superconductivity in thin films was thought to be a simple instance of Berezinskii-Kosterlitz-Thouless physics in which only two phases exist: a superconductor with algebraic long range order in which the vortices condense and an insulator where the vortex-antivortex pairs proliferate. However, since 1989 this view has been challenged as now a preponderance of experiments indicate that an intervening bosonic metallic state obtains upon the destruction of superconductivity. We review here a glassy model which is capable of capturing both of these features. The finite resistance arises from three features. First, the disordered insulator-superconductor transition in the absence of fermionic degrees of freedom (Cooper pairs only), is controlled by a diffusive fixed point\cite{CN} rather than the critical point of the clean system. Hence, the relevant physics that generates the Bose metal should arise from a term in the action in which different replicas are mixed. We show explicitly how such physics arises in the phase glass. Second, in 2D (not in 3D) the phase stiffness of the glass phase vanishes explicitly as has been shown in extensive numerical simulations\cite{ky,kosterlitz1,kosterlitz2}. Third, bosons moving in such a glassy environment fail to localize as a result of the false minima in the landscape. We calculate the conductivity explicitly using Kubo response and show that it turns on as a power law and has a vanishing Hall response as a result of underlying particle-hole symmetry. We show that when particle-hole symmetry is broken, the Hall conductance turns on with the same power law as does the longitudinal conductance.
cond-mat.str-el↗
Anomalous Dimension of the Electrical Current in the Normal State of the Cuprates from the Fractional Aharonov-Bohm Effect
We demonstrate quite generally how a conserved current can have an anomalous dimension. We show here that if the current in the normal state of the cuprates has an anomalous dimension, then the Aharonov-Bohm flux through a ring does not have the standard $eBA/\hbar$ form, where $A$ is the area and $B$ the external magnetic field, but instead is modified by a geometrical factor that depends directly on the anomalous dimension of the current. We calculate the signal in square and disk geometries. In both cases, the deviation from the standard result is striking and offers a fingerprint about what precisely is strange about the strange metal.
cond-mat.str-el↗
Vanishing Hall Conductance in the Phase Glass Bose Metal at Zero Temperature
Motivated in part by the numerical simulations [ky,kosterlitz1,kosterlitz2] which reveal that the energy to create a defect in a gauge or phase glass scales as $L^θ$ with $θ<0$ for 2D, thereby implying a vanishing stiffness, we re-examine the relevance of these kinds of models to the Bose metal in light of the new experiments [kapsym,armitage] which reveal that the Hall conductance is zero in the metallic state that disrupts the transition from the superconductor to the insulator in 2D samples. Because of the particle-hole symmetry in the phase glass model, we find that bosonic excitations in a phase glass background generate no Hall conductance at the Gaussian level. Furthermore, this result persists to any order in perturbation theory in the interactions. We show that when particle-hole symmetry is broken, the Hall conductance turns on with the same power law as does the longitudinal conductance. This prediction can be verified experimentally by applying a ground plane to the 2D samples.
cond-mat.str-el↗
Power-law liquid in cuprate superconductors from fermionic unparticles
Recent photoemission spectroscopy measurements [arXiv:1509.01611] on cuprate superconductors have inferred that over a wide range of doping, the imaginary part of the electron self-energy scales as $Σ^{\prime\prime}\sim(ω^2+π^2T^2)^a$ with $a=1$ in the overdoped Fermi-liquid state and $a<0.5$ in the optimal to underdoped regime. We show that this non-Fermi-liquid scaling behavior can naturally be explained by the presence of a scale-invariant state of matter known as unparticles. We evaluate analytically the electron self-energy due to interactions with fermionic unparticles. We find that, in agreement with experiments, the imaginary part of the self-energy scales with respect to temperature and energy as $Σ^{\prime\prime}\sim T^{2+2α}$ and $ω^{2+2α}$, where $α$ is the anomalous dimension of the unparticle propagator. In addition, the calculated occupancy and susceptibility of fermionic unparticles, unlike those of normal fermions, have significant spectral weights even at high energies. This unconventional behavior is attributed to the branch cut in the unparticle propagator which broadens the unparticle spectral function over a wide energy range and non-trivially alters the scattering phase space by enhancing (suppressing) the intrinsic susceptibility at low energies for negative (positive) $α$. Our work presents new evidence suggesting that unparticles might be important low-energy degrees of freedom in strongly coupled systems such as the cuprate superconductors.
cond-mat.str-el↗