Heavy-fermion Metals Research Articles

Anomalous Hall Effect and Quantum Criticality in Geometrically Frustrated Heavy Fermion Metals

Anomalous Hall Effect and Quantum Criticality in Geometrically Frustrated Heavy Fermion Metals

Precise Calorimetry of Small Metal Samples Using Noise Thermometry

AbstractWe describe a compact calorimeter that opens ultra-low-temperature heat capacity studies of small metal crystals in moderate magnetic fields. The performance is demonstrated on the canonical heavy fermion metal YbRh$$_{2}$$ 2 Si$$_{2}$$ 2 . Thermometry is provided by a fast current sensing noise thermometer. This single thermometer enables us to cover a wide temperature range of interest from 175 µK to 90 mK with temperature-independent relative precision. Temperatures are tied to the international temperature scale with a single-point calibration. A superconducting solenoid surrounding the cell provides the sample field for tuning its properties and operates a superconducting heat switch. Both adiabatic and relaxation calorimetry techniques, as well as magnetic field sweeps, are employed. The design of the calorimeter results in an addendum heat capacity which is negligible for the study reported. The keys to sample and thermometer thermalisation are the lack of dissipation in the temperature measurement and the steps taken to reduce the parasitic heat leak into the cell to the tens of fW level.

Excess heat capacity in magnetically ordered Ce heavy-fermion metals

Excess heat capacity in magnetically ordered Ce heavy-fermion metals

Deep learning bulk spacetime from boundary optical conductivity

We employ a deep learning method to deduce the bulk spacetime from boundary optical conductivity. We apply the neural ordinary differential equation technique, tailored for continuous functions such as the metric, to the typical class of holographic condensed matter models featuring broken translations: linear-axion models. We successfully extract the bulk metric from the boundary holographic optical conductivity. Furthermore, as an example for real material, we use experimental optical conductivity of UPd2Al3, a representative of heavy fermion metals in strongly correlated electron systems, and construct the corresponding bulk metric. To our knowledge, our work is the first illustration of deep learning bulk spacetime from boundary holographic or experimental conductivity data.

Two-dimensional heavy fermions in the van der Waals metal CeSiI.

Heavy-fermion metals are prototype systems for observing emergent quantum phases driven by electronic interactions1-6. A long-standing aspiration is the dimensional reduction of these materials to exert control over their quantum phases7-11, which remains a significant challenge because traditional intermetallic heavy-fermion compounds have three-dimensional atomic and electronic structures. Here we report comprehensive thermodynamic and spectroscopic evidence of an antiferromagnetically ordered heavy-fermion ground state in CeSiI, an intermetallic comprising two-dimensional (2D) metallic sheets held together by weak interlayer van der Waals (vdW) interactions. Owing to its vdW nature, CeSiI has a quasi-2D electronic structure, and we can control its physical dimension through exfoliation. The emergence of coherenthybridization of f and conduction electrons at low temperature is supported by the temperature evolution of angle-resolved photoemission and scanning tunnelling spectra near the Fermi level andby heat capacity measurements. Electrical transport measurements on few-layer flakes reveal heavy-fermion behaviour and magnetic order down to the ultra-thin regime. Our work establishes CeSiI and related materials as a unique platform for studying dimensionally confined heavy fermions in bulk crystals and employing 2D device fabrication techniques and vdW heterostructures12 to manipulate the interplay between Kondo screening, magnetic order and proximity effects.

Shot noise in a strange metal.

Strange-metal behavior has been observed in materials ranging from high-temperature superconductors to heavy fermion metals. In conventional metals, current is carried by quasiparticles; although it has been suggested that quasiparticles are absent in strange metals, direct experimental evidence is lacking. We measured shot noise to probe the granularity of the current-carrying excitations in nanowires of the heavy fermion strange metal YbRh2Si2. When compared with conventional metals, shot noise in these nanowires is strongly suppressed. This suppression cannot be attributed to either electron-phonon or electron-electron interactions in a Fermi liquid, which suggests that the current is not carried by well-defined quasiparticles in the strange-metal regime that we probed. Our work sets the stage for similar studies of other strange metals.

Transport Properties of Strongly Correlated Fermi Systems

Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high—Tc superconductors. Their transport properties are defined by strong inter-particle interactions, forming flat bands in these compounds. These properties do not coincide with those of conventional metals. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit linear temperature resistivity ρ(T)∝T. We analyze the magnetoresistance and show that under the application of the magnetic field, it becomes negative. It is shown that near a quantum phase transition, when the density of the electronic states diverges, semiclassical physics remains applicable to describe the resistivity ρ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when T exceeds the extremely low Debye temperature TD, the resistivity ρ(T) changes linearly with T since the mechanism of formation of the T-dependence ρ(T) is a similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of T-linear resistance, electron-phonon scattering leads to a lifetime of τ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant ℏ to the Boltzmann constant kB, Tτ∼ℏ/kB. We explain that due to the non-Fermi-liquid behavior, the real part of the frequency-dependent optical conductivity σoptR(ω) exhibits a scaling behavior and demonstrates the unusual power law behavior σoptR(ω)∝ω−1, rather than the well-known one shown by conventional metals, σoptR(ω)∝ω−2. All our theoretical considerations are illustrated and compared with the corresponding experimental facts. Our results are in a good agreement with experimental observations.

Quantum phase transition in CeCoIn5: Experimental facts and theory

The condensed-matter community is involved in a hot debate on the nature of quantum critical points (QCP) governing the low-temperature properties of heavy fermion metals. The smeared jump-like behavior revealed both in the residual resistivity and the Hall resistivity R H , along with the violation of the time invariance symmetry and the charge invariance , include the violation of quasiparticle-hole symmetry, and provide vital clues on the origin of both the non-Fermi-liquid behavior and QCP. For the first time, based on a number of important experimental data, we show that these experimental observations point out unambiguously that QCP of is accompanied by the symmetry violation, and QCP itself is represented by the topological fermion-condensation quantum phase transition (FCQPT) connecting two Fermi surfaces of different topological charges.

Quantum criticality enabled by intertwined degrees of freedom

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.

Magnetic Field as an Important Tool in Exploring the Strongly Correlated Fermi Systems and Their Particle–Hole and Time-Reversal Asymmetries

In this review, we consider the impact of magnetic field on the properties of strongly correlated heavy-fermion compounds such as heavy-fermion metals and frustrated insulators with quantum spin liquid. Magnetic field B can be considered a universal tool, allowing the exploration of the physics controlling the remarkable properties of heavy-fermion compounds. These vivid properties are T/B scaling, exhibited under the application of magnetic field B and at fixed temperature T, and the emergence of Landau Fermi liquid behavior under the application of magnetic field. We analyze the influence of quasiparticle–hole asymmetry on the properties of heavy-fermion (HF) compounds such as the universal scaling behavior of the thermopower S/T exhibited under the application of magnetic field B. We show that universal scaling is demonstrated by different HF compounds such as β-YbAlB4, YbRh2Si2, and strongly correlated layered cobalt oxide [BiBa0.66K0.36O2]CoO2. Analyzing YbRh2Si2, we show that the T/B scaling behavior of S/T is violated at the antiferromagnetic phase (AF) transition. The residual resistivity ρ0 and the density of states N0 experience jumps at the AF transition, causing two jumps in the thermopower and its sign reversal. Our consideration is based on the flattening of the single-particle spectrum that strongly affects ρ0 and N0 and leads to the violation of particle–hole symmetry. The particle–hole asymmetry generates the asymmetrical part Δσd(V) of tunneling differential conductivity σd(V), Δσd(V)=σd(V)−σd(−V), where V is the voltage bias. We demonstrate that in the presence of magnetic field, the quasiparticle–hole asymmetry vanishes, the LFL behavior is restored, and the asymmetry disappears. Our calculations of the mentioned properties of HF compounds, based on the fermion condensation theory, are in good agreement with the experiment and support our conclusion that the fermion condensation theory is capable of describing the properties of HF compounds, including those exhibited under the application of magnetic field.

Electronuclear Transition into a Spatially Modulated Magnetic State in YbRh_{2}Si_{2}.

The nature of the antiferromagnetic order in the heavy fermion metal YbRh_{2}Si_{2}, its quantum criticality, and superconductivity, which appears at low mK temperatures, remain open questions. We report measurements of the heat capacity over the wide temperature range 180 μK-80 mK, using current sensing noise thermometry. In zero magnetic field we observe a remarkably sharp heat capacity anomaly at 1.5mK, which we identify as an electronuclear transition into a state with spatially modulated electronic magnetic order of maximum amplitude 0.1 μ_{B}. We also report results of measurements in magnetic fields in the range 0 to 70mT, applied perpendicular to the c axis, which show eventual suppression of this order. These results demonstrate a coexistence of a large moment antiferromagnet with putative superconductivity.

Magnetic and electrical properties of a heavy-fermion compound EuRh2Al8

We report the magnetic, thermodynamic, and electrical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$, a Eu-based heavy fermion member in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families with an orthorhombic $Pbam$ structure. Magnetization studies reveal multiple phase transitions in the single crystals, including two successive antiferromagnetic transitions at ${T}_{N1}\ensuremath{\sim}12.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{N2}\ensuremath{\sim}8.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. These two transitions are closely related to competing magnetic interactions in the Shastry-Sutherland lattice, which further give rise to another in-plane spin-flop transition at 1/3 of the full magnetization below 5 K when the applied magnetic field is higher than 6 T within the $ab$ plane. In addition to these, specific heat measurements in ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ demonstrate a heavy fermion state with a large Sommerfeld coefficient $\ensuremath{\gamma}=393\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{mol}}^{\ensuremath{-}1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{K}}^{\ensuremath{-}2}$. Electrical transport measurement shows that its resistivity exhibits a ${T}^{2}$-dependence below ${T}_{N2}$ and a robust linear $T$-dependence above ${T}_{N1}$, which is also typical of a heavy fermion metal. Our work provides fundamental physical properties of ${\mathrm{EuRh}}_{2}{\mathrm{Al}}_{8}$ and promotes understanding of the complex magnetic interactions and unusual spin correlations in the ${\mathrm{RT}}_{2}{\mathrm{X}}_{8}$ families.

Field-induced Lifshitz transition in the magnetic Weyl semimetal candidate PrAlSi

Lifshitz transition (LT) refers to an abrupt change in the electronic structure and Fermi surface and is associated to a variety of emergent quantum phenomena. Amongst the LTs observed in known materials, the field-induced LT has been rare and its origin remains elusive. To understand the origin of field-induced LT, it is important to extend the material basis beyond the usual setting of heavy fermion metals. Here, we report on a field-induced LT in PrAlSi, a magnetic Weyl semimetal candidate with localized 4f electrons, through a study of magnetotransport up to 55 T. The quantum oscillation analysis reveals that across a threshold field B* ≈ 14.5 T the oscillation frequency (F1 = 43 T) is replaced by two new frequencies (F2 = 62 T and F3 = 103 T). Strikingly, the LT occurs well below the quantum limit, with obvious temperature-dependent oscillation frequency and field-dependent cyclotron mass. Our work not only enriches the rare examples of field-induced LTs but also paves the way for further investigation of the interplay among topology, magnetism, and electronic correlation.

Multiple superconducting phases in heavy-fermion metals

Symmetry breaking beyond a global U(1) phase is the key signature of unconventional superconductors. As prototypical strongly correlated materials, heavy-fermion metals provide ideal platforms for realizing unconventional superconductivity. In this article, we review heavy-fermion superconductivity, with a focus on those materials with multiple superconducting phases. In this context, we highlight the role of orbital-selective (matrix) pairing functions, which are defined as matrices in the space of effective orbital degrees of freedom such as electronic orbitals and sublattices as well as equivalent descriptions in terms of intra- and inter-band pairing components in the band basis. The role of quantum criticality and the associated strange-metal physics in the development of unconventional superconductivity is emphasized throughout. We discuss in some detail the recent experimental observations and theoretical perspectives in the illustrative cases of UTe2, CeRh2As2, and CeCu2Si2, where applied magnetic fields or pressure induce a variety of superconducting phases. We close by providing a brief overview of overarching issues and implications for possible future directions.

Spin chain on a metallic surface: Dissipation-induced order versus Kondo entanglement

We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, $J_k$, to a two-dimensional electron gas. At weak $J_k$ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large $J_k$ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a unique negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.

Pressure induced phase transition in heavy fermion metal UTe2: A first-principles study

Heavy fermion metals are a strongly correlated electronic system with large effective mass of quasi-electrons. It also exhibits abundant physical properties at ambient pressure. Using crystal structure predictions and first-principles calculations, we found that an eight-fold coordinated ambient-pressure Immm phase of UTe2 transforms into a ten-fold coordinated high-pressure I4/mmm phase at 9 GPa. Considering the strong correlation effect of f electrons, the PBE + U method was used in our calculation. The ELF calculation results show that the pressure will facilitate the lone pair electrons of Te in ambient-pressure phase of UTe2 to participate in chemical bonding in order to achieve the high-pressure I4/mmm phase. Additionally, we found that the bulk modulus of the I4/mmm phase can reach 137 GPa. The work provides a possible route for studying phase transitions of UTe2 under pressure.

Optical investigation of the heavy-fermion normal state in superconducting UTe2

The recently discovered superconductor, UTe$_2$, has attracted immense scientific interest due to the experimental observations that suggest odd-parity superconductivity. It is believed that the material becomes a heavy-fermion metal at low temperatures although details of the normal state are unclear. Using Fourier transform infrared spectroscopy (FTIR), the normal state electronic structure of UTe$_2$ was investigated at zero applied magnetic field. Combining the measured reflectivity with the dc resistivity, the complex optical conductivity was obtained over a large frequency range. The frequency dependence of the real part of the optical conductivity exhibits a MIR peak around 4000 cm$^{-1}$ and a narrow Drude peak that develops below 40 K. A combination of density functional and dynamic mean field theory (DFT + DMFT) gives spectra in close correspondence to the experiment. Via this comparison we attribute the prominent MIR peak to inter-band transitions involving a narrow U 5$f$ feature that develops near the Fermi level. In this regard, our data gives spectroscopic evidence for the existence of a low energy Kondo resonance at temperatures just above the onset of superconductivity and implicates heavy electrons in the formation of the superconducting state. We find that the coherent Kondo resonance is primarily associated with a collapse of scattering and less with a transfer of spectral weight.

Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment

This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.

Strongly Correlated Quantum Spin Liquids versus Heavy Fermion Metals: A Review.

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in and quasi-one dimensional (1D) quantum spin liquid in both and with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal , with , and on its sister compounds and , carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of and in its sister compounds and emerge, as well as establish connection of these (HF) metals with insulators , and . We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.

Nuclear-Order-Induced Quantum Criticality and Heavy-Fermion Superconductivity at Ultra-low Temperatures in YbRh2Si2

The tetragonal heavy-fermion metal YbRh2Si2 orders antiferromagnetically at TN = 70 mK and exhibits an unconventional quantum critical point (QCP) of Kondo-destroying type at BN = 60 mT, for the magnetic field applied within the basal (a, b) plane. Ultra-low-temperature magnetization and heat-capacity measurements at very low fields indicate that the 4f-electronic antiferromagnetic (AF) order is strongly suppressed by a nuclear-dominated hybrid order (“A-phase”) at TA ≤ 2.3 mK, such that quantum critical fluctuations develop at B ≈ 0 (Schuberth et al., Science, 2016, 351, 485–488). This enables the onset of heavy-fermion superconductivity (Tc = 2 mK) which appears to be suppressed by the primary antiferromagnetic order at elevated temperatures. Measurements of the Meissner effect reveal bulk superconductivity, with Tc decreasing under applied field to Tc < 1 mK at B > 20 mT. The observation of a weak but distinct superconducting shielding signal at a temperature as high as 10 mK suggests the formation of insulated random islands with emergent A-phase order and superconductivity. Upon cooling, the shielding signal increases almost linearly in temperature, indicating a growth of the islands which eventually percolate at T ≈ 6.5 mK. Recent electrical-resistivity results by Nguyen et al. (Nat. Commun., 2021, 12, 4341) confirm the existence of superconductivity in YbRh2Si2 at ultra-low temperatures. The combination of the results of Schuberth et al. (2016) and Nguyen et al. (2021) at ultra-low temperatures below BN, along with those previously established at higher temperatures in the paramagnetic state, provide compelling evidence that the Kondo-destruction quantum criticality robustly drives unconventional superconductivity.