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 atHm= 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. 

/pdf/unconventional-superconductivity-in-ute-sub-2-sub-1mg4qycs.pdf

Unconventional superconductivity in UTe<sub>2</sub>

The authors show, by combining the Fermi-surface formula and the first principle calculations, that the high-field superconducting phase of CeRh${}_{2}$As${}_{2}$ is a topological crystalline superconductor.

Topological crystalline superconductivity in locally noncentrosymmetric CeRh 2 As 2

Spin–orbit coupling induces a unique form of Zeeman interaction in momentum space in materials that lack inversion symmetry: the electron’s spin is locked on an effective magnetic field that is odd in momentum. The resulting interconnection between the electron’s momentum and its spin leads to various effects such as electric dipole spin resonance, anisotropic spin relaxation and the Aharonov–Casher effect, but also to electrically driven and optically driven spin galvanic effects. Over the past 15 years, the emergence of topological materials has widened this research field by introducing complex forms of spin textures and orbital hybridization. The vast field of Rashba-like physics is now blooming, with great attention paid to non-equilibrium mechanisms such as spin-to-charge conversion, but also to nonlinear transport effects. This Review aims to offer an overview of recent progress in the development of condensed matter research that exploits the unique properties of spin–orbit coupling in non-centrosymmetric heterostructures. Spin–orbit coupling in non-centrosymmetric heterostructures is called the Rashba effect. This Review highlights the latest progress covering new classes of materials with a variety of ‘Rashba-like’ spin–momentum locking schemes and new trends in non-equilibrium transport leading to enhanced functionalities in spin- and optoelectronics. 

Rashba-like physics in condensed matter

Spatial inversion symmetry in crystal structures is closely related to the superconducting (SC) and magnetic properties of materials. Recently, several theoretical proposals that predict various interesting phenomena caused by the breaking of the local inversion symmetry have been presented. However, experimental validation has not yet progressed owing to the lack of model materials. Here we present evidence for antiferromagnetic (AFM) order in CeRh_{2}As_{2} (SC transition temperature T_{SC}∼0.37 K), wherein the Ce site breaks the local inversion symmetry. The evidence is based on the observation of different extents of broadening of the nuclear quadrupole resonance spectrum at two crystallographically inequivalent As sites. This AFM ordering breaks the inversion symmetry of this system, resulting in the activation of an odd-parity magnetic multipole. Moreover, the onset of antiferromagnetism T_{N} within an SC phase, with T_{N}<T_{SC}, is quite unusual in systems wherein superconductivity coexists or competes with magnetism. Our observations show that CeRh_{2}As_{2} is a promising system to study how the absence of local inversion symmetry induces or influences unconventional magnetic and SC states, as well as their interaction. 

/pdf/observation-of-antiferromagnetic-order-as-odd-parity-2dgac6ng.pdf

Observation of Antiferromagnetic Order as Odd-Parity Multipoles inside the Superconducting Phase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>CeRh</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>As</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math>

Experiments show that the unconventional superconductor CeRh${}_{2}$As${}_{2}$ may host a ``quadrupole density wave''---a theorized complex ordering pattern among free electrons that has not yet been observed. 

/pdf/possible-quadrupole-density-wave-in-the-superconducting-3f6xejpj.pdf

Possible Quadrupole Density Wave in the Superconducting Kondo Lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>CeRh</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>As</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Materials with multiple superconducting phases are rare. Here, we report the discovery of two-phase unconventional superconductivity in CeRh2As2 Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 tesla, even though the transition temperature is only 0.26 kelvin. Furthermore, a transition between two different superconducting phases is observed in a c axis magnetic field. Local inversion-symmetry breaking at the cerium sites enables Rashba spin-orbit coupling alternating between the cerium sublayers. The staggered Rashba coupling introduces a layer degree of freedom to which the field-induced transition and high critical field seen in experiment are likely related.

Field-induced transition within the superconducting state of CeRh2As2

We report the discovery of two-phase unconventional superconductivity in CeRh$_2$As$_2$. Using thermodynamic probes, we establish that the superconducting critical field of its high-field phase is as high as 14 T, remarkable in a material whose transition temperature is 0.26 K. Furthermore, a $c$-axis field drives a transition between two different superconducting phases. In spite of the fact that CeRh$_2$As$_2$ is globally centrosymmetric, we show that local inversion-symmetry breaking at the Ce sites enables Rashba spin-orbit coupling to play a key role in the underlying physics. More detailed analysis identifies the transition from the low- to high-field states to be associated with one between states of even and odd parity.

Field-induced transition from even to odd parity superconductivity in CeRh$_2$As$_2$

CeRh2As2 has recently been reported to be a rare case of multi-phase unconventional superconductor [S. Khim et al., arXiv:2101.09522] close to a quantum critical point (QCP). Here, we present a comprehensive study of its normal state properties and of the phase (I) below To ~ 0.4 K which preempts superconductivity at Tc = 0.26 K. The 2nd-order phase transition at To presents signatures in specific heat and thermal expansion, but none in magnetization and ac-susceptibility, indicating a non-magnetic origin of phase I. In addition, an upturn of the in-plane resistivity at To points to a gap opening at the Fermi level in the basal plane. Thermal expansion indicates a strong positive pressure dependence of To , dTo/dp = 1.5 K/GPa, in contrast to the strong negative pressure coefficient observed for magnetic order in Ce-based Kondo lattices close to a QCP. Similarly, an in-plane magnetic field shifts To to higher temperatures and transforms phase I into another non-magnetic phase (II) through a 1st-order phase transition at about 9 T. Using renormalized band structure calculations, we found that the Kondo effect (TK ~ 30 K) leads to substantial mixing of the excited crystalline-electric-field (CEF) states into the ground state. This allows quadrupolar degrees of freedom in the resulting heavy bands at the Fermi level which are prone to nesting. The huge sensitivity of the quadrupole moment on hybridization together with nesting would cause an unprecedented case of phase transition into a quadrupole-density-wave (QDW) state at a temperature To << TK , which would explain the nature of phase I and II.

J. F. Landaeta

Papers

Field-induced transition within the superconducting state of CeRh2As2

Field-induced transition from even to odd parity superconductivity in CeRh$_2$As$_2$

Possible quadrupole density wave in the superconducting Kondo lattice CeRh2As2