Sylvia K. Lewin, Peter Czajka, Corey E. Frank, Gicela Saucedo Salas, Hyeok Yoon, Yun Suk Eo, Johnpierre Paglione, Andriy H. Nevidomskyy, John Singleton, Nicholas P. Butch
Heavy fermion UTe$_2$ is a promising candidate for topological superconductivity that also exhibits multiple high-field superconducting phases. The SC$_{\rm{FP}}$ phase has only been observed in off-axis magnetic fields in the $bc$ plane at fields greater than 40 teslas, a striking scale given its critical temperature of only 2 kelvins. Here, we extend measurements of this unique superconducting state outside of the $bc$ plane and reveal its core structure. The SC$_{\rm{FP}}$ phase is not confined to fields in the $bc$ plane and in fact wraps around the $b$ axis in a halo-like fashion. In other words, this superconducting state, which exists in fields above 73 teslas, is stabilized by a field component perpendicular to the magnetic easy axis. These remarkable field scales further underscore UTe$_2$'s unique magnetophilic superconducting tendencies and suggest an underlying pairing mechanism that is qualitatively distinct from known theories for field-enhanced superconductivity. Phenomenological modeling points to a two-component, non-unitary spin triplet order parameter with finite orbital momentum of the Cooper pairs as a natural explanation for the field-angle dependence of the upper critical field of the SC$_{\rm{FP}}$ phase.
A three-component Ginzburg-Landau theory for a triplet pairing is developed to understand the observed multiple phases in a new superconductor UTe$_2$ under pressure. Near the critical pressure $P_{\rm cr}$=0.2GPa where all components are perfectly degenerate the three successive superconducting transitions are predicted to occur. The $p$-wave pairing symmetry realized in UTe$_2$ is characterized by non-unitarity and chirality with point nodes, thus time reversal symmetry spontaneously broken.
The measurements (Phys.Rev.B {\bf 100}, 220504(R) (2019)) do not detect noticeable thermal conductivity in superconducting UTe$_2$ in the T=0 limit. At the same time the same crystals exhibit a large residual density of states comparable with its normal state value. The improvement of samples quality leads to the augmentation of critical temperature of transition to the superconducting state accompanied by the decreasing of residual specific heat ratio $C(T)/T$ at $T\to 0$. There is presented an analytic derivation of this inverse correlation property in concrete cases of triplet superconducti…
Reentrant superconductivity has been observed in the candidate spin-triplet superconductor UTe$_2$ as a function of the magnetic field applied along the hard axis. Resistivity measurements have shown, a broadened superconducting transition appears near the minimal $T_c$, highlighting the importance of superconducting fluctuations in this regime. We present a phenomenological study assuming a field-driven first-order transition between two superconducting states. We show that with quenched randomness, inhomogeneity-enhanced superconducting fluctuations near the transition could naturally accoun…
Two-dimensional flat band on the (011) surface of UTe$_2$: Implication for STM measurements with a superconducting tip
The University of Osaka（大阪大学）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）；Center for Spintronics Research Network, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科自旋电子学研究网络中心）；Division of Spintronics Research Network, Institute for Open and Transdisciplinary Research Initiatives, The University of Osaka（大阪大学开放与跨学科研究倡议院自旋电子学研究网络分部）
In most superconductors electrons form Cooper pairs in a spin-singlet state mediated by either phonons or by long-range interactions such as spin fluctuations. The superconductor UTe$_2$ is a rare material wherein electrons are believed to form pairs in a unique spin-triplet state with potential topological properties. While spin-triplet pairing may be mediated by ferromagnetic or antiferromagnetic fluctuations, experimentally, the magnetic properties of UTe$_2$ are unclear. By way of muon spin rotation/relaxation ($μ$SR) measurements on independently grown UTe$_2$ single crystals we demonstra…
Magnetic field induced superconductivity is a fascinating quantum phenomenon, whose origin is yet to be fully understood. The recently discovered spin triplet superconductor, UTe2, exhibits two such superconducting phases, with the second one reentering in the magnetic field of 45 T and persisting up to 65 T. More surprisingly, in order to induce this superconducting phase, the magnetic field has to be applied in a special angle range, not along any high symmetry crystalline direction. Here we investigated the evolution of this high-field induced superconducting phase under pressure. Two super…
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 recently discovered superconductor, UTe$_2$, has attracted immense scientific interest due to the experimental observations that suggest odd-parity superconductivity. It is believed that the material becomes a heavy-fermion metal at low temperatures although details of the normal state are unclear. Using Fourier transform infrared spectroscopy (FTIR), the normal state electronic structure of UTe$_2$ was investigated at zero applied magnetic field. Combining the measured reflectivity with the dc resistivity, the complex optical conductivity was obtained over a large frequency range. The fre…
The recent discovery of superconductivity in heavy Fermion compound UTe2, a candidate topological and triplet-paired superconductor, has aroused widespread interest. However, to date, there is no consensus on whether the stoichiometric sample of UTe2 is superconducting or not due to lack of reliable evidence to distinguish the difference between the nominal and real compositions of samples. Here, we are the first to clarify that the stoichiometric UT2 is non-superconducting at ambient pressure and under hydrostatic pressure up to 6 GPa, however we find that it can be compressed into supercondu…
Visualizing the Odd-parity Superconducting Order Parameter and its Quasiparticle Surface Band in UTe2
H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学）；Clarendon Laboratory, University of Oxford（牛津大学）；Department of Physics, University College Cork（科克大学）
We performed AC calorimetry and magnetoresistance measurements under pressure for H || a-axis (easy-magnetization axis) in the novel heavy-fermion superconductor UTe2. Thanks to the thermodynamic information, multiple superconducting phases have been revealed under pressure and magnetic field. The (H,T) phase diagram of superconductivity under pressure displays an abrupt increase of the upper critical field (Hc2) at low temperature and in the high field region, and a strong convex curvature of Hc2 at high temperature. This behavior of Hc2 and the multiple superconducting phases require a state…
This study investigates the spin susceptibility in U-based superconductor UTe$_2$ in the superconducting (SC) state by using Knight shift measurements for a magnetic field $H$ along the $a$ axis, which is the magnetic easy axis of UTe$_2$. Although a tiny anomaly ascribed to the SC diamagnetic effect was observed just below the SC transition temperature $T_{\rm c}$, the $a$-axis Knight shift in the SC state shows no significant decrease, following the extrapolation from the normal-state temperature dependence. This indicates that the spin susceptibility is nearly unchanged below $T_{\rm c}$. C…
Despite intense experimental efforts, the nature of the unconventional superconducting order parameter of UTe$_2$ remains elusive. This puzzle stems from different reported numbers of superconducting transitions at ambient pressure, as well as a complex pressure-temperature phase diagram. To bring new insights into the superconducting properties of UTe$_2$, we measured the heat capacity and electrical resistivity of single crystals under compressive uniaxial stress $σ$ applied along different crystallographic directions. We find that the critical temperature $T_{\rm c}$ of the single observed …
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…
Quantitative thermodynamic study of superconducting and normal states in UTe2 under pressure
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CEA（法国原子能和替代能源委员会）；Grenoble INP（格勒诺布尔国立理工学院）；IRIG（辐射与集成研究研究所）；PHELIQS（物理化学与量子科学实验室）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理学研究所）；Institute for Solid State and Materials Physics, TU Dresden University of Technology（德累斯顿工业大学固态与材料物理研究所）；CNRS, Institut Néel（法国国家科学研究中心内耳研究所）
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…
Topological surface states revealed by the Zeeman effect in superconducting UTe2
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Copenhagen（哥本哈根大学）；University of Cambridge（剑桥大学）；University of Maryland, College Park（马里兰大学帕克分校）；Charles University（查理大学）；Uppsala University（乌普萨拉大学）
The search for a material platform for topological quantum computation has recently focused on unconventional superconductors. Such material systems, where the superconducting order parameter breaks a symmetry of the crystal point group, are capable of hosting novel phenomena, including emergent Majorana quasiparticles. Unique among unconventional superconductors is the recently discovered UTe2, where spin-triplet superconductivity emerges from a paramagnetic normal state. Although UTe2 could be considered a relative of a family of known ferromagnetic superconductors, the unique crystal struct…
UTe$_2$ is a recently discovered promising candidate for a spin-triplet superconductor. In contrast to conventional spin-singlet superconductivity, spin-triplet superconductivity possesses spin and angular momentum degrees of freedom. To detect these degrees of freedom and obtain the solid evidence of spin-triplet superconductivity in UTe$_2$, we performed $^{125}$Te-NMR measurement. We previously reported that the shoulder signal appears in NMR spectra below the superconducting (SC) transition temperature $T_{\rm c}$ in $H \parallel b$, and that a slight decrease in the Knight shift along the…
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）
We theoretically study superconductivity in UTe$_2$, which is a recently-discovered strong candidate for an odd-parity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA$+U$ method and show the insulator-metal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of $U$, we clarify topological properties of possible superconductin…
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)…
Superconductivity induced by a magnetic field near metamagnetism is a striking manifestation of magnetically-mediated superconducting pairing. After being observed in itinerant ferromagnets, this phenomenon was recently reported in the orthorhombic paramagnet UTe$_2$. Under a magnetic field applied along the hard magnetization axis b, superconductivity is reinforced on approaching metamagnetism at $μ_0H_m$ = 35 T, but it abruptly disappears beyond $H_m$. On the contrary, field-induced superconductivity was reported beyond $μ_0H_m$ = 40-50 T in a magnetic field tilted by $\simeq25-30°$ from b i…
A spin-triplet superconducting state mediated by ferromagnetic (FM) spin fluctuations has been suggested to occur in the newly discovered heavy-fermion superconductor UTe$_2$. However, the recent neutron scattering measurements revealed the presence of antiferromagnetic (AFM) spin fluctuations in UTe$_2$. Here, we report the $^{125}$Te nuclear magnetic resonance (NMR) studies of a single-crystal UTe$_2$, suggesting the coexistence of FM and AFM spin fluctuations in UTe$_2$. Owing to the two different Te sites in the compound, we conclude that the FM spin fluctuations are dominant within ladder…
Motivated by the recent discovery of superconductivity in UTe$_2$, we analyze the stability and nodal structure of various triplet superconducting order parameters. Using a combination of symmetry group-theoretical analysis, phenomenological Landau free energy and weak-coupling BCS theory, we show that chiral nonunitary superconducting order can be stabilized on the border of ferromagnetism in UTe$_2$, even in the absence of long-range magnetic order. We further perform first principles density functional theory (DFT) calculations of the so-called "small" Fermi surface, excluding the contribut…
It was theoretically predicted more than 20 years ago [A.G. Lebed and K. Yamaji, {\it Phys. Rev. Lett.} {\bf80}, 2697 (1998)] that a triplet quasi-two-dimensional (Q2D) superconductor could restore its superconducting state in parallel magnetic fields, which are higher than its upper critical magnetic field, $H > H_{c2}(0)$. It is very likely that recently such phenomenon has been experimentally discovered in the Q2D superconductor UTe$_2$ by Nicholas Butch, Sheng Ran and their colleagues and has been confirmed by Japanese-French team. We review our previous theoretical results, using such a g…
Multiple superconducting order parameters are extremely rare. Here we show that a very small pressure can induce this phenomenon in the recently discovered heavy fermion superconductor UTe2. This nearly ferromagnetic system shows several intriguing phenomena, including an extraordinary reinforcement of superconductivity in very strong magnetic fields. We find that pressure can tune the system to a more correlated state and probable magnetic order. The superconducting critical temperature is strongly enhanced, reaching almost 3K, a new record for Ce- and U-based heavy fermion superconductors. M…
To investigate spin susceptibility in a superconducting (SC) state, we measured the $^{125}$Te-nuclear magnetic resonance (NMR) Knight shifts at magnetic fields ($H$) up to 6.5 T along the $b$ and $c$ axes of single-crystal UTe$_2$, a promising candidate for a spin-triplet superconductor. In the SC state, the Knight shifts along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) decreased slightly and the decrease in $K_b$ was almost constant up to 6.5 T. The reduction in $K_c$ decreased with increasing $H$, and $K_c$ was unchanged through the SC transition temperature at 5.5 T, excluding th…
We report on the crystal structure and electronic properties of the heavy fermion superconductor UTe2 at high pressure up to 11 GPa, as investigated by X-ray diffraction and electrical resistivity experiments. The X-ray diffraction measurements under high pressure using a synchrotron light source reveal anisotropic linear compressibility of the unit cell up to 3.5 GPa, while a pressure-induced structural phase transition is observed above 3.5-4GPa at room temperature, where the body-centered orthorhombic crystal structure with the space group Immm changes into a body-centered tetragonal struct…
