Heavy Fermion Quantum Criticality Research Articles

Gate-tunable heavy fermion quantum criticality in a moiré Kondo lattice

The authors propose a transition metal dichalcogenide moir\'e heterostructure that realizes a Kondo lattice and is capable of tuning across a quantum phase transition corresponding to the breakdown of Kondo screening. For a dual-gated setup, they theoretically identify the requisite gating conditions and find a quantum critical scenario where the local moments in a chiral spin-liquid state dissolve in the conduction electron Fermi sea to form an anomalous Hall heavy-fermion liquid. They discuss how the proposed gate-tunable Kondo lattice simulator can experimentally distinguish between various competing scenarios for the quantum phase transition, and thereby enable progress in the understanding of heavy-fermion quantum criticality.

Correlations among Tc, A, and Γ ο within FL region of T-p phase diagram of heavy-Fermion superconductors

Extensively reported experimental observations indicate that on varying a control parameter, such as pressure p, within the phase diagram of most quantum critical heavy fermion HF superconductors, one identifies a cascade of distinct electronic states which may be magnetic, of Kondo-type, non-conventional superconducting, Fermi Liquid, FL, or non-FL character. Of particular interest is the part of the phase diagram wherein superconductivity emerges from a strongly renormalized FL state. This region resembles the overdoped region of the T-doping phase diagram of cuprate superconductors. Remarkably, within this highly nontrivial region, one identifies a universal correlation among Tc and (θ is a characteristic energy scale and A is the coefficient of T 2 resistivity term). Commonly, these features are considered to be driven by a Spin-Fluctuation-mediated electron-electron scattering channel. On adopting such a channel and applying standard theories of Migdal-Eliashberg (superconductivity) and Boltzmann (transport), we derive analytic expressions that satisfactorily reproduce the aforementioned empirical correlations.

Nonlocal Kondo effect and quantum critical phase in heavy-fermion metals

Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations while a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in YbRh$_2$Si$_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy fermion quantum criticality.

Quantum phase transition in a two-dimensional Kondo-Heisenberg model: A dynamical Schwinger-boson large- N approach

Strange metal behavior arises in heavy fermion metals close to antiferromagnetic transitions. An increasing amount of experiments indicates a link of such behavior to a Kondo breakdown quantum critical point. To shed light on this intriguing problem, we study the 2D Kondo-Heisenberg model using a dynamical large-N multichannel Schwinger boson approach. We identify and characterize the quantum phase transition from an antiferromagnetically ordered ground state to a Kondo-dominated paramagnetic state, and attribute a jump in certain phase shift to Kondo breakdown. In addition, we calculate transport and thermodynamic quantities and discuss them in the context of the experimental observations in quantum critical heavy fermion systems.

Heavy fermion quantum criticality: The party is just beginning

Heavy fermion quantum criticality: The party is just beginning

Phase diagram and dynamics of the SU(N) symmetric Kondo lattice model

In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(\pi,\pi)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.

Dynamical Scaling of Charge and Spin Responses at a Kondo Destruction Quantum Critical Point.

Quantum critical points often arise in metals perched at the border of an antiferromagnetic order. The recent observation of singular and dynamically scaling charge conductivity in an antiferromagnetic quantum critical heavy fermion metal implicates beyond-Landau quantum criticality. Here we study the charge and spin dynamics of a Kondo destruction quantum critical point (QCP), as realized in an SU(2)-symmetric Bose-Fermi Kondo model. We find that the critical exponents and scaling functions of the spin and single-particle responses of the QCP in the SU(2) case are essentially the same as those of the large-N limit, showing that 1/N corrections are subleading. Building on this insight, we demonstrate that the charge responses at the Kondo destruction QCP are singular and obey ω/T scaling. This property persists at the Kondo destruction QCP of the SU(2)-symmetric Kondo lattice model.

Non-divergent Grüneisen parameter in quantum critical quasicrystal Yb15Al34Au51: Reflection of robustness of quantum criticality under pressure

The mechanism of not diverging Grüneisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb15Al34Au51 is analyzed. We construct the formalism for calculating the specific heat CV(T), the thermal-expansion coefficient α(T), and the Grüneisen parameter Γ(T) near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate CV(T), α(T), and Γ(T), which explains the measurements. Not diverging Γ(T) is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in Γ(T) at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed.

Bose-Fermi Anderson model with SU(2) symmetry: Continuous-time quantum Monte Carlo study

In quantum critical heavy fermion systems, local moments are coupled to both collective spin fluctuations and conduction electrons. As such, the Bose-Fermi Kondo model, describing the coupling of a local moment to both a bosonic and a fermionic bath, has been of extensive interest. For the model in the presence of SU(2) spin rotational symmetry, questions have been raised about its phase diagram. Here we develop a version of continuous-time Quantum Monte Carlo (CT-QMC) method suitable for addressing this issue; this procedure can reach sufficiently low temperatures while preserving the SU(2) symmetry. Using this method for the Bose-Fermi Anderson model, we clarify the renormalization-group fixed points and the phase diagram for the case with a constant fermionic-bath density of states and a power-law bosonic-bath spectral function $\rho_{b}(\omega) \propto \omega^{s}$ ($0<s<1$). We find two types of Kondo destruction QCP, depending on the power-law exponent $s$ in the bosonic bath spectrum. For $s^{*}<s<1$, both types of QCPs exist and, in the parameter regime accessible by an analytical $\epsilon$-expansion renormalization-group calculation (here $\epsilon=1-s$), the CT-QMC result is fully consistent with prior predictions by the latter method. For $s<s^{*}$, there is only one type of QCP. At both type of Kondo destruction QCPs, we find that the exponent of the local spin susceptibility $\eta$ obeys the relation $\eta=\epsilon$, which has important implications for Kondo destruction QCP in the Kondo lattice problem.

Charge Transfer Effect under Odd-Parity Crystalline Electric Field: Divergence of Magnetic Toroidal Fluctuation in β-YbAlB4

A novel property of the quantum critical heavy fermion superconductor $\beta$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $\beta$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion drives charge transfer between the 4f and 5d states at Yb, which makes the MT fluctuation as well as the electric dipole fluctuation diverge simultaneously with the critical Yb-valence fluctuation at the quantum critical point of the valence transition.

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

ABSTRACTIn this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu2Si2, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu2Si2. In YbRh2Si2, superconductivity appears to be suppressed at T ⪆ 10 mK by AF order (TN = 70 mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at TA slightly above 2 mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at Tc = 2 mK. Like the pressure – induced QCP in CeRhIn5, the magnetic field – induced one in YbRh2Si2 is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher Tcs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.

Converse effect of pressure on the quadrupolar and magnetic transition inCe3Pd20Si6

The heavy fermion compound Ce$_{3}$Pd$_{20}$Si$_{6}$ displays unconventional quantum criticality as the lower of two consecutive phase transitions is fully suppressed by magnetic field. Here we report on the effects of pressure as additional tuning parameter. Specific heat and electrical resistivity measurements reveal a converse effect of pressure on the two transitions, leading to the merging of both transitions at 6.2 kbar. The field-induced quantum criticality is robust under pressure tuning. We rationalize our findings within an extended version of the global phase diagram for antiferromagnetic heavy fermion quantum criticality.

Anomalous frequency and temperature-dependent scattering and Hund's coupling in the almost quantum critical heavy-fermion systemCeFe2Ge2

We present THz range optical conductivity data of a thin film of the near quantum critical heavy fermion compound CeFe$_2$Ge$_2$. Our complex conductivity measurements find a deviation from conventional Drude-like transport in a temperature range previously reported to exhibit unconventional behavior. We calculate the frequency dependent effective mass and scattering rate using an extended Drude model analysis. We find the inelastic scattering rate can be described by a temperature dependent power-law $\omega^{n(T)}$ where $n(T)$ approaches $\sim1.0 \pm 0.2$ at 1.5 K. This is compared to the $\rho \sim T^{1.5}$ behavior claimed in dc resistivity data and the $\rho \sim T^{2}$ expected from Fermi-liquid theory. In addition to a low temperature mass renormalization, we find an anomalous mass renormalization that persists to high temperature. We attribute this to a Hund's coupling in the Fe states in a manner similar to that recently proposed in the ferro-pnictides. CeFe$_2$Ge$_2$ appears to be a very interesting system where one may study the interplay between the usual $4f$ lattice Kondo effect and this Hund's enhanced Kondo effect in the $3d$ states.

Emergent gauge fields and their nonperturbative effects in correlated electrons

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum–space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high [Formula: see text] superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high [Formula: see text] cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Ordered Phases and Quantum Criticality in Cubic Heavy Fermion Compounds

Quantum criticality in cubic heavy fermion compounds remains much less explored than in quasi-two-dimensional systems. However, such materials are needed to broadly test the recently suggested global phase diagram for heavy fermion quantum criticality. Thus, to boost these activities, we review the field, with focus on Ce-based systems with temperature-magnetic field or temperature-pressure phase diagrams that may host a quantum critical point. To date, CeIn3 and Ce3Pd20Si6 are the only two among these compounds where quantum critical behaviour has been systematically investigated. Interestingly, both show Fermi surface reconstructions as function of the magnetic field that may be understood in terms of Kondo destruction quantum criticality.

Heavy-fermion quantum criticality and destruction of the Kondo effect in a nickel oxypnictide.

A quantum critical point arises at a continuous transformation between distinct phases of matter at zero temperature. Studies in antiferromagnetic heavy-fermion materials have revealed that quantum criticality has several classes, with an unconventional type that involves a critical destruction of the Kondo entanglement. To understand such varieties, it is important to extend the materials basis beyond the usual setting of intermetallic compounds. Here we show that a nickel oxypnictide, CeNiAsO, exhibits a heavy-fermion antiferromagnetic quantum critical point as a function of either pressure or P/As substitution. At the quantum critical point, non-Fermi-liquid behaviour appears, which is accompanied by a divergent effective carrier mass. Across the quantum critical point, the low-temperature Hall coefficient undergoes a rapid sign change, suggesting a sudden jump of the Fermi surface and a destruction of the Kondo effect. Our results imply that the enormous materials basis for the oxypnictides, which has been so crucial in the search for high-temperature superconductivity, will also play a vital role in the effort to establish the universality classes of quantum criticality in strongly correlated electron systems.

Novel Metallic Phase Emerging from Quantum Criticality: We Couldn��t Observe Electrons at Low Energies

The emergence of non-Fermi liquids near metallic quantum criticality is an essential feature in the system of strongly correlated electrons, where electron quasiparticles decay into other types of collective excitations. As a result, novel metallic phases appear without electrons, showing various exotic non-Fermi liquid physics beyond the Landau Fermi-liquid theory. In this review, we discuss what electrons disintegrate into, which allows us to classify theories for quantum critical metals into the Hertz-Moriya-Millis, Kondo breakdown, and local quantum criticality scenarios. We discuss both the goodness and the weakness of each theoretical framework, recalling experimental aspects for heavy-fermion quantum criticality.

Electronic structure of LuRh2Si2: ‘small’ Fermi surface reference to YbRh2Si2

We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms zSi within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield zSi = 0.379 c in good agreement with numerical lattice relaxation.This value of zSi is suggested for future band structure calculations on LuRh2Si2 and YbRh2Si2. LuRh2Si2 with a full f electron shell represents the ‘small’ Fermi surface configuration of YbRh2Si2. Our experimentally and ab intio derived quantum oscillation frequencies of LuRh2Si2 differ significantly from the results of earlier measurements on YbRh2Si2. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh2Si2 at high magnetic fields. Yet, the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborate models to describe the Fermi surface of YbRh2Si2.

Destruction of the Kondo effect in the cubic heavy-fermion compound Ce3Pd20Si6

How ground states of quantum matter transform between one another reveals deep insights into the mechanisms stabilizing them. Correspondingly, quantum phase transitions are explored in numerous materials classes, with heavy-fermion compounds being among the most prominent ones. Recent studies in an anisotropic heavy-fermion compound have shown that different types of transitions are induced by variations of chemical or external pressure, raising the question of the extent to which heavy-fermion quantum criticality is universal. To make progress, it is essential to broaden both the materials basis and the microscopic parameter variety. Here, we identify a cubic heavy-fermion material as exhibiting a field-induced quantum phase transition, and show how the material can be used to explore one extreme of the dimensionality axis. The transition between two different ordered phases is accompanied by an abrupt change of Fermi surface, reminiscent of what happens across the field-induced antiferromagnetic to paramagnetic transition in the anisotropic YbRh2Si2. This finding leads to a materials-based global phase diagram--a precondition for a unified theoretical description.

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau–Ginzburg–Wilson paradigm. The Landau–Ginzburg–Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.