Nematic Fermi Fluids in Condensed Matter Physics

Abstract

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classical nematics generally occur in liquids of rod-like molecules; given that electrons are point-like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. That such phases exist in nature was established by dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007. In this paper, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

30 pages, 7 figures (some in color); to appear in Annual Reviews of Condensed Matter Physics. Edited version.

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• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
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• On the origin of non-monotonic doping dependence of the in-plane resistivity anisotropy in Ba(Fe${}_{1-x}{T}_x$)${}_2$As${}_2$, $T$ = Co, Ni and Cu
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• Measurement of the elastoresistivity coefficients of the underdoped iron-arsenide Ba(Fe${}_{0.975}$Co${}_{0.025}$)${}_2$As${}_2$
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• Tilt-Induced Anisotropic to Isotropic Phase Transition at $\nu =5/2$
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• Ultrafast observation of critical nematic fluctuations and giant magnetoelastic coupling in iron pnictides
• Magnetic interactions in iron superconductors: A review
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• Pure nematic quantum critical point accompanied by a superconducting dome
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• Electronic Structure of the Cuprate Superconducting and Pseudogap Phases from Spectroscopic Imaging STM
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• Normal state properties of quantum critical metals at finite temperature
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• DC resistivity near a nematic quantum critical point: Effects of weak disorder and acoustic phonons
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• Controlling competing orders via non-equilibrium acoustic phonons: emergence of anisotropic electronic temperature
• Low frequency Raman response near Ising-nematic quantum critical point: a memory matrix approach
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• Competition between superconductivity and nematic order in high-$T_c$ superconductor
• Nematic magnetoelastic effect contrasted between Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and FeSe
• Origin of the DC and AC conductivity anisotropy in iron-based superconductors: scattering rate versus spectral weight effects
• Coupled Ferromagnetic and Nematic Ordering of Fermions in an Optical Flux Lattice
• Structural-transition-induced quasi two-dimensional Fermi surface in FeSe
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• Nematicity of correlated systems driven by anisotropic chemical phase separation
• Transport signatures of spatially modulated electronic nematic phases
• Interplay between nematicity and Bardasis-Schrieffer modes in the short-time dynamics of unconventional superconductors
• Haldane Sashes in Quantum Hall Spectra
• Antagonistic in-plane resistivity anisotropies from competing fluctuations in underdoped cuprates
• Effective pairing theory for strongly correlated d-wave superconductors
• Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
• Observation of a Critical Charge Mode in a Strange Metal
• Nematic insulator at charge neutrality in twisted bilayer graphene
• Spin and the Coulomb Gap in the Half-Filled Lowest Landau Level
• Anisotropic composite fermions and fractional quantum Hall effect
• Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior
• Impact of ordering competition on the global phase diagram of iron pnictides
• Preferred magnetic excitations in Sr${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$
• Numerical evidence of electron hydrodynamic whirlpools in graphene samples
• Quadrupolar charge dynamics in the nonmagnetic FeSe${}_{1-x}$S${}_x$ superconductors
• Tuning a random field mechanism in a frustrated magnet
• Pomeranchuk Instability in a non-Fermi Liquid from Holography
• Spontaneous fourfold-symmetry breaking driven by electron-lattice coupling and strong correlations in high-$T_c$ cuprates
• Strain-tuned quantum criticality in electronic Potts-nematic systems
• Thermodynamic evidence for broken fourfold rotational symmetry in the hidden-order phase of URu2Si2
• Competing magnetic orders in quantum critical Sr${}_3$Ru${}_2$O${}_7$
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Driving force of the orbital-relevant electronic nematicity in Fe-based superconductors
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Vortex and disclination structures in a nematic-superconductor state
• Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa${}_2$Cu${}_4$O${}_8$
• Stripe Symmetry of Short-range Charge Density Waves in Cuprate Superconductors
• Classification of electronic nematicity in three-dimensional crystals and quasicrystals
• Spin-Phonon Resonances in Nearly Polar Metals with Spin-Orbit Coupling
• Raman scattering as a probe of charge nematic fluctuations in iron based superconductors
• Two-dimensional Fermi liquid dynamics with density and quadrupolar interactions
• Interwoven atypical quantum states in CeLiBi${}_2$
• Discovery of Orbital Ordering in Bi2Sr2CaCu2O8+x
• Intertwined Spin and Orbital Density Waves in MnP Uncovered by Resonant Soft X-ray Scattering
• Inhomogeneous superconductivity in LuxZr1-xB12 dodecaborides with dynamic charge stripes
• Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Electron Pairing and Nematicity in LaAlO${}_3$/SrTiO${}_3$ Nanostructures
• Role of Fermi surface for the pressure-tuned nematic transition in the BaFe${}_2$As${}_2$ family
• Nematic state stabilized by off-site Coulomb interaction in iron-based superconductors
• Potential Lifshitz transition at optimal substitution in nematic pnictide Ba${}_{1-x}$Sr${}_x$Ni${}_2$As${}_2$
• Ultrafast measurements under anisotropic strain reveal near equivalence of competing charge orders in TbTe${}_3$
• In-situ tunable giant electrical anisotropy in a grating gated AlGaN/GaN two-dimensional electron gas
• Nonlinear uniaxial pressure dependence of $T_c$ in iron-based superconductors
• Competition between spin-induced charge instabilities in underdoped cuprates
• Holographic RG flows with nematic IR phases
• Searching for non-Fermi liquids under holographic light
• Revisiting the phase diagram of LaFe${}_{1-x}$Co${}_x$AsO on single crystals by thermodynamic methods
• Correlation-driven electronic nematicity in the Dirac semimetal BaNiS2
• Topological quantum phases of ${}^4$He confined to nanoporous materials
• Nanoscale phase separation and pseudogap in the hole-doped cuprates from fluctuating Cu-O-Cu bonds
• Orbital and spin order in oxide two-dimensional electron gases
• Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide
• Intertwined Orders and the Physics of High Temperature Superconductors
• Disorder-Induced Electronic Nematicity
• Laser-induced coherent control of an electronic nematic quantum phase transition
• Direct observation of spin excitation anisotropy in the paramagnetic orthorhombic state of BaFe${}_{2-x}$Ni${}_x$As${}_2$
• Apparent temperature-induced reorientation of quantum Hall stripes
• Highly-Anisotropic Even-Denominator Fractional Quantum Hall State in an Orbitally-Coupled Half-Filled Landau Level
• Piezoresistivity as a Fingerprint of Ferroaxial Transitions
• Ising nematic fluid phase of hard-core dimers on the square lattice
• Flat Bands and Enigma of Metamagnetic Quantum Critical Regime in Sr3Ru2O7
• Stability of multielectron bubbles in high Landau levels
• Strain-induced spin-nematic state and nematic susceptibility arising from $2\times 2$ Fe clusters in KFe${}_{0.8}$Ag${}_{1.2}$Te${}_2$
• Impact of the first order antiferromagnetic phase transition on the paramagnetic spin excitations and nematic phase of SrFe${}_2$As${}_2$
• Unveiling a nematic quantum critical point in multi-orbital systems
• Electronic origin of structural transition in 122 Fe based superconductors
• Two-loop disorder effects on the nematic quantum criticality in $d$-wave superconductors
• Local Structure of Mott Insulating Iron Oxychalcogenides La${}_2$O${}_2$Fe${}_2$O$M$${}_2$ ($M$ = S, Se)
• Additional electron pairing in a d-wave superconductor driven by nematic order
• Universal collective modes in 2 dimensional chiral superfluids
• Random-strain-induced correlations in materials with intertwined nematic and magnetic orders
• Odd frequency pairing in a quantum critical metal
• Morphing of 2D Hole Systems at $\nu =3/2$ in Parallel Magnetic Fields: Compressible, Stripe, and Fractional Quantum Hall Phases
• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors
• Unconventional non-Fermi liquid state caused by nematic criticality in cuprates
• Probing three-state Potts nematic fluctuations by ultrasound attenuation
• Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet
• Local electronic nematicity in the one-band Hubbard model
• Distinguishing XY from Ising Electron Nematics
• Defect-induced electronic smectic state at the surface of nematic materials
• Theories for charge-driven nematicity in kagome metals
• Rotation of the dislocation grid in multilayer FeSe films and visualization of electronic nematic domains via orbital-selective tunneling
• Three-state Potts nematic order in stacked frustrated spin models with SO(3) symmetry
• Orbital order in a bosonic $p$-band triangular lattice
• Pomeranchuk-Nematic instability in the presence of a weak magnetic field
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Pairing by a dynamical interaction in a metal
• Enhancement of superconductivity by electronic nematicity in cuprate superconductors
• Fermi Liquid near a q=0 Charge Quantum Critical Point
• Thermoelectric signature of the nematic phase in iron-based superconductor
• Anomalous coupling between magnetic and nematic orders in quantum Hall systems
• Electron pairing with gapless excitations in mixed double layers
• Nematic fluctuations in the non-superconducting iron pnictide BaFe${}_{1.9-x}$Ni${}_{0.1}$Cr${}_x$As${}_2$
• Surface Nematic Order in Iron Pnictides
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• Discovery of an Intermediate Nematic State in a Bilayer Kagome Metal ScV6Sn6
• Observation of the novel type of ordering: Spontaneous ferriquadrupolar order
• Interplay between Multipolar Order and Multipole-Induced Superconductivity in PrTi${}_2$Al${}_{20}$
• Magnetic-field-tuned randomness in inhomogeneous altermagnets
• Strain tuning and anisotropic spin correlations in iron-based systems
• c-axis pressure induced antiferromagnetic order in optimally P-doped BaFe2(As0.70P0.30)2 superconductor
• Phase Separation in Two-Dimensional Electron Systems: Experimental View
• Pressure study of nematicity and quantum criticality in Sr${}_3$Ru${}_2$O${}_7$ for an in-plane field
• Signatures of electronic correlations and spin-susceptibility anisotropy in nuclear magnetic resonance
• Spontaneous Fermi surface deformation in the three-band Hubbard model: A variational Monte Carlo study
• Nematic order on the surface of a three-dimensional topological insulator
• Recent Progress of Point Contact Spectroscopy as a Probe of Correlated Electron States
• Characteristic energy of the nematic-order state and its connection to enhancement of superconductivity in cuprate superconductors
• Controlling inversion and time-reversal symmetries by subcycle pulses in the one-dimensional extended Hubbard model
• Stability of quantum degenerate Fermi gases of tilted polar molecules
• Unusual band splitting and superconducting gap evolution with sulfur substitution in FeSe
• Flavored anisotropic black holes
• One-dimensional scattering of two-dimensional fermions near quantum criticality
• Nematic order driven by superconducting correlations
• Nematic phase in a two-dimensional Hubbard model at weak coupling and finite temperature
• Influence of orbital nematic order on spin responses in Fe-based superconductors
• Possible Nematic Order Driven by Magnetic Fluctuations in Iron Pnictides
• Breakdown of Landau Fermi liquid theory: restrictions on the degrees of freedom of quantum electrons
• Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric Effect
• Orientation of hole quantum Hall nematic phases in an out-of-plane electric field
• Spin loop-current textures in Hubbard models
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Quantum criticality and optical conductivity in a two-valley system
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• Spontaneous breaking of four-fold rotational symmetry in two-dimensional electron systems as a topological phase transition
• Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations
• Critical behavior of itinerant fermions - role of finite size effects
• A Ginzburg-Landau approach to the vortex-domain wall interaction in superconductors with nematic order
• Fermi surface instabilities at finite Temperature
• Itinerant fermions on a triangular lattice: unconventional magnetism and other ordered states
• Chiral superconductivity in nematic states
• Bose-Einstein condensate of Dirac magnons: Pumping and collective modes
• Strong-coupling expansion of multi-band interacting models: mapping onto the transverse-field $J_1$-$J_2$ Ising model
• Drift velocity of edge magnetoplasmons due to magnetic edge channels
• Resistive anisotropy in the charge density wave phase of Kagome superconductor CsV3Sb5 thin films
• Angular Dependent Spectral-Weight Transfer and Evidence for Symmetry Broken In-Plane Charge Response in Ca${}_{1.9}$Na${}_{0.1}$CuO${}_2$Cl${}_2$
• Superconductivity near a nematoelastic quantum critical point
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Strain-activated structural anisotropy in BaFe2As2
• The Symmetry Principle in Condensed Matter Physics (I)
• Laser induced $\mathcal{P}\mathcal{T}$-symmetry breaking in the fluctuations of electronic fluids
• Quantum Hall stripes in high-density GaAs/AlGaAs quantum wells
• Electronic confinement and ordering instabilities in colossal magnetoresistive bilayer manganites
• Fractional quantum Hall effect in strained graphene: stability of Laughlin states in disordered (pseudo)magnetic fields
• Effects of Chemical Pressure on Superconductivity in Electrochemically Intercalated (TMA)yFe2(Se1-xSx)2 (TMA = Tetramethylammonium)
• Ubiquity of rotational symmetry breaking in superconducting films, from Fe(Te,Se)/Bi${}_2$Te${}_3$ to Nb, and the effect of measurement geometry
• Entanglement smectic and stripe order
• Even-denominator fractional quantum Hall states with spontaneously broken rotational symmetry
• Decoupling of Lattice and Orbital Degrees of Freedom in an Iron-Pnictide Superconductor
• Acoustic lattice instabilities at the magneto-structural transition in Fe${}_{1.057(7)}$Te
• Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
• Stripe order in quasicrystals
• Orbital selective order and ${\mathbb{Z}}_3$ Potts nematicity from a non-Fermi liquid
• Coincidence detection probability of $(\gamma ,2e)$ photoemission measurement
• Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La${}_{1.65}$Eu${}_{0.2}$Sr${}_{0.15}$CuO${}_4$
• Valley polarization of Landau levels driven by residual strain in the ZrSiS surface band
• Observation of new plasmons in the fractional quantum Hall effect: interplay of topological and nematic orders
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Post-experiment coincidence detection techniques for direct detection of two-body correlations
• Measurements of nematic susceptibility with phase sensitive nuclear magnetic resonance in pulsed strain fields
• Electronic Liquid Crystal Physics of Underdoped Cuprates
• Effective field theory of an anomalous Hall metal from interband quantum fluctuations
• Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal
• Nematicity in LaFeAsO single crystals studied by elastoresistance, high-resolution thermal expansion and shear-modulus measurements
• Phonon Induced Energy Relaxation in Quantum Critical Metals
• Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets
• Cavity QED Control of Quantum Hall Stripes
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons
• Signatures of three-state Potts nematicity in spin excitations of the van der Waals antiferromagnet FePSe${}_3$
• Critical theory of Pomeranchuk transitions via high-dimensional bosonization
• Interplay of Quantum and Thermal Fluctuations in Two-Dimensional Randomly Pinned Charge Density Waves
• Coincidence detection techniques for direct measurement of many-body correlations in strongly correlated electron systems
• Coexistence of stripe order and superconductivity in NaAlSi
• Can electronic quantum criticality drive phonon-induced linear-in-temperature resistivity?
• Unconventional superconductivity mediated solely by isotropic electron-phonon interaction
• Electromagnetic response of cuprate superconductors with coexisting electronic nematicity
• Generalized susceptibilities and Landau parameters for anisotropic Fermi liquids