High-pressure studies on heavy fermion systems

In this review article, we give a brief overview of heavy fermions, which are prototype examples of strongly correlated electron systems. We introduce the application of physical pressure in heavy fermion systems to construct their pressure phase diagrams and to study the close relationship between superconductivity（SC） and other electronic instabilities, such as antiferromagnetism（AFM）, ferromagnetism（FM）, and valence transitions. Field-angle dependent heat capacity and point-contact spectroscopic measurements under pressure are taken as examples to illustrate their ability to investigate novel physical properties of the emergent electronic states.

Electronic structure of heavy fermion system CePt_2In_7 from angle-resolved photoemission spectroscopy

We have carried out high-resolution angle-resolved photoemission measurements on the Ce-based heavy fermion compound CePt2In7that exhibits stronger two-dimensional character than the prototypical heavy fermion system CeCoIn5.Multiple Fermi surface sheets and a complex band structure are clearly resolved. We have also performed detailed band structure calculations on CePt2In7. The good agreement found between our measurements and the calculations suggests that the band renormalization effect is rather weak in CePt2In7. A comparison of the common features of the electronic structure of CePt2In7and CeCoIn5indicates that CeCoIn5shows a much stronger band renormalization effect than CePt2In7. These results provide new information for understanding the heavy fermion behaviors and unconventional superconductivity in Ce-based heavy fermion systems.

Magnetism, heat capacity, magnetocaloric effect, and magneto-transport properties of heavy fermion antiferromagnet CeGaSi

We synthesize high-quality single crystal of CeGaSi by a Ga self-flux method and investigate its physical properties through magnetic susceptibility,specific heat and electrical resistivity measurements as well as high pressure effect.Magnetic measurements reveal that an antiferromagnetic order develops below T_(m)~10.4 K with magnetic moments orientated in the ab plane.The enhanced electronic specific heat coefficient and the negative logarithmic slope in the resistivity of CeGaSi indicate that the title compound belongs to the family of Kondo system with heavy fermion ground states.The max magnetic entropy change-ΔS_(M)^(max)(μ_(0)H⊥c,μ_(0)H=7 T) around T_(m) is found to reach up to 11.85 J·kg^(-1)·K^(-1).Remarkably,both the antiferromagnetic transition temperature and-ln T behavior increase monotonically with pressure applied to 20 kbar(1 bar=10~5 Pa),indicating that much higher pressure will be needed to reach its quantum critical point.

Tuning the Heavy Fermion State of CeFeGe3 by Ru Doping

We successfully synthesize a series of polycrystalline CeRuxFe1-xCe3（0≤x≤0.5）samples,which are characterized using powder x-ray diffraction,resistivity and specific heat measurements.The expansion of the lattice constants with increasing x demonstrates the successful doping of Ru into the CeFeGe3 lattice.Upon doping,it is found that the temperature up to which Landau-Fermi liquid behavior is observed in the resistivity is reduced.Meanwhile,there is also a pronounced increase in the resistivity coefficient and residual resistivity,as well as a clear upturn in C/T at low temperatures,suggesting that Ru doping may tune the system towards a quantum critical point.

Localized 4f-electrons in the quantum critical heavy fermion ferromagnet CeRh_(6)Ge_(4)

Ferromagnetic quantum critical points were predicted to be prohibited in clean itinerant ferromagnetic systems,yet such a phenomenon was recently revealed in CeRh_(6)Ge_(4),where the Curie temperature can be continuously suppressed to zero under a moderate hydrostatic pressure.Here we report the observation of quantum oscillations in CeRh_(6)Ge_(4)from measurements using the cantilever and tunnel-diode oscillator methods in fields up to 45 T,clearly demonstrating that the ferromagnetic quantum criticality occurs in a clean system.In order to map the Fermi surface of CeRh_(6)Ge_(4),we performed angle-dependent measurements of quantum oscillations at ambient pressure,and compared the results to density functional theory calculations.The results are consistent with the Ce 4f electrons remaining localized and not contributing to the Fermi surface,suggesting that localized ferromagnetism is a key factor for the occurrence of a ferromagnetic quantum critical point in CeRh_(6)Ge_(4).

Simulating heavy fermion physics in optical lattice： Periodic Anderson model with harmonic trapping potential

The periodic Anderson model （PAM）, where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding of heavy fermion materials. Motivated by recent proposals for simulating the Kondo lattice model （KLM） in terms of alkaline-earth metal atoms, we take another step toward the simulation of PAM, which includes the crucial charge/valence fluctuation of local f-electrons beyond purely low-energy spin fluctuation in the KLM. To realize PAM, a transition induced by a suitable laser between the electronic excited and ground state of alkaline-earth metal atoms （^1S0←→^3P0） is introduced. This leads to effective hybridization between local electrons and conduction electrons in PAM. Generally, the SU（N） version of PAM can be realized by our proposal, which gives a unique opportunity to detect large-N physics without complexity in realistic materials. In the present work, high-temperature physical features of standard [SU（2）] PAM with harmonic trapping potential are analyzed by quantum Monte Carlo and dynamic mean-field theory, where the Mott/orbital-selective Mott state was found to coexist with metallic states. Indications for near-future experiments are provided. We expect our theoretical proposal and （hopefully） forthcoming experiments will deepen our understanding of heavy fermion systems. At the same time, we hope these will trigger further studies on related Mott physics, quantum criticality, and non-trivial topology in both the inhomogeneous and nonequilibrium realms.

Scaling behavior of the thermopower of the archetypal heavy-fermion metal YbRh2Si2

We reveal and explain the scaling behavior of the thermopower S/T exhibited by the archetypal heavy-fermion （HF） metal YbRh2Si2 under the application of magnetic field B at temperature T. We show that the same scaling is demonstrated by different HF compounds such as/3-YbA1B4 and the strongly correlated layered cobalt oxide [BiBa0.66K0.3602]CoO2. Using YbRh2Si2 as an example, we demonstrate that the scaling behavior of SIT is violated at the antiferromagnetic phase transition, while both the residual resistivity Po and the density of states, N, experience jumps at the phase transition, causing the thermopower to make two jumps and change its sign. Our elucidation is based on flattening of the single-particle spectrum that profoundly affects Po and N. To depict the main features of the SIT behavior, we construct a T-B schematic phase diagram of YbRh2Si2. Our calculated SIT for the HF compounds are in good agreement with experimental facts and support our observations.

Interplay of superconductivity and d-f correlation in CeFeAs_(1-x)P_xO_(1-y)F_y

The recent discovery of high-temperature superconductivity in iron-based pnictides （chalcogenides） not only trig- gers tremendous enthusiasm in searching for new superconducting materials, but also opens a new avenue to the study of the Kondo physics. CeFeAsO is a parent compound of the 1111-type iron-based superconductors. It shows 3d- antiferromagnetic （AFM） ordering below 139 K and 4f-AFM ordering below 4 K. On the other hand, the phosphide CeFePO is a ferromagnetically corelated heavy-fermion （HF） metal with Kondo scale TK 10 K. These properties set up a new platform for research of the interplay among magnetism, Kondo effect, and superconductivity （SC）. In this review, we present the recent progress in the study of chemical pressure effect in CeFeAsOl_yFy （y = 0 and 0.05）. This P/As-doping in CeFeAsO serves as an effective controlling parameter which leads to two magnetic critical points, Xcl -- 0.4 and Xc2 - 0.92, associated with suppression of 3d and 4f magnetism, respectively. We also observe a turning point of AFM-FM ordering of Ce3＋ moment at Xc3 - 0.37. The SC is absent in the phase diagram, which is attributed to the destruction to Cooper pair by Ce-FM fluctuations in the vicinity of Xcl. We continue to investigate CeFeAsl-xPxO0.95Fo.os. With the separation of xcl and xc3, this chemical pressure results in a broad SC region 0〈 x 〈 0.53, while the original HF behavior is driven away by 5% F- doping. Different roles of P and F dopings are addressed, and the interplay between SC and Ce-4f magnetism is also discussed.

Optical study on intermediate-valence compounds Yb_(1-x)Lu_xAl_3

We report an optical spectroscopy study on intermediate valence system Ybl-xLuxA13 with x = 0, 0.25, 0.5, 0.75, and 1. The Kondo temperature in the system is known to increase with increasing Lu concentration. Therefore, it is expected that the energy scale of the hybridization gap should increase with increasing Lu concentration based on the periodic Anderson model. On the contrary, we find that the spectral structure associated with the hybridization effect shifts monotonically to lower energy. Furthermore, the Lu substitution results in a substantial increase of the free carrier spectral weight and less pronounced plasma frequency reduction upon lowering temperature. We attribute the effect to the disruption of the Kondo lattice periodicity by the random substitution of Yb by Lu. The work highlights the importance of the lattice periodicity of the rare earth element for understanding the Kondo lattice phenomena.

CeAu_(2)In_(4):A candidate of quasi-one-dimensional antiferromagnetic Kondo lattice

Needle-like single crystals of CeAu_(2)In_(4)have been grown from In flux and characterized as a new candidate of quasi-one-dimensional Kondo lattice compound by crystallographic,magnetic,transport,and specific-heat measurements down to very low temperatures.We observe an antiferromagnetic transition at T_(N)≈0.9 K,a highly non-mean-field profile of the corresponding peak in specific heat,and a large Sommerfeld coefficientγ=369 mJ·mol^(-1)·K^(-2).The Kondo temperature T_(K)is estimated to be 1.1 K,being low and comparable to TN.While Fermi liquid behavior is observed deep into the magnetically ordered phase,the Kadowaki-Woods ratio is much reduced relative to the expected value for Ce compounds with Kramers doublet ground state.Markedly,this feature shares striking similarities to that of the prototypical quasi-one-dimensional compounds YbNi_(4)P_(2) and CeRh_(6)Ge_(4) with tunable ferromagnetic quantum critical point.Given the shortest Ce-Ce distance along the needle direction,CeAu_(2)In_(4)appears to be an interesting model system for exploring antiferromagnetic quantum critical behaviors in a quasi-one-dimensional Kondo lattice with enhanced quantum fluctuations.

Growth and characterization of CaCu_3Ru_4O_(12) single crystal

High-quality single crystals of A-site ordered perovskite oxides CaCu3Ru4O12 were synthesized by flux method with Cu O serving as a flux. The typical size of these single crystals was around 1 × 1 × 1 mm^3 and the lattice constant was determined to be 7.430 ± 0.0009 ？A by using x-ray single crystal diffraction. The surfaces of the samples were identified to be（100） surface. The high quality of the single crystal samples was confirmed by the rocking curve data which have a full width at half maximum of approximately 0.02 degree. The x-ray photoelectron spectroscopy measurement was performed and the temperature-dependent specific heat, magnetic susceptibility, and electric resistivity were measured along the [100]direction of the single crystals. All these measurements showed that the physical properties of Ca Cu3Ru4O12 single crystals are similar to that of polycrystals. However, the single crystals have a lower Curie susceptibility tail and a smaller residual resistivity than polycrystals, which indicates that the amount of paramagnetic impurities can be controlled by tuning the number of defects in CaCu3Ru4O12 samples.

Degenerate antiferromagnetic states in spinel oxide LiV2O4

The magnetic and electronic properties of spinel oxide LiV2O4 have been systematically studied by using the spin-polarized first-principles electronic structure calculations.We find that a series of magnetic states,in which the ferromagnetic(FM)V4 tetrahedra are linked together through the corner-sharing antiferromagnetic(AFM)V4 tetrahedra,possess degenerate energies lower than those of other spin configurations.The large number of these energetically degenerated states being the magnetic ground state give rise to strong magnetic frustration as well as large magnetic entropy in LiV2O4.The corresponding band structure and density of states of such a typical magnetic state in this series,i.e.,the ditetrahedron(DT)AFM state,demonstrate that LiV2O4 is in the vicinity of a metal-insulator transition.Further analysis suggests that the t2g and eg orbitals of the V atoms play different roles in the magnetic exchange interactions.Our calculations are consistent with previous experimental measurements and shed light on understanding the exotic magnetism and the heavy-fermion behavior of LiV2O4.

Pressure effect in the Kondo semimetal CeRu4Sn6 with nontrivial topology

Kondo semimetal CeRu4Sn6 is attracting renewed attention due to the theoretically predicted nontrivial topology in its electronic band structure. We report hydrostatic and chemical pressure effects on the transport properties of single- and poly-crystalline samples. The electrical resistivity p （T） is gradually enhanced by applying pressure over a wide temperature range from room temperature down to 25 mK. Two thermal activation gaps estimated from high- and low-temperature windows are found to increase with pressure. A flat p（T） observed at the lowest temperatures below 300 mK appears to be robust against both pressure and field. This feature as well as the increase of the energy gaps calls for more intensive investigations with respect to electron correlations and band topology.

Superfluid response in heavy fermion superconductors

Motivated by a recent London penetration depth measurement [H. Kim, et al., Phys. Rev. Lett. 114, 027003 （2015）] and novel composite pairing scenario [O. Erten, R. Flint, and P. Coleman, Phys. Rev. Lett. 114, 027002 （2015）] of the Yb-doped heavy fermion superconductor CeCoIns, we revisit the issue of superfluid response in the microscopic heavy fermion lattice model. However, from the literature, an explicit expression for the superfluid response function in heavy fermion superconductors is rare. In this paper, we investigate the superfiuid density response function in the celebrated Kondo- Heisenberg model. To be specific, we derive the corresponding formalism from an effective fermionic large-N mean-field pairing Hamiltonian whose pairing interaction is assumed to originate from the effective local antiferromagnetic exchange interaction. Interestingly, we find that the physically correct, temperature-dependent superfiuid density formula can only be obtained if the external electromagnetic field is directly coupled to the heavy fermion quasi-particle rather than the bare conduction electron or local moment. Such a unique feature emphasizes the key role of the Kondo-screening-renormalized heavy quasi-particle for low-temperature/energy thermodynamics and transport behaviors. As an important application, the theoretical result is compared to an experimental measurement in heavy fermion superconductors CeCoIn5 and Yb-doped Ce1-xYbxCoIn5 with fairly good agreement and the transition of the pairing symmetry in the latter material is explained as a simple doping effect. In addition, the requisite formalism for the commonly encountered nonmagnetic impurity and non-local electrodynamic effect are developed. Inspired by the success in explaining classic 115-series heavy fermion superconductors, we expect the present theory will be applied to understand other heavy fermion superconductors such as CeCu2Si2 and more generic multi-band superconductors.

Strongly correlated new state Fermi systems as a of matter

The aim of this review paper is to expose a new state of matter exhibited by strongly correlated Fermi systems represented by various heavy-fermion （HF） metals, two-dimensional liquids like 3He, compounds with quantum spin liquids, quasicrystals, and systems with one-dimensional quantum spin liquid. We name these various systems HF compounds, since they exhibit the behavior typical of HF metals. In HF compounds at zero temperature the unique phase transition, dubbed throughout as the fermion condensation quantum phase transition （FCQPT） can occur; this FCQPT creates flat bands which in turn lead to the specific state, known as the fermion condensate. Unlimited increase of the effective mass of quasiparticles signifies FCQPT; these quasiparticles determine the thermodynamic, transport and relaxation properties of HF compounds. Our discussion of numerous salient experimen- tal data within the framework of FCQPT resolves the mystery of the new state of matter. Thus, FCQPT and the fermion condensation can be considered as the universal reason for the non-Fermi liquid behavior observed in various HF compounds. We show analytically and using arguments based completely on the experimental grounds that these systems exhibit universal scaling behavior of their thermodynamic, transport and relaxation properties. Therefore, the quantum physics of different HF compounds is universal, and emerges regardless of the microscopic structure of the compounds. This uniform behavior allows us to view it as the main characteristic of a new state of matter exhibited by HF compounds.

Itinerant to relocalized transition of felectrons in the Kondo insulator CeRu_(4)Sn_(6)

The three-dimensional electronic structure and the nature of Ce 4f electrons of the Kondo insulator CeRu_(4)Sn_(6)are investigated by angle-resolved photoemission spectroscopy,utilizing tunable photon energies.Our results reveal(i)the three-dimensional k-space nature of the Fermi surface,(ii)the localized-to-itinerant transition of f electrons occurs at a much high temperature than the hybridization gap opening temperature,and(iii)the“relocalization”of itinerant f-electrons below 25 K,which could be the precursor to the establishment of magnetic order.

Fermi surface gapping in the hidden order state of PrFe_(4)P_(12);by point-contact spectroscopy

We have applied point-contact spectroscopy(PCS) to investigate the nonmagnetic hidden order(HO) state of the skutterudite compound PrFe_(4)P_(12) with its transition temperature THO~6.5 K. Its point-contact conductance curves exhibit a reproducible gap structure in the HO state below THOand its temperature dependent gap magnitude follows a BCS-like mean-field behavior.A Fano-like conductance shape is observed to emerge below the coherence temperature of PrFe_(4)P_(12). In a magnetic field, the gap feature is gradually suppressed and evolves into a pronounced Fano peak, signaling the heavy fermion state and vividly demonstrating the competition between HO and the formation of heavy fermion states. Our results strongly suggest the itinerant characteristic of f electrons in PrFe_(4)P_(12), which constrains theoretical models to explain the HO mechanism.

Electronic structure of LaIrIn5and f-electron character in its related Ce-115 compounds

LaIrIn5 is a reference compound of the heavy-fermion superconductor LaIrIn5.The lack of f electrons in LaIrIn5 indicates that there should not be any f electron participating in the construction of its Fermi surface.Thus the electronic structure comparison between LaIrIn5 and LaIrIn5 provides a good platform to study the properties of f electrons.Here angle-resolved photoemission spectroscopy(ARPES)measurements and density functional theory(DFT)calculations are performed to study the electronic structures of LaIrIn5 and LaIrIn5.We find the valence band structures of the two materials are similar to each other,except for the absence of f bands in LaIrIn5.By analyzing the Fermi crossings of the three conduction bands of the two materials quantitatively,we find the volumes of the electron pocketsαandβaround the M′point become larger from LaIrIn5 to LaIrIn5,while the hole pocketγaround theΓ′point becomes smaller.Together with the calculation results,we confirm that this is mainly originated from the f-electron contribution,while the lattice-constant difference between LaIrIn5 and LaIrIn5 only has a finite influence.We also give a summary of the f-electron character in its related Ce-115 heavy fermion compounds.Our results may be essential for the complete microscopic understanding of the 115 compounds and the related heavy-fermion systems.