We analyze the scaling theory of two-dimensional metallic electron systems in the presence of critical bosonic fluctuations with small wave vectors, which are either due to a U(1) gauge field, or generated by an Ising nematic quantum critical point. The one-loop dynamical exponent z=3 of these critical systems was shown previously to be robust up to three-loop order. We show that the cancellations preventing anomalous contributions to z at three-loop order have special reasons, such that anomalous dynamical scaling emerges at four-loop order.
We consider a model of spinful fermions on the triangular lattice which exhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase transition is driven by simultaneous mass inversion of a pair of Dirac fermions, with short range interactions being perturbatively irrelevant. The second CI-NI transition is driven by a single quadratic band touching point protected by momentum space topology and C_6 lattice symmetry. A one-loop renormalization group analysis shows that short range interaction…
We revisit the problem of electrons on a square lattice below half filling close to an Ising-nematic quantum critical point. For Fermi surfaces with sufficiently strong antinodal nesting, the static nematic susceptibility is maximal at the antinodal nesting wave vector within a simple RPA calculation. We present a detailed analysis of the nematic susceptibility within Eliashberg theory and show that the strong interaction between Fermions in the antinodal regions shifts the maximum of the nematic susceptibility to slightly larger wave vectors. The corresponding order is akin to the incommensur…
To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero temperature the function diverges logarithmically at q=0. Away from Van Hove filling the ground state polarization function exhibits finite peaks at finite wave vectors. A nematic instability driven by a sufficiently strong attraction in the d-wave charge channel thus leads naturally to a spatially modulated nematic state, with a modulation vector that increases in le…
Strong electron interactions can drive metallic systems toward a variety of well-known symmetry-broken phases, but the instabilities of correlated metals with strong spin-orbit coupling have only recently begun to be explored. We uncovered a multipolar nematic phase of matter in the metallic pyrochlore Cd$_2$Re$_2$O$_7$ using spatially resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic nematic phases, this multipolar phase spontaneously breaks rotational symmetry while preserving translational invariance. However, it has the distinguishing property …
Understanding superconductivity requires detailed knowledge of the normal electronic state from which it emerges. A nematic electronic state that breaks the rotational symmetry of the lattice can potentially promote unique scattering relevant for superconductivity. Here, we investigate the normal transport of superconducting FeSe$_{1-x}$S$_x$ across a nematic phase transition using high magnetic fields up to 69 T to establish the temperature and field-dependencies. We find that the nematic state is an anomalous non-Fermi liquid, dominated by a linear resistivity at low temperatures that can tr…
We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $Ω/γ(T)$ at small momenta, where $γ(T)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte-…
The interplay between the nematic order and magnetism in FeSe is not yet well understood. There is a controversy concerning the relationship between orbital and spin degrees of freedom in FeSe and their relevance for superconductivity. Here we investigate the effect of S substitution on the nematic transition temperature ($T_{\rm n}$) and the low-energy spin fluctuations (SF) in FeSe single crystals. We show that the low-energy SF emerge below the nematic transition. The difference between the onset temperature for the critical SF ($T_{\rm SF}$) and $T_{\rm n}$ is small for FeSe but significan…
It is shown that metamagnetic transition in metals can occur via the formation of electronic nematic order. We consider a simple model where the spin-dependent Fermi surface instability gives rise to the formation of an electronic nematic phase upon increasing the applied Zeeman magnetic field. This leads to two consecutive metamagnetic transitions that separate the nematic phase from the low-field and high-field 'isotropic' metallic phases. Possible connection to the physics of the bilayer Ruthenate, Sr$_3$Ru$_2$O$_7$, is also discussed.
We derive from a microscopic model the effective theory of nematic order in a system with a spontaneous quantum anomalous Hall effect in two dimensions. Starting with a model of two-component fermions (a spinor field) with a quadratic band crossing and short range four-fermion marginally relevant interactions we use a 1/N expansion and bosonization methods to derive the effective field theory for the hydrodynamic modes associated with the conserved currents and with the local fluctuations of the nematic order parameter. We focus on the vicinity of the quantum phase transition from the isotropi…
The instability of a Fermi surface against Ising nematic order destroys the quasiparticle character of the low-energy degrees of freedom. Therefore, observables exhibit deviations from Fermi liquid behavior which gives rise to the term Ising nematic quantum critical metal. To obtain a theoretical description we use a finite-temperature version of Eliashberg theory which allows to treat the strong coupling between quantum and thermal fluctuations in the absence of well-defined quasiparticles. Here, we use this self-consistent, diagrammatic approach to compute, in particular, the nematic suscept…
Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin $\frac 1 2$ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting $T_c$ enclosing the nematic quantum critical point. For temperatures above $T_c$, we see strikingly non-Fermi liquid behavior, including a "nodal - anti nodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low frequency o…
The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recent…
We study the interaction effect in a three dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instability towards forming these ordered phases. The charge density wave phase is similar as that of a Weyl semimetal while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimental…
Identification, understanding, and manipulation of novel magnetic textures is essential for the discovery of new quantum materials for future spin-based electronic devices. In particular, materials that manifest a large response to external stimuli such as a magnetic field are subject to intense investigation. Here, we study the kagome-net magnet YMn$_{6}$Sn$_{6}$ by magnetometry, transport, and neutron diffraction measurements combined with first principles calculations. We identify a number of nontrivial magnetic phases, explain their microscopic nature, and demonstrate that one of them host…
Nematic phase intertwines closely with high-Tc superconductivity in iron-based superconductors. Its mechanism, which is closely related to the pairing mechanism of superconductivity, still remains controversial. Comprehensive characterization of how the electronic state reconstructs in the nematic phase is thus crucial. However, most experiments focus only on the reconstruction of band dispersions. Another important characteristic of electronic state, the spectral weight, has not been studied in details so far. Here, we studied the spectral weight transfer in the nematic phase of FeSe$_{0.9}$S…
High-resolution time- and angle-resolved photoemission measurements were made on FeSe superconductors. With ultrafast photoexcitation, two critical excitation fluences that correspond to two ultrafast electronic phase transitions were found only in the $d_{yz}$-orbit-derived band near the Brillouin-zone center within our time and energy resolution. Upon comparison to the detailed temperature dependent measurements, we conclude that there are two equilibrium electronic phase transitions (at approximately 90 and 120 K) above the superconducting transition temperature, and an anomalous contributi…
We show, by means of dynamical mean-field theory calculations, that the experimental fingerprints of the nematic order in iron-based superconductors are intrinsically connected with the electronic correlations in the Hund's correlated metallic state and they can not be accessed via a renormalized quasiparticle picture. In particular, our results show that: (i) in a metal in which correlations are dominated by the Hund's coupling the nematic ordering does not produce a rigid energy shift in the photoemission spectra, but a much richer spectral weight redistribution which mirrors the experimenta…
Hexagonal Kagome lattice is a multiband system with a quadratic band crossing point, in contrast with honeycomb lattice with linear band crossing point, which has exotic correlated effect and can produce various novel quantum states. Here we investigate the phase diagram of the fermions on the hexagonal Kagome lattice as a function of interaction, temperature and lattice anisotropy, by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. For weak interaction, the quadratic band-crossing point is broken to linear band crossing point and the sys…
In frustrated magnets when magnetic ordering is suppressed down to low temperature, the formation of a quantum spin liquid becomes a possibility. How such a spin liquid manifests in the presence of conduction electrons is a question with potentially rich physical consequences, particularly when both the localized spins and conduction electrons reside on frustrated lattices. We propose a novel mechanism for symmetry breaking in systems where conduction electrons hybridize with a quantum spin liquid through Kondo couplings. We apply this to the pyrochlore iridate Pr2Ir2O7, which exhibits an anom…
Correlation-driven enhancement of pairing in a nematic Hund's metal
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；HUN-REN-BME-BCE Quantum Technology Research Group（匈牙利研究与创新网络-布达佩斯技术与经济大学-布达佩斯理工大学量子技术研究组）；Istituto dei Sistemi Complessi (ISC-CNR)（复杂系统研究所）
We consider two-dimensional metals near a Pomeranchuk instability which breaks 90$^\circ$ lattice rotation symmetry. Such metals realize strongly-coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation, and hence a non-zero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the $d$-wave channel acts as a rand…
Theoretically, it is commonly held that in metals near a nematic quantum critical point the electronic excitations become incoherent on the entire `hot' Fermi surface, triggering non Fermi liquid behavior. However, such conclusions are based on electron-only theories, ignoring a symmetry-allowed coupling between the electronic nematic variable and a suitable crystalline lattice strain. Here we show that including this coupling leads to entirely different conclusions because the critical fluctuations are mostly cutoff by the non-critical lattice shear modes. At sufficiently low temperatures the…
The theoretical understanding of the nematic state of iron-based superconductors and especially of FeSe is still a puzzling problem. Although a number of experiments calls for a prominent role of local correlations and place iron superconductors at the entrance of a Hund metal state, the effect of the electronic correlations on the nematic state has been theoretically poorly investigated. In this work we study the nematic phase of iron superconductors accounting for local correlations, including the effect of the Hund's coupling. We show that Hund's physics strongly affects the nematic propert…
We discuss the finite temperature properties of the fermion correlation function near the fixed point theory of the nematic quantum critical point (QCP) of a metallic Fermi system. We show that though the fixed point theory is above its upper critical dimension, the equal time fermion correlation function takes on a universal scaling form in the vicinity of the QCP. We find that in the quantum critical regime, this equal-time correlation function has an ultra local behavior in space, while the low-frequency behavior of the equal-position auto correlation function is that of a Fermi liquid up t…
Recent magneto-transport experiments have provided compelling evidence for the presence of an energetically isolated threefold Q-valley degeneracy in few-layer transition metal dichalcogenides. We study the flavor SU(3) symmetry breaking when each Landau level triplet is one-third filled or empty and predict that a pure flavor nematic phase and a flavorless charge-density-wave phase will occur respectively below and above a critical magnetic field. Surprisingly, electrons carry flavor-dependent electric dipole moments even at zero magnetic field, rendering the nematics ferroelectric, allowing …
Moiré superlattice systems such as transition metal dichalcogenide heterobilayers have garnered significant recent interest due to their promising utility as tunable solid state simulators. Recent experiments on a WSe$_2$/WS$_2$ heterobilayer detected incompressible charge ordered states that one can view as generalized Wigner crystals. The tunability of the hetero-TMD Moiré system presents an opportunity to study the rich set of possible phases upon melting these charge-ordered states. Here we use Monte Carlo simulations to study these intermediate phases in between incompressible charge-orde…
In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\, η/s$, where $η$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $η$ scales in the same manner as a chiral conductivity, and the ratio $η/s$ diverges …
We study the properties of $s$-wave superconductivity induced around a nematic quantum critical point in two-dimensional metals. The strong Landau damping and the Cooper pairing between incoherent fermions have dramatic mutual influence on each other, and hence should be treated on an equal footing. This problem is addressed by analyzing the self-consistent Dyson-Schwinger equations for the superconducting gap and Landau damping rate. We solve the equations at zero temperature without making any linearization, and show that the superconducting gap is maximized at the quantum critical point and…
Recent finding of an {\it unusual} in-plane resistivity anisotropy in the underdoped 122-family at high temperature ($T$) suggests an orbital nematic (ON) order, posing a challenge to extant theories. The {\it sign} of the anisotropy contradicts expectations from weakly correlated as well as pure spin-only nematic views. Here, we show how such an ON order with accompanying structural distortion arises from {\it residual}, intersite and inter-orbital two-body interactions in an incoherent "bad metal" close to Mottness. Enhancement of orbital-selective incoherence is shown to be necessary for un…
Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group c…
Correlated Metals, Metamagnetism, and Orbital Nematic Order in moiré Materials with Neural Quantum States
ETH Zürich（苏黎世联邦理工学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Electronic nematicity, proposed to exist in a number of transition metal materials, can have different microscopic origins. In particular, the anisotropic resistivity and meta-magnetic jumps observed in Sr3Ru2O7 are consistent with an earlier proposal that the isotropic-nematic transition is generically first order and accompanied by meta-magnetism when tuned by a magnetic field. However, additional striking experimental features such as a non-Fermi liquid resistivity and critical thermodynamic behavior imply the presence of an unidentified quantum critical point (QCP). Here we show that orbit…
We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes''. We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective m…
It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical wings are predicted to appear in the phase diagram in a spatially varying magnetic field, but not in a homogeneous one.
In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to…
Understanding optical conductivity data in the optimally doped cuprates in the framework of quantum criticality requires a strongly-coupled quantum critical metal which violates hyperscaling. In the simplest scaling framework, hyperscaling violation can be characterized by a single non-zero exponent $θ$, so that in a spatially isotropic state in $d$ spatial dimensions, the specific heat scales with temperature as $T^{(d-θ)/z}$, and the optical conductivity scales with frequency as $ω^{(d-θ-2)/z}$ for $ω\gg T$, where $z$ is the dynamic critical exponent. We study the Ising-nematic critical poin…
Using functional renormalization group methods, we study an effective low-energy model describing the Ising-nematic quantum critical point in two-dimensional metals. We treat both gapless fermionic and bosonic degrees of freedom on equal footing and explicitly calculate the momentum and frequency dependent effective interaction between the fermions mediated by the bosonic fluctuations. Following earlier work by S.-S. Lee for a one-patch model, Metlitski and Sachdev [Phys. Rev. B {\bf{82}}, 075127] recently found within a field-theoretical approach that certain three-loop diagrams strongly modi…
We examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in d-wave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/N_f expansion, where N_f is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large N_f theory, the nematic order has a large anomalous dimension, and the fermion spectral functions a…
The in-plane resistivity anisotropy has been studied with the Montgomery method on two detwinned parent compounds of the iron-based superconductors, NaFeAs and FeTe. For NaFeAs, the resistivity in the antiferromagnetic (AFM) direction is smaller than that in the ferromagnetic (FM) direction, similar to that observed in BaFe2As2 before. While for FeTe, the resistivity in the AFM direction is larger than that in the FM direction. We show that these two opposite resistivity anisotropy behaviors could be attributed to the strong Hund's rule coupling effects: while the iron pnictides are in the iti…
Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Carl Zeiss SMT GmbH（卡尔蔡司SMT有限公司）；Ariel University（阿里埃勒大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
The electronic nematic state without magnetization emerges in various strongly correlated metals such as Fe-based and cuprate superconductors. To understand this universal phenomenon, we focus on the nematic state in Ti-oxypnictide BaTi2(As,Sb)2O, which is expressed as the three-dimensional 10-orbital Hubbard model. The antiferromagnetic fluctuations are caused by the Fermi surface nesting. Interestingly, we find the spin-fluctuation-driven orbital order due to the strong orbital-spin interference, which is described by the Aslamazov-Larkin vertex correction (AL-VC). The predicted intra-unit-c…
