Valence and magnetic ordering in intermediate valence compounds: TmSe versus SmB(6)

Unconventional superconductivity in UTe2

The novel spin-triplet superconductor candidate UTe₂was discovered only recently at the end of 2018 and already attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe₂is a heavy-fermion paramagnet, but following the discovery of superconductivity, it has been expected to be close to a ferromagnetic instability, showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. This view might be too simplistic. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5fUranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure for field applied along the three axis of this orthorhombic structure. Special attention will be given to the occurrence of a metamagnetic transition atH_m= 35 T for a magnetic field applied along the hard magnetic axisb. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention is paid on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe₂is extremely rich, exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature-field-pressure phase diagrams. There is evidence for spin-triplet pairing. Experimental indications exist for chiral superconductivity and spontaneous time reversal symmetry breaking in the superconducting state. Different theoretical approaches will be described. Notably we discuss that UTe₂is a possible example for the realization of a fascinating topological superconductor. Exploring superconductivity in UTe₂reemphasizes that U-based heavy fermion compounds give unique examples to study and understand the strong interplay between the normal and superconducting properties in strongly correlated electron systems.

Wide temperature AC-calorimetry equipped in a constant loading cubic-anvil-type pressure apparatus

AC-calorimetry was developed for a cubic-anvil-type pressure apparatus, which can explore the electromagnetic properties of matter over temperatures of 2-300 K and pressures of 0-15 GPa. This method was designed to observe the specific heat of fragile crystals that are difficult to mold into desired forms, such as β-Na_0.33V₂O₅ and BaFe₂S₃. The calorimeter has two main components: a thermometer and a heater. We employed an AuFe (0.07 mol. %)-Chromel thermocouple and NiCr alloy foil/wire as the thermometer and heater, respectively. Using this calorimetry, we successfully observed the pressure dependencies of several transition temperatures in β-Na_0.33V₂O₅ and the jump in the specific heat (ΔC_ac/T) at the superconducting transition in Pb-metal when under pressure. Meanwhile, the pressure dependencies of the observed ΔC_ac/T do not coincide with the literature, which may be attributed to the pressure dependence of the thermoelectric power for the AuFe-Chromel thermocouple at around 5 K.

Probing insulators under pressure

Applying pressure on a material can reveal many physical properties and is a very efficient tool to understand its physics. Resistivity measurements have been the ideal probe to study metals under pressure. However, in the case of insulators, resistivity, or conductivity, it is often not the appropriate quantity characterizing the material. In this work, we present a newly developed in situ pressure tuning system that can be used over a wide temperature range (2 K-300 K) and allows changing the pressure at any temperature. We also present AC calorimetry and capacitance/loss measurements under pressure and demonstrate how this combination can be used to characterize a material that is too insulating for standard resistivity techniques.

Valence transition in topological Kondo insulator

We investigate the valence transition in three-dimensional topological Kondo insulator through slave-boson analysis of periodic Anderson model. By including the effect of intra-atomic Coulomb correlation [Formula: see text] between conduction and local electrons, we find a first-order valence transition from Kondo region to mixed valence state upon ascending of local f- level above a critical [Formula: see text], and this valence transition usually occurs very close to or simultaneously with a topological transition. Near the parameter region of zero-temperature valence transition, rise of temperature can generate a thermal valence transition from mixed valence to Kondo region, accompanied by a first-order topological transition. Remarkably, above a critical [Formula: see text] which is considerably smaller than that generating paramagnetic valence transition, the original continuous antiferromagnetic transition is shifted to first order one, at which a discontinuous valence shift takes place. Upon increasing [Formula: see text], the paramagnetic valence transition approaches then converges with the first-order antiferromagnetic transition, leaving a significant valence shift on the magnetic boundary. The continuous antiferromagnetic transition, first-order antiferromagnetic transition, paramagnetic valence transition and topological transitions are all summarized in a global phase diagram. Our proposed exotic transition processes can help to understand the thermal valence variation as well as the valence shift around the pressure-induced magnetic transition in topological Kondo insulator candidates and in other heavy-fermion systems.

Magnetic field-tuned Fermi liquid in a Kondo insulator

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field-typically of order 100 T-means that very little is known about this insulator-metal transition. Here we show that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text], owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only [Formula: see text] 11 T. A peak in the strength of electronic correlations near [Formula: see text], which is evident in transport and susceptibility measurements, suggests that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text] may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

[Formula: see text] classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator

Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a [Formula: see text]-classification formula for these states. By calculating the [Formula: see text] index, the antiferromagnetic insulating states are classified into AFTI or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB₆, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems.

Quantum phase transition and destruction of Kondo effect in pressurized SmB6

SmB₆ has been a well-known Kondo insulator for decades, but recently attracts extensive new attention as a candidate topological system. Studying SmB₆ under pressure provides an opportunity to acquire the much-needed understanding about the effect of electron correlations on both the metallic surface state and bulk insulating state. Here we do so by studying the evolution of two transport gaps (low temperature gap E_l and high temperature gap E_h) associated with the Kondo effect by measuring the electrical resistivity under high pressure and low temperature (0.3 K) conditions. We associate the gaps with the bulk Kondo hybridization, and from their evolution with pressure we demonstrate an insulator-to-metal transition at ∼4 GPa. At the transition pressure, a large change in the Hall number and a divergence tendency of the electron-electron scattering coefficient provide evidence for a destruction of the Kondo entanglement in the ground state. Our results raise the new prospect for studying topological electronic states in quantum critical materials settings.

Pressure-induced exotic states in rare earth hexaborides

Finding the exotic phenomena in strongly correlated electron systems (SCESs) and understanding the corresponding microphysics have long been the research frontiers of condensed matter physics. The remarkable examples for the intriguing phenomena discovered in past years include unconventional superconductivity, heavy Fermion behaviors, giant magneto-resistance and so on. A fascinating type of rare earth hexaboride RB6 (R  =  Sm, Yb, Eu and Ce) belongs to a strongly correlated electron system (SCES), but shows unusual ambient-pressure and high-pressure behaviors beyond the phenomena mentioned above. Particularly, the recent discovery of the coexistence of an unusual metallic surface state and an insulating bulk state in SmB6, known to be a Kondo insulator decades ago, by theoretical calculations and many experimental measurements creates new interest for the investigation of the RB6. This significant progress encourages people to revisit the RB6 with an attempt to establish a new physics that links the SCES and the unusual metallic surface state which is a common feature of a topological insulator (TI). It is well known that pressure has the capability of tuning the electronic structure and modifying the ground state of solids, or even inducing a quantum phase transition which is one of the kernel issues in studies of SCESs. In this brief review, we will describe the progress in high pressure studies on the RB6 based on our knowledge and research interests, mainly focusing on the pressure-induced phenomena in YbB6 and SmB6, especially on the quantum phase transitions and their connections with the valence state of the rare earth ions. Moreover, some related high-pressure results obtained from CeB6 and EuB6 are also included. Finally, a summary is given in the conclusions and perspectives section.

Pressure-Resistant Intermediate Valence in the Kondo Insulator SmB_{6}

Resonant x-ray emission spectroscopy was used to determine the pressure dependence of the f-electron occupancy in the Kondo insulator SmB_{6}. Applied pressure reduces the f occupancy, but surprisingly, the material maintains a significant divalent character up to a pressure of at least 35 GPa. Thus, the closure of the resistive activation energy gap and onset of magnetic order are not driven by stabilization of an integer valent state. Over the entire pressure range, the material maintains a remarkably stable intermediate valence that can in principle support a nontrivial band structure.

Heavy fermions. Unconventional Fermi surface in an insulating state

Insulators occur in more than one guise; a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here, we report the observation of an unusual insulating state with an electrically insulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high-purity single crystals of the Kondo insulator SmB6, which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB6 and LaB6. The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behavior.