non-Fermi Liquid Behavior Research Articles

Quantum phase transition inside the superconducting dome of Ba(Fe1−xCox)2As2 from diamond-based optical magnetometry

Unconventional superconductivity often emerges in close proximity to a magnetic instability. Upon suppressing the magnetic transition down to zero temperature by tuning the carrier concentration, pressure, or disorder, the superconducting transition temperature Tc acquires its maximum value. A major challenge is the elucidation of the relationship between the superconducting phase and the strong quantum fluctuations expected near a quantum phase transition (QPT) that is either second order (i.e. a quantum critical point) or weakly first order. While unusual normal state properties, such as non-Fermi liquid behavior of the resistivity, are commonly associated with strong quantum fluctuations, evidence for its presence inside the superconducting dome are much scarcer. In this paper, we use sensitive and minimally invasive optical magnetometry based on NV-centers in diamond to probe the doping evolution of the T = 0 penetration depth in the electron-doped iron-based superconductor Ba(Fe1−xCox)2As2. A non-monotonic evolution with a pronounced peak in the vicinity of the putative magnetic QPT is found. This behavior is reminiscent to that previously seen in isovalently-substituted BaFe2(As1−xPx)2 compounds, despite the notable differences between these two systems. Whereas the latter is a very clean system that displays nodal superconductivity and a single simultaneous first-order nematic–magnetic transition, the former is a charge-doped and significantly dirtier system with fully gapped superconductivity and split second-order nematic and magnetic transitions. Thus, our observation of a sharp peak in λ(x) near optimal doping, combined with the theoretical result that a QPT alone does not mandate the appearance of such peak, unveils a puzzling and seemingly universal manifestation of magnetic quantum fluctuations in iron-based superconductors and unusually robust quantum phase transition under the dome of superconductivity.

Quantum Critical Point in the Itinerant Ferromagnet Ni_{1-x}Rh_{x}.

We report a chemical substitution-induced ferromagnetic quantum critical point in polycrystalline Ni_{1-x}Rh_{x} alloys. Through magnetization and muon spin relaxation measurements, we show that the ferromagnetic ordering temperature is suppressed continuously to zero at x_{crit}=0.375 while the magnetic volume fraction remains 100% up to x_{crit}, pointing to a second order transition. Non-Fermi liquid behavior is observed close to x_{crit}, where the electronic specific heat C_{el}/T diverges logarithmically, while immediately above x_{crit} the volume thermal expansion coefficient α_{V}/T and the Grüneisen ratio Γ=α_{V}/C_{el} both diverge logarithmically in the low temperature limit, further indication of a ferromagnetic quantum critical point in Ni_{1-x}Rh_{x}.

Particle-Hole Duality, Emergent Fermi Liquids, and Fractional Chern Insulators in Moiré Flatbands

Moiré flatbands, occurring, e.g., in twisted bilayer graphene at magic angles, have attracted ample interest due to their high degree of experimental tunability and the intriguing possibility of generating novel strongly interacting phases. Here we consider the core problem of Coulomb interactions within fractionally filled spin and valley polarized Moiré flatbands and demonstrate that the dual description in terms of holes, which acquire a nontrivial hole dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. In experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent interaction-driven Fermi liquid states at electronic filling fractions down to around 1/3 and 2/3, respectively. At even lower filling fractions, the electron density still faithfully tracks the single-hole dispersion while exhibiting distinct non-Fermi liquid behavior. Most saliently, we provide microscopic evidence that high temperature fractional Chern insulators can form in twisted bilayer graphene aligned with hexagonal boron nitride.

Eliashberg equations for an electron–phonon version of the Sachdev–Ye–Kitaev model: Pair breaking in non-Fermi liquid superconductors

We present a theory that is a non-Fermi-liquid counterpart of the Abrikosov–Gor’kov pair-breaking theory due to paramagnetic impurities in superconductors. To this end we analyze a model of interacting electrons and phonons that is a natural generalization of the Sachdev–Ye–Kitaev-model. In the limit of large numbers of degrees of freedom, the Eliashberg equations of superconductivity become exact and emerge as saddle-point equations of a field theory with fluctuating pairing fields. In its normal state the model is governed by non-Fermi liquid behavior, characterized by universal exponents. At low temperatures a superconducting state emerges from the critical normal state. We study the role of pair-breaking on Tc, where we allow for disorder that breaks time-reversal symmetry. For small Bogoliubov quasi-particle weight, relevant for systems with strongly incoherent normal state, Tc drops rapidly as function of the pair breaking strength and reaches a small but finite value before it vanishes at a critical pair-breaking strength via an essential singularity. The latter signals a breakdown of the emergent conformal symmetry of the non-Fermi liquid normal state.

Influence of Ce doping and thickness on the structure and non-Fermi liquid behavior of LaNiO3 thin films

Thin films of La1-xCexNiO3 (x = 0, 0.1, and 0.3) are grown with two different thickness (8 and 24 nm) on single-crystal LaAlO3 (001) (LAO) substrate using pulsed laser deposition. The films with x = 0 and 0.1 are highly oriented toward the (00l) axis despite different thickness, whereas the higher doped films (x = 0.3) of both thicknesses show two crystallographic orientations. A significant shifting of Raman modes is observed due to increased Ce doping, clearly indicating a large change in Ni–O–Ni bond-angle and NiO6 octahedra distortion. Also, Raman modes show a red-shift in all the thin films with increases in temperature. These films remain metallic until low temperatures. The resistivity increases with increased Ce doping as well as with increased thickness. The resistivity data fit well with the power-law equation, indicating a non-Fermi liquid state. This study helps to distinguish the effects of Ce doping and thickness on the structure and Raman modes.

Unveiling Quadrupolar Kondo Effect in the Heavy Fermion Superconductor PrV2Al20

Heavy fermion metals hosting multipolar local moments set a new stage for exploring exotic spin-orbital entangled quantum phases. In such systems, the quadrupolar Kondo effect serves as the key ingredient in the orbital-driven non-Fermi liquid (NFL) behavior and quantum critical phenomena. The cubic heavy fermion superconductor Pr$Tr_2$Al$_{20}$ ($Tr$: Ti, V) is a prime candidate for realizing the quadrupolar Kondo lattice. Here, we present a systematic study of the NFL phenomena in PrV$_2$Al$_{20}$ based on magnetoresistance (MR), magnetic susceptibility and specific heat measurements. Upon entering the NFL regime, we observe a universal scaling behavior expected for the quadrupolar Kondo lattice in PrV$_2$Al$_{20}$, which indicates a prominent role of the quadrupolar Kondo effect in driving the NFL behavior. Deviations from this scaling relation occur below $\sim 8$ K, accompanied by a sign change in the MR and a power-law divergence in the specific heat. This anomalous low-temperature state points to the presence of other mechanisms which are not included in the theory, such as heavy fermion coherence or multipolar quantum critical fluctuations.

Disorder-driven non-Fermi liquid behavior in itinerant ferromagnet α-Co5Ge3

The physical properties of itinerant ferromagnet -Co5Ge3 with both strong disorder and spin fluctuations was studied. The dc and ac susceptibility show that both spin fluctuations and disorder dominate the physical properties. In the spin glass phase, with a coexisting ferromagnetic state (30 K), both non-Fermi liquid behavior and large exponent of scaling relation of are observed and attributed to the spin fluctuations and disorder induced by cobalt defects. Upon the increase of external field, Fermi liquid behavior restores due to the suppression of spin fluctuations and disorder. In addition, a large anomalous Hall coefficient Rs is observed. Our results suggest that -Co5Ge3 is a typical itinerant ferromagnet to explore the interplay of disorder and spin fluctuations.

Pairing and non-Fermi liquid behavior in partially flat-band systems: Beyond nesting physics

While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.

Kondo temperature equation for the Fermi liquid and the non-Fermi liquid regime for a two-channel anderson model

Multichannel Kondo resonance causes non-Fermi liquid behavior in many systems, as nanostructured metallic quantum dots and metallic alloys. The Kondo effect occurs at low temperatures and its indicating parameter is the Kondo temperature TK. This parameter can be used to renormalize thermodynamic and transport properties. The Kondo temperature is an important quantity to analyze the antiferromagnetic interaction between a localized spin and itinerant ones in a fermionic bath. There are many different definitions of the Kondo temperature. One of them is that it universalizes magnetic impurity susceptibility. This version was created for the one-channel Anderson model, but it is also valid in two-channel Anderson models, where a single magnetic impurity interacts with the conduction band electrons by two different channels. If the two coupling parameters are different, the model exhibits the well known Fermi liquid regime. When the coupling parameters are equal, the model displays the non-Fermi liquid regime. Each one shows different universal magnetic susceptibility behavior with appropriate TK value. In this article, Numerical Renormalization Group method is applied to study the Kondo temperature systematically. Different values of the coupling parameters in a two-channel Anderson model are examined. Finally, a single analytic expression for the Kondo temperature, valid in the Fermi and non-Fermi liquid regime, is presented.

Specific heat, entropy and magnetic properties of high Tc superconductivity within the planar t−t′−J−V model

The finite temperature properties of the high Tc cuprates are investigated by an exact method at optimal doping using t−t′−J−V model. The role of next-nearest-neighbor (NNN) hopping interaction t′ and nearest-neighbor Coulomb repulsion V on the total energy, specific heat, entropy, magnetic properties, etc. in the superconducting, as well as normal phase, are considered. Specific heat curves show a single peak structure in the parameter range suitable for existence of superconducting phase. Two peak structure in the specific heat curve is observed at sufficiently large values of V∕t. An asymmetry in specific heat curves and peak positions is observed for the hole- and electron-doped cuprates. Existence of a metallic phase is detected for positive t′∕t for V∕t ≤ 4J. Entropy calculation shows the system goes to a more disordered state with negative t′∕t and V∕t. A non-Fermi liquid behavior is revealed at low temperatures for positive t′ and small values of V . An asymmetry in Neel temperature is observed for the hole- and electron-doped cuprates. An unsaturated ferromagnetic phase emerges with an increase of V∕t. Schematic magnetic phase diagrams are shown.

A new quasi-one-dimensional compound Ba3TiTe5 and superconductivity induced by pressure

We report systematic studies of a new quasi-one-dimensional (quasi-1D) compound, Ba3TiTe5, and the high-pressure induced superconductivity therein. Ba3TiTe5 was synthesized at high pressure and high temperature. It crystallizes into a hexagonal structure (P63/mcm), which consists of infinite face-sharing octahedral TiTe6 chains and Te chains along the c axis, exhibiting a strong 1D characteristic structure. The first-principles calculations demonstrate that Ba3TiTe5 is a well-defined 1D conductor; thus, it can be considered a starting point to explore the exotic physics induced by pressure by enhancing the interchain hopping to move the 1D conductor to a high-dimensional metal. For Ba3TiTe5, high-pressure techniques were employed to study the emerging physics dependent on interchain hopping, such as the Umklapp scattering effect, spin/charge density wave (SDW/CDW), superconductivity and non-Fermi liquid behavior. Finally, a complete phase diagram was plotted. The superconductivity emerges at 8.8 GPa, near which the Umklapp gap is mostly suppressed. Tc is enhanced and reaches a maximum of ~6 K at ~36.7 GPa, where the SDW/CDW is completely suppressed, and a non-Fermi liquid behavior appears. Our results suggest that the appearance of superconductivity is associated with the fluctuation due to the suppression of the Umklapp gap and that the enhancement of the Tc is related to the fluctuation of the SDW/CDW.

Non-Fermi-liquid types of behavior associated with a magnetic quantum critical point in Sr(Co1−xNix)2As2 single crystals

Electron-doped Sr(Co{1-x}Ni{x})2As2 single crystals with compositions x = 0 to 0.9 were grown out of self-flux and SrNi2As2 single crystals out of Bi flux. The crystals were characterized using single-crystal x-ray diffraction (XRD), magnetic susceptibility chi(H,T), isothermal magnetization M(H,T), heat capacity Cp(H,T), and electrical resistivity ho(H,T) measurements versus applied magnetic field H and temperature T. The chi(T) data show that the crystals exhibit an antiferromagnetic (AFM) ground state almost immediately upon Ni doping on the Co site. Ab-initio electronic-structure calculations for x = 0 and x = 0.15 indicate that a flat band with a peak in the density of states just above the Fermi energy is responsible for this initial magnetic-ordering behavior on Ni doping. The Curie-Weiss-like T dependence of \chi in the paramagnetic (PM) state indicates dominant ferromagnetic (FM) interactions. The small ordered moments ~0.1 muB per transition metal atom and the values of the Rhodes-Wohlfarth ratio indicate that the magnetism is itinerant. The Cp(T) at low T exhibits Fermi-liquid behavior for 0 < x < 0.15 whereas an evolution to a logarithmic non-Fermi-liquid (NFL) behavior is found for x = 0.2 to 0.3. The logarithmic dependence is suppressed in an applied magnetic field. The low- T rho(H = 0,T) data show a T^2 dependence for 0 < x < 0.20 and a power-law dependence with n < 2 for x = 0.20 and 0.30. These low-T NFL behaviors observed in the Cp and rho measurements are most evident near the quantum-critical concentration x ~ 0.3 at which a T = 0 composition-induced transition from the AFM phase to the PM phase occurs.

Skyrmions and spirals in MnSi under hydrostatic pressure

The archetype cubic chiral magnet MnSi is home to some of the most fascinating states in condensed matter such as skyrmions and a non-Fermi liquid behavior in conjunction with a topological Hall effect under hydrostatic pressure. Using small angle neutron scattering, we study the evolution of the helimagnetic, conical and skyrmionic correlations with increasing hydrostatic pressure. We show that the helical propagation vector smoothly reorients from $\langle 111 \rangle$ to $\langle100\rangle$ at intermediate pressures. At higher pressures, above the critical pressure, the long-range helimagnetic order disappears at zero magnetic field. Nevertheless, skyrmion lattices and conical spirals form under magnetic fields, in a part of the phase diagram where a topological Hall effect and a non-Fermi liquid behavior have been reported. These unexpected results shed light on the puzzling behavior of MnSi at high pressures and the mechanisms that destabilize the helimagnetic long-range order at the critical pressure.

Heavy fermion quantum criticality at dilute carrier limit in CeNi2\u2212\u03b4(As1\u2212xPx)2

We study the quantum phase transitions in the nickel pnctides, CeNi2−δ(As1−xPx)2 (δ ≈ 0.07–0.22) polycrystalline samples. This series displays the distinct heavy fermion behavior in the rarely studied parameter regime of dilute carrier limit. We systematically investigate the magnetization, specific heat and electrical transport down to low temperatures. Upon increasing the P-content, the antiferromagnetic order of the Ce-4f moment is suppressed continuously and vanishes at xc ~ 0.55. At this doping, the temperature dependences of the specific heat and longitudinal resistivity display non-Fermi liquid behavior. Both the residual resistivity ρ0 and the Sommerfeld coefficient γ0 are sharply peaked around xc. When the P-content reaches close to 100%, we observe a clear low-temperature crossover into the Fermi liquid regime. In contrast to what happens in the parent compound x = 0.0 as a function of pressure, we find a surprising result that the non-Fermi liquid behavior persists over a nonzero range of doping concentration, xc < x < 0.9. In this doping range, at the lowest measured temperatures, the temperature dependence of the specific-heat coefficient is logarithmically divergent and that of the electrical resistivity is linear. We discuss the properties of CeNi2−δ(As1−xPx)2 in comparison with those of its 1111 counterpart, CeNi(As1−xPx)O. Our results indicate a non-Fermi liquid phase in the global phase diagram of heavy fermion metals.

Comprehensive studies of the transformation between antiferromagnetic CeCoGe3 and heavy fermion CeFeGe3 compounds

We report extensive studies of a series of alloys CeCo1−xFexGe3 in which suppression of the antiferromagnetic order in CeCoGe3 with temperature decreasing to 0 K was observed as a result of substitution of Co with Fe. Unusual temperature dependences were observed of a number of parameters characterizing these compounds: magnetic susceptibility, specific heat, electrical resistivity, magnetoresistance and thermoelectric power, which may be indication towards non-Fermi liquid behaviour connected with quantum critical point (QCP) or can result from a quantum Griffiths phase (QGP) formation. The three AFM transitions found previously for a single crystal CeCoGe3 compound were also detected in our high quality polycrystalline samples, including the case of x>0. All measurements, especially those of magnetocaloric effect (MCE), suggest that for samples with x≥0.1 the contribution of ferromagnetic component, known already for x=0 from the neutron diffraction experiments, increases significantly, with the AFM contribution still present at low temperatures. Finally, the use of different complementary methods enabled construction of a comprehensive magnetic phase diagram of CeCo1−xFexGe3 system.

Lattice models for non-Fermi liquids with tunable transport scalings

A variety of exotic non-fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The "standard" approach to studying these NFLs is by coupling a Fermi liquid to quantum critical fluctuations, which potentially can drive the system into a NFL. In this work we seek for an alternative understanding of these various NFLs in a unified framework. We first construct two "elementary" randomness-free models with four-fermion interactions only, whose many properties can be analyzed exactly in certain limit just like the Sachdev-Ye-Kitaev (SYK) model. The most important new feature of our models is that, the fermion scaling dimension in the conformal invariant solution in the infrared limit is tunable by charge density. Then based on these elementary models, we propose two versions of lattice models with four fermion interactions which give us non-fermi liquid behaviors with DC resistivity scaling $\varrho \sim T^\alpha$ in a finite temperature window, and $\alpha \in [1, 2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.

Thermal radiation as a probe of one-dimensional electron liquids

Motivated by recent developments in the field of plasmonics, we develop the theory of radiation from one-dimensional electron liquids, showing that the spectrum of thermal radiation emitted from the system exhibits signatures of non-Fermi liquid behavior. We derive a multipole expansion for the radiation based on the Tomonaga-Luttinger liquid model. While the dipole radiation pattern is determined by the conductivity of the system, we demonstrate that the quadrupole radiation can reveal important features of the quantum liquid, such as the Luttinger parameter. Radiation offers a probe of the interactions of the system, including Mott physics as well as nonlinear Luttinger liquid behavior. We show that these effects can be probed in current experiments on effectively one-dimensional electron liquids, such as carbon nanotubes.

Superconductivity above a quantum critical point in a metal: Gap closing versus gap filling, Fermi arcs, and pseudogap behavior

We consider a quantum-critical metal with interaction mediated by fluctuations of a critical order parameter. This interaction gives rise to two competing tendencies -- pairing and non-Fermi liquid behavior. Due to competition, the pairing develops below a finite $T_p $, however its prominent feedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At $T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor -- the density of states (DOS) and the spectral function (SF) have sharp gaps which close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip, which {\it fills in} with increasing $T$. The SF in this region shows either the same behavior as the DOS, or has a peak at $\omega =0$ (the Fermi arc), depending on the position on the Fermi surface. We argue that phase fluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$, while $T_p$ marks the onset of pseugogap behavior. We compare our theory with the behavior of optimally doped cuprates.

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions.

Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi-liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N_{f} theory, and the ε=4-d method with a fermion flavor number N_{f} and spatial dimension d, we obtain the anomalous dimensions of electrons (η_{f}=0.366/N_{f}) in large N_{f} theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr_{2}Se_{4} or SrSi_{2} when the system undergoes a TQPT.

Topological quantum critical point in a triple-Weyl semimetal: Non-Fermi-liquid behavior and instabilities

We study the quantum critical phenomena emerging at the transition from triple-Weyl semimetal to band insulator, which is a topological phase transition described by the change of topological invariant. The critical point realizes a new type of semimetal state in which the fermion dispersion is cubic along two directions and quadratic along the third. Our renormalization group analysis reveals that, the Coulomb interaction is marginal at low energies and even arbitrarily weak Coulomb interaction suffices to induce an infrared fixed point. We compute a number of observable quantities, and show that they all exhibit non-Fermi liquid behaviors at the fixed point. When the interplay between the Coulomb and short-range four-fermion interactions is considered, the system becomes unstable below a finite energy scale. The system undergoes a first-order topological transition when the fermion flavor $N$ is small, and enters into a nematic phase if $N$ is large enough. Non-Fermi liquid behaviors are hidden by the instability at low temperatures, but can still be observed at higher temperatures. Experimental detection of the predicted phenomena is discussed.