Strange metals as ersatz Fermi liquids

Abstract

A long standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature ($T$). In this paper we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency ($\omega$) dependent conductivity satisfies $\omega /T$ scaling, we argue that the $T$-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are `ersatz Fermi liquids' with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion/time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes which necessarily imply other exotic phenomena.

arXiv comment6 pages + 4 pages appendices. v3 various minor corrections

References in corpus (39)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Charged AdS Black Holes and Catastrophic Holography
• Renormalization Group Approach to Interacting Fermions
• Quantum Criticality in Heavy Fermion Metals
• Locally critical quantum phase transitions in strongly correlated metals
• The break up of heavy electrons at a quantum critical point
• Progress and perspectives on the electron-doped cuprates
• Strange metal in magic-angle graphene with near Planckian dissipation
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Non-Fermi liquids from holography
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Quantum critical point lying beneath the superconducting dome in iron-pnictides
• Powerlaw optical conductivity with a constant phase angle in high Tc superconductors
• The remarkable underlying ground states of cuprate superconductors
• Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
• Direct measurement of the upper critical field in a cuprate superconductor
• Holographic duality and the resistivity of strange metals
• Peculiar properties of a charged dilatonic black hole in AdS_5
• Semi-Holographic Fermi Liquids
• Detection and Implications of a Time-reversal breaking state in underdoped Cuprates
• Locally critical umklapp scattering and holography
• Linear in Temperature Resistivity and Associated Mysteries
• Correlation between linear resistivity and $T_c$ in the Bechgaard salts and the pnictide superconductor Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$
• A global inversion-symmetry-broken phase inside the pseudogap region of YBa${}_2$Cu${}_3$O${}_y$
• Scale-invariant magnetoresistance in a cuprate superconductor
• Observation of Magnetic Order in a $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.6}$ Superconductor
• Memory matrix theory of magnetotransport in strange metals
• The Strange Metal State of the Electron-Doped Cuprates
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Singular charge fluctuations at a magnetic quantum critical point
• Mottness in a doped organic superconductor
• Universal Tc depression by irradiation defects in underdoped and overdoped cuprates
• Absence of static orbital current magnetism at the apical oxygen site in HgBa${}_2$CuO${}_{4+\delta }$ from NMR
• No Evidence for Orbital Loop Currents in Charge Ordered YBa${}_2$Cu${}_3$O${}_{6+x}$ from Polarized Neutron Diffraction
• Comment on "No Evidence for Orbital Loop Currents in Charge Ordered $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+\mathrm{x}}$ from Polarized Neutron Diffraction"
• Local Quantum Criticality in the Two-dimensional Dissipative Quantum XY Model
• Observable NMR signal from circulating current order in YBCO
• Quantum oscillations from the reconstructed Fermi surface in electron-doped cuprate superconductors
• Absence of $\mu$SR evidence for magnetic order in the pseudogap phase of Bi${}_{2+x}$Sr${}_{2-x}$CaCu${}_2$O${}_{8+\delta }$

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