Scattering mechanisms and electrical transport near an Ising nematic quantum critical point

Abstract

Electrical transport properties near an electronic Ising-nematic quantum critical point in two dimensions are of both theoretical and experimental interest. In this work, we derive a kinetic equation valid in a broad regime near the quantum critical point using the memory matrix approach. The formalism is applied to study the effect of the critical fluctuations on the dc resistivity through different scattering mechanisms, including umklapp, impurity scattering, and electron-hole scattering in a compensated metal. We show that electrical transport in the quantum critical regime exhibits a rich behavior that depends sensitively on the scattering mechanism and the band structure. In the case of a single large Fermi surface, the resistivity due to umklapp scattering crosses over from $\rho \sim T^2$ at low temperature to sublinear at high temperature. The crossover temperature scales as $q_0^3$, where $q_0$ is the minimal wavevector for umklapp scattering. Impurity scattering leads to $\rho -{\rho }_0\sim T^{\alpha }$ (${\rho }_0$ being the residual resistivity), where $\alpha$ is either larger than 2 if there is only a single Fermi sheet present, or 4/3 in the case of multiple Fermi sheets. Finally, in a perfectly compensated metal with an equal density of electrons and holes, the low temperature behavior depends strongly on the structure of "cold spots" on the Fermi surface, where the coupling between the quasiparticles and order parameter fluctuations vanishes by symmetry. In particular, for a system where cold spots are present on some (but not all) Fermi sheets, $\rho \sim T^{5/3}$. At higher temperatures there is a broad crossover regime where $\rho$ either saturates or $\rho \sim T$, depending on microscopic details. We discuss these results in the context of recent quantum Monte Carlo simulations of a metallic Ising nematic critical point, and experiments in certain iron-based superconductors.

arXiv comment11 pages main text, 19 pages appendix, 13 figures

References in corpus (46)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• A Common Thread: the pairing interaction for the unconventional superconductors
• Nematic order in iron superconductors - who is in the driver's seat?
• Evidence for an electron nematic phase transition in underdoped iron pnictide superconductors
• Nematic Fermi Fluids in Condensed Matter Physics
• An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
• Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Resistivity as a function of temperature for models with hot spots on the Fermi surface.
• Interplay of disorder and spin fluctuations in the resistivity near a quantum critical point
• Nematic quantum critical point without magnetism in FeSe1-xSx superconductors
• Soft Fermi Surfaces and Breakdown of Fermi Liquid Behavior
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• The key ingredients of the electronic structure of FeSe
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Perturbative non-Fermi liquids from dimensional regularization
• Conductivity of a clean one-dimensional wire
• Non-Fermi liquids and the Wiedemann-Franz law
• Bosonization of Fermi liquids
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• Memory matrix theory of magnetotransport in strange metals
• Electronic nematic susceptibility of iron-based superconductors
• Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
• Quantum Criticality in Electron-doped BaFe_{2-x}Ni_xAs_2
• Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
• Monte Carlo Studies of Quantum Critical Metals
• Thermal Conductivity of Spin-1/2 Chains
• Suppression of electronic correlations by chemical pressure from FeSe to FeS
• Quantum Boltzmann equation of composite fermions interacting with a gauge field
• Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals
• DC resistivity at the onset of spin density wave order in two-dimensional metals
• Lattice effects on nematic quantum criticality in metals
• Electrical resistivity near Pomeranchuk instability in two dimensions
• Multiscale quantum criticality: Pomeranchuk instability in isotropic metals
• Elastic coupling and spin-driven nematicity in iron-based superconductors
• Lower bounds for the conductivities of correlated quantum systems
• Electron Mass Enhancement near a Nematic Quantum Critical Point in NaFe${}_{1-x}$Co${}_x$As
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Equivalence of single-particle and transport lifetimes from hybridization fluctuations
• Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors
• Conductivity close to antiferromagnetic criticality

Cited by in corpus (34)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Universal theory of strange metals from spatially random interactions
• Large $N$ theory of critical Fermi surfaces
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Quenched nematic criticality separating two superconducting domes in an iron-based superconductor under pressure
• Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor
• Electronic nematic states tuned by isoelectronic substitution in bulk FeSe1-xSx
• Coexistence of orbital and quantum critical magnetoresistance in FeSe${}_{1-x}$S${}_x$
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Loop current fluctuations and quantum critical transport
• Anomalous high-magnetic field electronic state of the nematic superconductors FeSe${}_{1-x}$S${}_x$
• Scattering in the Ising Model Using Quantum Lanczos Algorithm
• Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals
• Resistivity near a nematic quantum critical point: Impact of acoustic phonons
• Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals
• Signatures of a Quantum Griffiths Phase close to an Electronic Nematic Quantum Phase Transition
• Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals
• Specific Heat of a Quantum Critical Metal
• Orientational order parameters for arbitrary quantum systems
• DC resistivity near a nematic quantum critical point: Effects of weak disorder and acoustic phonons
• Low frequency Raman response near Ising-nematic quantum critical point: a memory matrix approach
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Quadrupolar charge dynamics in the nonmagnetic FeSe${}_{1-x}$S${}_x$ superconductors
• Fluctuation Spectrum of Critical Fermi Surfaces
• Incoherent transport in a model for the strange metal phase: Memory-matrix formalism
• Observation of non-Fermi liquid physics in a quantum critical metal via quantum loop topography
• Fractionalized Fermi liquids and the cuprate phase diagram
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Electronic nematic order in the normal state of strontium ruthenate
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Superconductivity near a nematoelastic quantum critical point
• Can electronic quantum criticality drive phonon-induced linear-in-temperature resistivity?
• Phonon Induced Energy Relaxation in Quantum Critical Metals
• Decoupled nematic and magnetic criticality in FeSe${}_{1-x}$S${}_x$