DC resistivity near a nematic quantum critical point: Effects of weak disorder and acoustic phonons

Abstract

We calculate the resistivity associated with an Ising-nematic quantum critical point in the presence of disorder and acoustic phonons in the lattice model. We use the memory-matrix transport theory, which has a crucial advantage compared to other methods of not relying on the existence of well-defined quasiparticles in the low-energy effective theory. As a result, we obtain that by including an inevitable interaction between the nematic fluctuations and the elastic degrees of freedom of the lattice (parametrized by the nemato-elastic coupling ${\kappa }_{\text{latt}}$), the resistivity $\rho (T)$ of the system as a function of temperature obeys a universal scaling form described by $\rho (T)\sim T\ln (1/T)$ at high temperatures, reminiscent of the paradigmatic strange metal regime observed in many strongly correlated compounds. For a window of temperatures comparable with ${\kappa }_{\text{latt}}^{3/2}{\epsilon }_F$ (where ${\epsilon }_F$ is the Fermi energy of the microscopic model), the system displays another regime in which the resistivity is consistent with a description in terms of $\rho (T)\sim T^{\alpha }$, where the effective exponent roughly satisfies the inequality $1\lesssim \alpha \lesssim 2$. However, in the low-temperature limit (i.e., $T\ll {\kappa }_{\text{latt}}^{3/2}{\epsilon }_F$), the properties of the quantum critical state change in an important way depending on the types of disorder present in the system: It can either recover a conventional Fermi liquid described by $\rho (T)\sim T^2$ or it could exhibit yet another non-Fermi liquid regime characterized by the scaling form $\rho (T)-{\rho }_0\sim T^2\ln T$. Our results emphasize the key role played by both phonon and disorder effects in the scenario of nematic quantum criticality and might be fundamental for addressing recent transport experiments in some iron-based superconductors.

arXiv comment18 pages, 9 figures

References in corpus (47)

• Nematic order in iron superconductors - who is in the driver's seat?
• Nematic Fermi Fluids in Condensed Matter Physics
• Theory of Electron Nematic Order in LaOFeAs
• Divergent nematic susceptibility in an iron arsenide superconductor
• Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Electrical Resistivity Anisotropy from Self-Organized One-Dimensionality in High-Temperature Superconductors
• 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
• On the low energy properies of fermions with singular interactions
• Effects of nematic fluctuations on the elastic properties of iron arsenide superconductors
• Spontaneous time reversal symmetry breaking in the pseudogap state of high-Tc superconductors
• Holographic quantum matter
• Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking
• Large N expansion for frustrated and doped quantum antiferromagnets
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• Nematicity, magnetism and superconductivity in FeSe
• Gauge-invariant response functions of fermions coupled to a gauge field
• The key ingredients of the electronic structure of FeSe
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Conductivity of a clean one-dimensional wire
• Non-Fermi liquids and the Wiedemann-Franz law
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• Memory matrix theory of magnetotransport in strange metals
• Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states
• Nematic State of the Pnictides Stabilized by the Interplay Between Spin, Orbital, and Lattice Degrees of Freedom
• Novel magnetic order in pseudogap state of high Tc copper oxides superconductors
• Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
• 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
• Global Phase Diagram for Magnetism and Lattice Distortion of Fe-pnictide Materials
• Lattice effects on nematic quantum criticality in metals
• Quenched nematic criticality separating two superconducting domes in an iron-based superconductor under pressure
• Chiral non-Fermi Liquids
• A controlled expansion for certain non-Fermi liquid metals
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
• Elastic coupling and spin-driven nematicity in iron-based superconductors
• Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
• Pairing instability near a lattice-influenced nematic quantum critical point
• Anomalous high-magnetic field electronic state of the nematic superconductors FeSe${}_{1-x}$S${}_x$
• Resistivity near a nematic quantum critical point: Impact of acoustic phonons
• Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals
• Controlling competing orders via non-equilibrium acoustic phonons: emergence of anisotropic electronic temperature
• Memory matrix theory of the dc resistivity of a disordered antiferromagnetic metal with an effective composite operator
• Controlled calculation of the thermal conductivity for a spinon Fermi surface coupled to a $U(1)$ gauge field
• Thermal and thermoelectric transport coefficients for a two-dimensional SDW metal with weak disorder: A memory matrix calculation

Cited by in corpus (14)

• Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals
• 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
• 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
• Low-temperature T-linear resistivity in the strange metal phase of overdoped cuprate superconductors due to umklapp scattering from a spin excitation
• 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
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Electronic nematic order in the normal state of strontium ruthenate
• Superconductivity near a nematoelastic quantum critical point
• Correlation between the strength of low-temperature T-linear normal-state resistivity and $T_{\mathrm{c}}$ in overdoped electron-doped cuprate superconductors