A Rigorous Formalism of Unconventional Symmetry Breaking in Fermi Liquid Theory and Its Application to Nematicity in FeSe

Abstract

Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the "density-wave equation" that gives the thermodynamically stable form factor, similarly to the superconducting-gap equation. In addition, a rigorous expression of the Ginzburg-Landau free-energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based superconductor FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss behavior of the nematic susceptibility at higher T, and the deviation from the Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii) Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c\propto T_c^b$ with $b\sim 3$. (Note that b=0 in the BCS theory.) These results lead to a conclusion that the nematicity in FeSe is the bond+orbital order due to the "paramagnon interference mechanism". The present theory paves the way for solving various unconventional phase transition systems.

arXiv comment19 pages, 10 figures

References in corpus (72)

• Nematic order in iron superconductors - who is in the driver's seat?
• Functional renormalization group approach to correlated fermion systems
• Theory of Electron Nematic Order in LaOFeAs
• Orbital Fluctuation Mediated Superconductivity in Iron Pnictides: Analysis of Five Orbital Hubbard-Holstein Model
• Unconventional Fermi surface instabilities in the Kagome Hubbard Model
• Time-reversal symmetry-breaking charge order in a kagome superconductor
• Competing electronic orders on Kagome lattices at van Hove filling
• Effects of nematic fluctuations on the elastic properties of iron arsenide superconductors
• Self-energy-functional approach to systems of correlated electrons
• Renormalization group analysis of the 2D Hubbard model
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors
• Comparison of Ab initio Low-Energy Models for LaFePO, LaFeAsO, BaFe2As2, LiFeAs, FeSe and FeTe: Electron Correlation and Covalency
• Electronic instabilities of kagome metals: saddle points and Landau theory
• Origin of the tetragonal-to-orthorhombic (nematic) phase transition in FeSe: a combined thermodynamic and NMR study
• Lack of coupling between superconductivity and orthorhombic distortion in stoichiometric single-crystalline FeSe
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• Nematicity and quantum paramagnetism in FeSe
• Nematic quantum critical point without magnetism in FeSe1-xSx superconductors
• In-plane electronic anisotropy of underdoped "122" Fe-arsenide superconductors revealed by measurements of detwinned single crystals
• Detection and Implications of a Time-reversal breaking state in underdoped Cuprates
• Self-Consistent Vertex Correction Analysis for Iron-Based Superconductors: Mechanism of Coulomb-Interaction-Driven Orbital Fluctuations
• Concepts relating magnetic interactions, intertwined electronic orders and strongly correlated superconductivity
• Bond order in two-dimensional metals with antiferromagnetic exchange interactions
• Structural quantum criticality and superconductivity in iron-based superconductor Ba(Fe1-xCox)2As2
• Observation of incipient charge nematicity in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$
• Nematic susceptibility of hole- and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements
• Anomalous Transport Phenomena in Fermi Liquids with Strong Magnetic Fluctuations
• Origin of Orthorhombic Transition, Magnetic Transition, and Shear Modulus Softening in Iron Pnictide Superconductors: Analysis based on the Orbital Fluctuation Theory
• Magnetism, superconductivity, and spontaneous orbital order in iron-based superconductors: who comes first and why?
• Momentum-dependent sign-inversion of orbital polarization in superconducting FeSe
• Mechanism of exotic density-wave and beyond-Migdal unconventional superconductivity in kagome metal AV3Sb5 (A=K, Rb, Cs)
• Nematicity and magnetism in FeSe and other families of Fe-based superconductors
• Charge induced nematicity in FeSe
• Sign-reversing orbital polarization in the nematic phase of FeSe due to the $C_2$ symmetry-breaking in the self-energy
• Distinctive momentum dependence of the band reconstruction in the nematic state of FeSe thin film
• Nematicity with a twist: rotational symmetry breaking in a moiré superlattice
• The Nematic Energy Scale and the Missing Electron Pocket in FeSe
• Spin-Fluctuation-Driven Nematic Charge-Density-Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin-Type Vertex Correction
• Revealing the immediate formation of two-fold rotation symmetry in charge-density-wave state of Kagome superconductor CsV${}_3$Sb${}_5$ by optical polarization rotation measurement
• High-Tc Superconductivity near the Anion Height Instability in Fe-based Superconductors: Analysis of LaFeAsO${}_{1-x}$H${}_x$
• Diagonal Nematicity in the Pseudogap Phase of HgBa${}_2$CuO${}_{4+\delta }$
• Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe${}_2$As${}_2$
• Effect of Nonmagnetic Impurity in Nearly Antiferromagnetic Fermi Liquid: Magnetic Correlations and Transport Phenomena
• Incommensurate nematic fluctuations in the two-dimensional Hubbard model
• Linear Response Theory for Shear Modulus $C_{66}$ and Raman Quadrupole Susceptibility: Significant Evidence for Orbital Nematic Fluctuations in Fe-Based Superconductors
• Orbital Nematic Instability in Two-Orbital Hubbard Model: Renormalization-Group + Constrained RPA Analysis
• Emergent XY electronic nematicity in iron-based superconductors
• Pure nematic quantum critical point accompanied by a superconducting dome
• Lifted electron pocket and reversed orbital occupancy imbalance in FeSe
• Multistage Electronic Nematic Transitions in Cuprate Superconductors: Functional-Renormalization-Group Analysis
• Nematicity, magnetism and superconductivity in FeSe under pressure: Unified explanation based on the self-consistent vertex correction theory
• Origin of diverse nematic orders in Fe-based superconductors: 45${}^{\circ }$ rotated nematicity in AFe${}_2$As${}_2$ (A=Cs, Rb)
• Electron Mass Enhancement near a Nematic Quantum Critical Point in NaFe${}_{1-x}$Co${}_x$As
• Superconductivity without hole-pocket in electron-doped FeSe: Analysis beyond the Migdal-Eliashberg formalism
• Competing Unconventional Charge-Density-Wave States in Cuprate Superconductors: Spin-Fluctuation-Driven Mechanism
• Orbital order in FeSe - the case for vertex renormalization
• $SU(4)$ Valley + Spin Fluctuation Interference Mechanism for Nematic Order in Magic Angle Twisted Bilayer Graphene: Impact of Vertex Corrections
• Non-local $d_{xy}$ nematicity and the missing electron pocket in FeSe
• Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in CeB6
• Bond Directional Anapole Order in a Spin-Orbit Coupled Mott Insulator Sr${}_2$(Ir${}_{1-x}$Rh${}_x$)O${}_4$
• Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems
• Fully gapped s-wave superconductivity enhanced by magnetic criticality in heavy fermion system
• Hexadecapole fluctuation mechanism for s-wave heavy fermion superconductor CeCu2Si2: Interplay between intra- and inter-orbital Cooper pairs
• Emergence of Charge Loop Current in Geometrically Frustrated Hubbard Model: Functional Renormalization Group Study
• Elastoresistance measurements on CaKFe${}_4$As${}_4$ and KCa${}_2$Fe${}_4$As${}_4$F${}_2$ with the Fe site of $C_{2v}$ symmetry
• Hidden antiferro-nematic order in Fe-based superconductor BaFe${}_2$As${}_2$ and NaFeAs above $T_S$
• Kinetic Energy, Condensation Energy, Optical Sum Rule and Pairing Mechanism in High-Tc Cuprates
• Theoretical Prediction of the Nematic Orbital-Ordered State in Ti-Oxypnictide Superconductor BaTi2(As,Sb)2O
• In-plane anisotropy of transport coefficients in the electronic nematic states: Universal origin of the nematicity in Fe-based superconductors
• $d$- and $p$-wave quantum liquid crystal orders in cuprate superconductors, $\kappa$-(BEDT-TTF)${}_2$X, and coupled chain Hubbard models: functional-renormalization-group analysis
• Thermodynamic Signatures of Diagonal Nematicity in RbFe${}_2$As${}_2$ Superconductor

Cited by in corpus (20)

• Charge-loop current order and Z3 nematicity mediated by bond-order fluctuations in kagome metal AV3Sb5 (A=Cs,Rb,K)
• Multiscale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains
• Unconventional density waves and superconductivities in Fe-based superconductors and other strongly correlated electron systems
• Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals
• Nevanlinna.jl: A Julia implementation of Nevanlinna analytic continuation
• Real-space Loop Current Pattern in Time-reversal-symmetry Breaking Phase in Kagome Metals
• Correlation-driven electronic nematicity in the Dirac semimetal BaNiS2
• Quantum-metric-induced giant and reversible nonreciprocal transport phenomena in chiral loop-current phases of kagome metals
• Low temperature phase transitions under CDW state in kagome metals AV3Sb5 (A=Cs,Rb,K): Significance of mix-type Fermi surface electron correlations
• Three-dimensional bond-order instability in infinite-layer nickelates due to nonlocal quantum interference
• Origin of switchable quasiparticle-interference chirality in loop-current phase of kagome metals measured by scanning-tunneling-microscopy
• Coherence Length of Electronic Nematicity in Iron-Based Superconductors
• Unified mechanism of charge-density-wave and high-$T_c$ superconductivity protected from oxygen vacancies in bilayer nickelates
• Odd-parity quadrupole order and induced nonreciprocal transport in the kagome metal CsTi${}_3$Bi${}_5$ driven by quantum interference
• Robust $T$-Linear Resistivity due to SU(4) Valley + Spin Fluctuation Mechanism in Magic Angle Twisted Bilayer Graphene
• Giant Impurity Effects on Charge Loop Current Order States in Kagome Metals
• Microscopic evidence for imaginary charge density wave in a kagome metal
• Topological electron and phonon flat bands in novel kagome superconductor XPd5 (X=Ca, Sr, Ba)
• Microscopic origin of period-four stripe charge-density-wave in kagome metal CsV${}_3$Sb${}_5$
• Superconductivity and the quasiparticle mass enhancement near the CDW critical point using Bethe-Salpeter method: Application to cuprates