The orthorhombic uranium dichalcogenide UTe$_2$ displays superconductivity below 1.7 K, with the anomalous feature of retaining 50$\%$ of normal state (ungapped) carriers, according to heat capacity data from two groups. Incoherent transport that crosses over from above 50 K toward a low temperature, Kondo lattice Fermi liquid regime indicates strong magnetic fluctuations and the need to include correlation effects in theoretical modeling. We report density functional theory plus Hubbard U (DFT+U) results for UTe$_2$ to provide a platform for modeling its unusual behavior, focusing on ferromagnetic (FM, time reversal breaking) long range correlations along the ${\hat a}$ axis as established by magnetization measurements and confirmed by our calculations. States near the Fermi level are dominated by the $j=\frac{5}{2}$ configuration, with the $j_z=\pm\frac{1}{2}$ sectors being effectively degenerate and half-filled. Unlike the small-gap insulating nonmagnetic electronic spectrum, the FM Fermi surfaces are large (strongly metallic) and display low dimensional features, reminiscent of the FM superconductor UGe$_2$.
Single crystals of the unconventional superconductor UTe$_2$ have been grown in various conditions which result in different superconducting transition temperature as well as normal state properties. Stoichiometry of the samples has been characterized by the single-crystal X-ray crystallography and electron microprobe analyses. Superconducting samples are nearly stoichiometric within an experimental error of about 1 \%, while non-superconducting sample significantly deviates from the ideal composition. The superconducting UTe$_2$ showed that the large density of states was partially gapped in …
The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after 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. The competition between different types of magnetic interactions and the duality between the local and itinerant character…
We investigate the intrinsic anomalous thermal Hall effect as an effective probe of the order parameters of non-unitary pairing states of the putative spin-triplet superconductor UTe$_2$. We consider all symmetry-allowed non-unitary states under magnetic fields comprehensively, and calculate the anomalous Hall conductivity arising from time-reversal symmetry-breaking Weyl point nodes of the gap functions, assuming three types of Fermi surfaces; ellipsoid-shaped, cylinder-shaped, and ring-shaped ones, which are predicted by previous band calculations. We find the nonzero anomalous thermal Hall …
UTe2 is a promising candidate for spin-triplet superconductors, in which a paramagnetic normal state becomes superconducting due to spin fluctuations. The subsequent discovery of various unusual superconducting properties has promoted the use of UTe2 as an exciting playground to study unconventional superconductivity, but fathoming the normal state fermiology and its influence on the superconductivity still requires further investigation. Here, we theoretically show that electron correlation induces a dramatic change in the normal state fermiology with an emergent correlated Fermi surface (FS)…
We report the first observation of the de Haas-van Alphen (dHvA) effect in the novel spin-triplet superconductor UTe2 using high quality single crystals with the high residual resistivity ratio (RRR) over 200. The dHvA frequencies, named alpha and beta, are detected for the field directions between c and a-axes. The frequency of branch beta increases rapidly with the field angle tilted from c to a-axis, while branch alpha splits, owing to the maximal and minimal cross-sectional areas from the same Fermi surface. Both dHvA branches, alpha and beta reveal two kinds of cylindrical Fermi surfaces …
The crystal structure of the new superconductor UTe2 has been investigated for the first time at low temperature (LT) of 2.7 K, just closely above the superconducting transition temperature of about 1.7 K by single crystal neutron diffraction, in order to prove, whether the orthorhombic structure of type Immm (Nr. 71 Int. Tabl.) reported for room temperature (RT) persists down to the superconducting phase and can be considered as a parent symmetry for the development of spin triplet superconductivity. Our results show that the RT structure reported previously obtained by single crystal X-Ray d…
Hidden magnetic order within the pressure induced superconducting dome of UTe2
New Cornerstone Science Laboratory, Center for Correlated Matter and School of Physics, Zhejiang University（浙江大学相关物质研究中心新Cornerstone科学实验室）；National Key Laboratory of Surface Physics and Chemistry（表面物理与化学国家重点实验室）；Nanhu Laser Laboratory（南湖激光实验室）；Max Planck Inst（马克斯·普朗克研究所）
A lot of attention has been drawn to superconductivity in UTe$_2$, with suggestions of time-reversal symmetry breaking triplet chiral superconducting order parameter. The chirality of the order parameter has been attributed to an accidental near degeneracy of two superconducting components belonging to 1D irreps $B_{2u}$ and $B_{3u}$ of the relevant $D_{2h}$ point group, and it has been argued that the chiral $B_{2u}+iB_{3u}$ combination is selected by ferromagnetic fluctuations. In this work we present a possible explanation of the near-degeneracy as a result of an accidental $C_4$ symmetry o…
The normal-state out of which unconventional superconductivity in UTe$_2$ emerges is studied in detail using a variety of thermodynamic and transport probes. Clear evidence for a broad Schottky-like anomaly with roughly R ln 2 entropy around $T^{*} \approx 12$K is observed in all measured quantities. Comparison with high magnetic field transport data allows the construction of an $H\text{-}T$ phase diagram resembling that of the ferromagnetic superconductor URhGe. The low field electronic Grüneisen parameter of $T^{*}$ and that of the metamagnetic transition at $H_m \approx 35$T are comparable…
Multiple unconventional superconducting phases are suspected to be driven by magnetic fluctuations in the heavy-fermion paramagnet UTe$_2$, and a challenge is to identify the signatures of the electronic correlations, including the magnetic fluctuations, in the bulk physical quantities. Here, we investigate thoroughly the anisotropy of the electrical resistivity of UTe$_2$ under intense magnetic fields up to 70~T, for different electrical-current and magnetic-field configurations. Two characteristic temperatures and an anisotropic low-temperature Fermi-liquid-like coefficient $A$, controlled b…
We have performed the $^{125}$Te-nuclear magnetic resonance (NMR) measurement in the field along the $b$ axis on the newly discovered superconductor UTe$_2$, which is a candidate of a spin-triplet superconductor. The nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ abruptly decreases below a superconducting (SC) transition temperature $T_c$ without showing a coherence peak, indicative of UTe$_2$ being an unconventional superconductor. It was found that the temperature dependence of $1/T_1T$ in the SC state cannot be understood by a single SC gap behavior but can be explaine…
Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature $T_c$. Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin $S=0$, although they can also form parallel spin-triplet Cooper pairs with $S=1$ and an odd parity wavefunction. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation. Because spin-triplet pairing is usually mediated by ferromagnetic (FM…
UTe$_2$ is a recently discovered unconventional superconductor that has attracted much interest due to its many intriguing properties - a large residual density-of-states in the superconducting state, re-entrant superconductivity in high magnetic fields, and potentially spin-triplet topological superconductivity. Our ac calorimetry, electrical resistivity, and x-ray absorption study of UTe$_2$ under applied pressure reveals key new insights on the superconducting and magnetic states surrounding pressure-induced quantum criticality at P$_{c1}$ = 1.3 GPa. First, our specific heat data at low pre…
Fermi-liquid versus non-Fermi-liquid/'strange-metal' fits to the electrical resistivity in the quantum critical magnetic regime of an unconventional superconductor
Low-temperature electrical and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor UTe2 to determine the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallographic a- and b-axes reveal a vanishingly small residual fermionic component of the thermal conductivity. The magnetic field dependence of the residual term follows a rapid, quasi-linear increase consistent with the presence of nodal quasiparticles, rising toward the a-axis up…
Non-magnetic impurities can lift the accidental degeneracy of unconventional pairing states, such as the $(d + i g)$-wave state recently proposed for Sr$_2$RuO$_4$. This type of effect would lead to a superconducting double transition upon impurity doping. In a model calculation it is shown how this behavior depends on material parameters and how it could be detected.
We consider the energy of the filled quasiparticle's Fermi sea of a macroscopic superconducting ring threaded by an hc/2e-vortex, when the material of the ring is of an unconventional pairing symmetry. The energy relative to the one for the hc/e-vortex configuration is finite, positive, and inversely proportional to ring's inner radius. We argue that the existence of this energy in unconventional superconductors removes the commonly assumed degeneracy between the odd and the even vortices, with the loss of the concomitant hc/2e periodicity in external magnetic field as a consequence. This macr…
Unconventional superconductivity emerging along with the strange-metal behavior in UAs2 under pressure
National Laboratory of Solid State Microstructures and Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理系，先进微结构协同创新中心）；College of Advanced Interdisciplinary Studies & Nanhu Laser Laboratory, National University of Defense Technology（国防科技大学高级跨学科研究院与南湖激光实验室）
Two-dimensional transition metal dichalcogenides entwine interaction, spin-orbit coupling, and topology. Hole-doped systems lack spin degeneracy: states are indexed with spin and valley specificity. This unique structure offers new possibilities for correlated phases and phenomena. We realize an unconventional superconducting pairing phase which is an equal mixture of a spin singlet and the $m = 0$ spin triplet. It is stable against large in-plane magnetic fields, and its topology allows quasiparticle excitations of net nonzero Berry curvature via pair-breaking circularly polarized light.
Most superconducting materials have an inversion center in their crystal lattices. One of few exceptions is the recently discovered heavy-fermion superconductor CePt3Si [E. Bauer et al, Phys. Rev. Lett. 92, 027003 (2004)]. In this paper, we analyze the implications of the lack of inversion symmetry for the superconducting pairing. We show that the order parameter is an odd function of momentum, and that there always are lines of zeros in the excitation energy gap for one-component order parameters, which seems to agree with the experimental data. The superconducting phase can be non-uniform, e…
According to the "no-node" theorem, many-body ground state wavefunctions of conventional Bose-Einstein condensations (BEC) are positive-definite, thus time-reversal symmetry cannot be spontaneously broken. We find that multi-component bosons with spin-orbit coupling provide an unconventional type of BECs beyond this paradigm. We focus on the subtle case of isotropic Rashba spin-orbit coupling and the spin-independent interaction. In the limit of the weak confining potential, the condensate wavefunctions are frustrated at the Hartree-Fock level due to the degeneracy of the Rashba ring. Quantum …
Sr$_2$RuO$_4$ is the best candidate for spin-triplet superconductivity, an unusual and elusive superconducting state of fundamental importance. In the last three decades Sr$_2$RuO$_4$ has been very carefully studied and despite its apparent simplicity when compared with strongly correlated high-$T_{c}$ cuprates, for which the pairing symmetry is understood, there is no scenario that can explain all the major experimental observations, a conundrum that has generated tremendous interest. Here we present a density-functional based analysis of magnetic interactions in Sr$_{2}$RuO$_{4}$ and discuss…
Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermi…
Chiral superconductors, a unique class of unconventional superconductors in which the complex superconducting order parameter winds clockwise or counter-clockwise in the momentum space, represent a topologically non-trivial system with direct implications for topological quantum computing. Intrinsic chiral superconductors are extremely rare, with only a few arguable examples including heavy fermion metals (UTe$_2$, UPt$_3$) and perovskite superconductor Sr$_2$RuO$_4$. Chiral molecules with neither mirror nor inversion symmetry have been widely investigated, in which the spin degeneracy may be …
We review the status of cooling techniques aimed at achieving the deepest quantum degeneracy for atomic Fermi gases. We first discuss some physical motivations, providing a quantitative assessment of the need for deep quantum degeneracy in relevant physics cases, such as the search for unconventional superfluid states. Attention is then focused on the most widespread technique to reach deep quantum degeneracy for Fermi systems, sympathetic cooling of Bose-Fermi mixtures, organizing the discussion according to the specific species involved. Various proposals to circumvent some of the limitation…
Spontaneous symmetry breaking constitutes a paradigmatic classification scheme of matter. However, broken symmetry also entails domain degeneracy that often impedes identification of novel low symmetry states. In quantum matter, this is additionally complicated by competing intertwined symmetry breaking orders. A prime example is that of unconventional superconductivity and density-wave orders in doped cuprates in which their respective symmetry relation remains a key question. Using uniaxial pressure as a domain-selective stimulus in combination with x-ray diffraction, we unambiguously reveal…
We use quantum oscillation measurements to distinguish between spin and orbital components of the lowest energy quasiparticle excitations in YBa2Cu3O6.54, each of which couple differently to a magnetic field. Our measurements reveal the phase of the observed quantum oscillations to remain uninverted over a wide angular range, indicating that the twofold spin degeneracy of the Landau levels is virtually unaltered by the magnetic field. The inferred suppression of the spin degrees of freedom indicates a spin density-wave is responsible for creation of the small Fermi surface pockets in underdope…
Disproportionation in 3d compounds can give rise to an unconventional electron-hole Bose liquid with a very rich phase diagram from a Bose metal, charge ordering insulator to an inhomogeneous Bose superfluid. Optimal conditions for the disproportionation driven high-T_c superconductivity are shown to realize only for several Jahn-Teller d^n configurations that permit the formation of well defined local composite bosons. These are the high-spin d^4, low-spin d^7, and d^9 configurations given the octahedral crystal field, and the d^1, high-spin d^6 configurations given the tetrahedral crystal fi…
Using both the self-consistent Bogoliubov-de Gennes formulation and non-self-consistent T-matrix approach, we perform a comprehensive investigation of the in-gap bound states induced by a localized single impurity in iron-based superconductors. We focus on studying signatures associated with the unconventional sign-changed s-wave pairing symmetry. For a non-magnetic impurity, we find that there are two in-gap bounds, symmetric with respect to zero energy, only in the sign changed s-wave pairing state, not in the sign-unchanged s-wave state, due to the existence of non-trivial Andreev bound sta…
High-$T_c$ cuprates like $La_{2-x}Sr_{x}CuO_{4}$ and $YBa_{2-x}Cu_{3}O_{6+x}$ are considered as a system of the electron and hole polar pseudo-Jahn-Teller $CuO_{4}$ centers $[{CuO}_{4}^{7-}]_{JT}$ and $[CuO_{4}^{5-}]_{JT}$, respectively, or a system of the local bosons moving in a lattice of the hole centers. Ground manifold of the polar centers includes three terms $^{1}A_{1g}$ (Zhang-Rice singlet), $^{1}E_{u}$, $^{3}E_{u}$ with different spin multiplicity, orbital degeneracy and parity that provides an unconventional multi-mode behaviour of the cuprates. The spin subsystem of the copper oxid…
Using the self-consistent tight-binding Bogoliubov-de Gennes formalism we have studied the effect of nearest neighbor spin-singlet bond (SB) correlations on Josephson coupling and proximity effect in graphene SNS Josephson junctions with conventional s-wave superconducting contacts. Despite the s-wave superconducting state in the contacts, the SB pairing state inside the junction has d-wave symmetry and clean, sharp interface junctions resemble a 'bulk-meets-bulk' situation with very little interaction between the two different superconducting states. In fact, due to a finite-size suppression …
