Incommensurate Spin Fluctuations in the Spin-Triplet Superconductor Candidate UTe_{2}

Sudden adiabaticity signals reentrant bulk superconductivity in UTe2

There has been a recent surge of interest in UTe2 due to its unconventional magnetic field (H)-reinforced spin-triplet superconducting phases persisting at fields far above the simple Pauli limit for H ∥ [ 010 ] . Magnetic fields in excess of 35 T then induce a field-polarized magnetic state via a first-order-like phase transition. More controversially, for field orientations close to H ∥ [ 011 ] and above 40 T, electrical resistivity measurements suggest that a further superconducting state may exist. However, no Meissner effect or thermodynamic evidence exists to date for this phase making it difficult to exclude alternative scenarios. In this paper, we describe a study using thermal, electrical, and magnetic probes in magnetic fields of up to 55 T applied between the [010] (b) and [001] (c) directions. Our MHz conductivity data reveal the field-induced state of low or vanishing electrical resistance; our simultaneous magnetocaloric effect measurements (i.e. changes in sample temperature due to changing magnetic field) show the first definitive evidence for adiabaticity and thermal behavior characteristic of bulk field-induced superconductivity.

Absence of Spontaneous Magnetic Fields due to Time-Reversal Symmetry Breaking in Bulk Superconducting UTe_{2}

We have investigated the low-temperature local magnetic properties in the bulk of molten salt-flux (MSF)-grown single crystals of the candidate odd-parity superconductor UTe_{2} by zero-field muon spin relaxation (μSR). In contrast to previous μSR studies of UTe_{2} single crystals grown by a chemical vapor transport method, we find no evidence of magnetic clusters or electronic moments fluctuating slow enough to cause a discernible relaxation of the zero-field μSR asymmetry spectrum. Consequently, our measurements on MSF-grown single crystals rule out the generation of spontaneous magnetic fields in the bulk that would occur near impurities or lattice defects if the superconducting state of UTe_{2} breaks time-reversal symmetry. This result suggests that UTe_{2} is characterized by a single-component superconducting order parameter.

A review of UTe2at high magnetic fields

Uranium ditelluride (UTe2) is recognized as a host material to unconventional spin-triplet superconductivity, but it also exhibits a wealth of additional unusual behavior at high magnetic fields. One of the most prominent signatures of the unconventional superconductivity is a large and anisotropic upper critical field that exceeds the paramagnetic limit. This superconductivity survives to 35 T and is bounded by a discontinuous magnetic transition, which itself is also field-direction-dependent. A different, reentrant superconducting phase emerges only on the high-field side of the magnetic transition, in a range of angles between the crystallographicbandcaxes. This review discusses the current state of knowledge of these high-field phases, the high-field behavior of the heavy fermion normal state, and other phases that are stabilized by applied pressure.

Superconducting spin reorientation in spin-triplet multiple superconducting phases of UTe2

Superconducting (SC) state has spin and orbital degrees of freedom, and spin-triplet superconductivity shows multiple SC phases because of the presence of these degrees of freedom. However, the observation of spin-direction rotation occurring inside the SC state (SC spin rotation) has hardly been reported. Uranium ditelluride, a recently found topological superconductor, exhibits various SC phases under pressure: SC state at ambient pressure (SC1), high-temperature SC state above 0.5 gigapascal (SC2), and low-temperature SC state above 0.5 gigapascal (SC3). We performed nuclear magnetic resonance (NMR) and ac susceptibility measurements on a single-crystal uranium ditelluride. The b axis spin susceptibility remains unchanged in SC2, unlike in SC1, and decreases below the SC2-SC3 transition with spin modulation. These unique properties in SC3 arise from the coexistence of two SC order parameters. Our NMR results confirm spin-triplet superconductivity with SC spin parallel to b axis in SC2 and unveil the remaining of spin degrees of freedom in SC uranium ditelluride.

Magnetic-field-sensitive charge density waves in the superconductor UTe2

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices^1-4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe₂ (refs. ^5-8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field H_c2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg-Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe₂.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Chiral superconductivity in UTe2 probed by anisotropic low-energy excitations

Chiral spin-triplet superconductivity is a topologically nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The heavy-fermion superconductor UTe₂ exhibits peculiar properties of spin-triplet pairing, and the possible chiral state has been actively discussed. However, the symmetry and nodal structure of its order parameter in the bulk, which determine the Majorana surface states, remains controversial. Here we focus on the number and positions of superconducting gap nodes in the ground state of UTe₂. Our magnetic penetration depth measurements for three field orientations in three crystals all show the power-law temperature dependence with exponents close to 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near the k_y- and k_z-axes in momentum space. These results can be consistently explained by a chiral B_3u + iA_u non-unitary state, providing fundamentals of the topological properties in UTe₂.

An emerging global picture of heavy fermion physics

Recent progresses using state-of-the-art experimental techniques have motivated a number of new insights on heavy fermion physics. This article gives a brief summary of the author's research along this direction. We discuss five major topics including: (1) development of phase coherence and two-stage hybridization; (2) two-fluid behavior and hidden universal scaling; (3) quantum phase transitions and fractionalized heavy fermion liquid; (4) quantum critical superconductivity; (5) material-specific properties. These cover the most essential parts of heavy fermion physics and lead to an emerging global picture beyond conventional theories based on mean-field or local approximations.

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.

Non-conventional superconductivity in magnetic In and Sn nanoparticles

We report on experimental evidence of non-conversional pairing in In and Sn nanoparticle assemblies. Spontaneous magnetizations are observed, through extremely weak-field magnetization and neutron-diffraction measurements, to develop when the nanoparticles enter the superconducting state. The superconducting transition temperature TC shifts to a noticeably higher temperature when an external magnetic field or magnetic Ni nanoparticles are introduced into the vicinity of the superconducting In or Sn nanoparticles. There is a critical magnetic field and a critical Ni composition that must be reached before the magnetic environment will suppress the superconductivity. The observations may be understood when assuming development of spin-parallel superconducting pairs on the surfaces and spin-antiparallel superconducting pairs in the core of the nanoparticles.

Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature T_c (ref. ¹). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. ²), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction³. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation^4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations³, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity⁶. Indeed, UTe₂, which has a T_c ≈ 1.6 K (refs. ^7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability^7-14, although it also has antiferromagnetic (AF) spin fluctuations^15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe₂ is coupled to a sharp magnetic excitation, termed resonance^17-23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability^17-23, its observation in UTe₂ suggests that AF spin fluctuations may also induce spin-triplet pairing²⁴ or that electron pairing in UTe₂ has a spin-singlet component.

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.