Scanning Tunneling Microscopy is a cornerstone technique for visualizing the electronic density of states with atomic resolution (typically below 0.1 nm). While the field of view of most STM setups extends up to a few microns, obtaining atomic resolution over these large areas is often impractical and excessively time-consuming. This is due to the need to acquire maps with a point number reaching 10^7 or more with a full current or conductance vs voltage curve at each point. The standard procedure is to make large scale maps and then select small regions to zoom-in for high-resolution atomic scale analysis. However, this approach fails to address a question which is often critical: Does a specific atomic-scale modulation of the electronic density of states persist over much larger, mesoscopic length scales? Here we present a new method: Replica STM (R-STM), that overcomes this limitation, allowing the study of atomic-scale phenomena up to micron length scales. We obtained new large-area STM tunneling conductance maps in UTe_2 and FeSe, spanning areas over 200 nm in size. In these large scale maps we discovered periodic signals with wavelengths significantly exceeding interatomic distances. We show that these large-wavelength periodic signals are replicas of the underlying atomic-scale density of states modulations. R-STM leverages these replica signals to efficiently track atomic-scale features over large areas. We discuss the influence of phase slips, disorder and defects in the replicas. Our results suggest that atomic scale modulations of the superconducting density of states could persist over large length scales in FeSe. R-STM provides a new capability for STM to compare atomic scale with micrometer scale phenomena. The proof of principle of R-STM can be extended to any other scanning probe microscopy experiment where a periodic signal is traced as a function of position.

From a very detailed NMR study of UBe 13 , researchers could reconcile the results of macroscopic measurements pointing to a fully gapped superconducting state, with those of their microscopic probe. But they could also go much further, and identify precisely, thanks to Knight shift anisotropy measurements, the intricate symmetry of the spin-triplet superconducting order parameter in this system. These result on the oldest discovered uranium-based heavy fermion superconductor, could be a strong source of inspiration for UTe 2 , today’s star of the field, which still resist a consensus on the exact state of its superconducting phases.

The existence of multiple superconducting phases induced by either pressure or magnetic field is one of the most striking features of superconductivity of UTe2, among the many unusual superconducting properties of this system. Here we report thermodynamic measurements of the superconducting phase diagram combining pressure and magnetic fields up to 30 T. We show that the high-field superconducting phase at ambient pressure continuously evolves under pressure into the zero-field high-temperature superconducting phase, which occurs above 0.2 GPa.

We report on the synthesis of single crystals of the kagome compound UV6Sn6, and present the results of magnetization, electrical resistivity, heat capacity, x-ray, and neutron diffraction experiments to characterize the structure and magnetic properties. UV6Sn6 crystallizes in a large supercell of the HfFe6Ge6 parent structure with an hexagonal symmetry in which some of the U atoms are shifted by c/2 in an ordered fashion. Below TN1 29 K, an incommensurate magnetic structure with a temperature-dependent wave vector (0, 0, kz) is observed. Below TN2 = 23.5 K, the wave vector locks in to (0,0,0.5), forming an antiferromagnetic ground state. The U moments align along the c axis retaining a large magnetic anisotropy. These findings highlight the role of the 5 f orbitals from uranium in this structural family in driving both magnetic ordering and structural modulation and distinguish UV6Sn6 from its lanthanide-based analogs.

The spatially uniform electronic density characteristic of a metal can become unstable at low temperatures, leading to the formation of charge density waves (CDWs). These CDWs, observed in dichalcogenides, cuprates, and pnictides arise from features in the atomic lattice and its interaction with the electronic band structure that facilitate charge ordering. However, CDWs are rarely observed in presence of Kondo screening and heavy fermion quasiparticles. The heavy fermion topological superconductor candidate UTe_2 presents a notable exception, exhibiting a CDW whose origin remains elusive. Here we report high resolution Scanning Tunneling Microscopy (STM) experiments that reveal the primitive wavevectors of the CDW in UTe_2. This allows for a refined identification of the nesting wavevectors in the electronic bandstructure. Although these wavevectors have no specific influence on the bulk properties, for example on antiferromagnetic fluctuations, they cause the interactions leading to the CDW at the surface. The heavy fermion hybridization pattern is spatially modulated specifically at the nesting wavevectors, suggesting that surface induced modifications in the U 5f electron valence enable a novel form of purely electron-driven charge ordering.

Details of the electronic band structure in unconventional superconductors are key to the understanding of their fundamental ground state. The potential spin-triplet superconductor UTe_2, with T_c≈ 2.1K, has attracted attention recently. Its main Fermi surface consists of weakly corrugated, two-dimensional Fermi-surface cylinders that run along the crystallographic c axis. In addition, there is evidence for the presence of an additional small three-dimensional band. This has been discussed controversially as it may be essential for the realization of superconductivity in UTe_2. Here, we investigate the angle-resolved magnetoresistance and Hall effect in bulk crystalline samples with current along the c axis in fields up to 60T. We observe low-frequency magnetic quantum oscillations with light effective masses that are most pronounced for magnetic field applied along the a axis. Two distinct frequencies indicate two separate changes in the Fermi-surface topology, likely connected with Lifshitz transitions. We discuss the origin of these oscillations in terms of magnetic breakdown, quantum interference, and other potential mechanisms.

The electrical resistivity of the unconventional superconductor UTe$_2$ shows very anisotropic behavior in the normal state depending on the current direction. In the present paper we show that the maximum in the resistivity $\rho_c$ for current applied along the $c$ axis at $T^{\rm max}_{\rho_c} \approx 14.75$~K follows the minimum in the thermal expansion $T_\alpha^\star$ along $b$ axis. Under a magnetic field applied along the $b$ axis, $T^{\rm max}_{\rho_c}$ can be tracked up to the critical point of the first order metamagnetic transition, which is located near 6~K and 34.5~T. Surprisingly, at the metamagnetic field $H_m$ the resistivity $\rho_c$ shows a steplike decrease while the resistivities $\rho_a$ and $\rho_b$, for current along the $a$ and $b$ axis, respectively, show a steplike increase. Under hydrostatic pressure $T^{\rm max}_{\rho_c}$ and $H_m$ decrease significantly up to the critical pressure $p_c$ at which superconductivity is suppressed and a long range antiferromagnetic order appears. We show that the phase diagram at different pressures can be scaled by $T^{\rm max}_{\rho_c}$ in field and temperature suggesting that this temperature scale is governing the main interactions in the normal state.

Abstract The potential spin-triplet heavy-fermion superconductor UTe2 exhibits signatures of multiple distinct superconducting phases. For field aligned along the b axis, a metamagnetic transition occurs at μ 0 H m ≈ 35 T. It is associated with magnetic fluctuations that may be beneficial for the field-reinforced superconductivity surviving up to H m. Once the field is tilted away from the b towards the c axis, a reentrant superconducting phase emerges just above H m. In order to better understand this remarkably field-resistant superconducting phase, we conducted magnetic-torque and magnetotransport measurements in pulsed magnetic fields. We determine the record-breaking upper critical field of μ 0 H c2 ≈ 73 T and its evolution with angle. Furthermore, the normal-state Hall effect experiences a drastic suppression indicative of a reduced band polarization above H m in the angular range around 30° caused by a partial compensation between the applied field and an exchange field. This promotes the Jaccarino-Peter effect as a likely mechanism for the reentrant superconductivity above H m.

Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1 – 4 ). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands 2 , 5 – 10 . Their energy-level separation is typically hundreds of meV (refs. 3 , 6 , 11 ). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states 12 , 13 . Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu 2 Si 2 , which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14 ). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.

The recently discovered superconductor UTe$_2$, with a T$_c$ between 1.5~K and 2~K, is attracting much attention due to strong suspicion of spin-triplet and topological superconductivity. Its properties under magnetic field are also remarkable, with field-reinforced and field-induced superconducting phases. Here, we report the first complete thermodynamic determination of the phase diagram for fields applied along the three crystallographic directions. Measurements were performed up to 36~T along the hard magnetisation $b$~axis in order to follow the superconducting transition up to the metamagnetic transition at $H_{m} = 34.75$~T. They reveal the existence of a phase transition line within the superconducting phase, and drastic differences occurring between these two phases. Detailed analysis supports a different spin state between the two phases, implying a low-field spin-triplet to high-field spin-singlet transition, a unique case among superconductors, giving insight on the mechanisms leading to spin-triplet superconductivity.

book of the Young investigators online workshop on unconventional superconductivity in heavy fermions 17-19 of January, 2022

The recently discovered superconductor UTe 2 with a T c between 1.5 K and 2 K, has attracted much attention due to indications of spin-triplet and topological superconductivity. Its properties under magnetic field are also remarkable, with field-reinforced and field-induced superconducting phases. Here, we report the first complete thermodynamic determination of the phase diagram for fields applied along the three crystallographic directions. Measurements were performed up to 36 T along the hard b axis in order to follow the superconducting transition up to the metamagnetic transition at H m = 34 . 75 T. They demonstrate the existence of a phase transition line within the superconducting phase, and drastic differences occurring between these two phases. Detailed analysis supports a different spin state between the two phases, possibly a spin-triplet to spin-singlet transition.

Abstract The potential spin-triplet heavy-fermion superconductor UTe2 exhibits signatures of multiple distinct superconducting phases. For field aligned along the b axis a metamagnetic transition occurs at μ0Hm ≈ 35 T. It is associated with a spin reorientation inducing magnetic fluctuations that may be beneficial for the field-enhanced superconductivity surviving up to Hm. Once the field is tilted away from the b towards the c axis, a re-entrant superconducting phase emerges just above Hm(θ). However, under pressure this phase detaches from Hm. In order to better understand this remarkably field-resistant phase we investigate magnetic torque and electrical magnetotransport in pulsed magnetic fields. The observed zero-Hall signal evidences the superconducting nature of this distinct high-field phase. We determine its record-breaking upper critical field of μ0Hc2 ≈ 75 T. Furthermore, we provide evidence for a strong angle-dependent reduction of magnetic scattering, likely accompanied by changes in the electronic band structure induced by the tilted field.

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.

We report the magnetoresistance in the novel spin-triplet superconductor UTe2 under pressure close to the critical pressure Pc, where the superconducting phase terminates, for field along the three a, b and c-axes in the orthorhombic structure. The superconducting phase for H // a-axis just below Pc shows a field-reentrant behavior due to the competition with the emergence of magnetic order at low fields. The upper critical field Hc2 for H // c-axis shows a quasi-vertical increase in the H-T phase diagram just below Pc, indicating that superconductivity is reinforced by the strong fluctuations which persist even at high fields above 20T. Increasing pressure leads to the disappearance of superconductivity at zero field with the emergence of magnetic order. Surprisingly, field-induced superconductivity is observed at high fields, where a spin-polarized state is realized due to the suppression of the magnetic ordered phases; the spin-polarized state is favorable for superconductivity, whereas the magnetic ordered phase at low field seems to be unfavorable. The huge Hc2 in the spin-polarized state seems to imply a spin-triplet state. Contrary to the a- and c-axes, no field-reinforcement of superconductivity occurs for magnetic field along the b-axis. We compare the results with the field-reentrant superconductivity above the metamagnetic field, Hm for the field direction tilted by about 30 deg. from b to c-axis at ambient pressure as well as the field-reentrant (-reinforced) superconductivity in ferromagnetic superconductors, URhGe and UCoGe.

We investigate ytterbium gallium garnet Yb3Ga5O12 in the paramagnetic phase above the supposed magnetic transition at T-lambda approximate to 54 mK. Our study combines susceptibility and specific heat measurements with neutron scattering experiments and theoretical calculations. Below 500 mK, the elastic neutron response is strongly peaked in the momentum space. Along with that, the inelastic spectrum develops flat excitation modes. In magnetic field, the lowest energy branch follows a Zeeman shift in agreement with the field-dependent specific heat data. An intermediate state with spin canting away from the field direction is evidenced in small magnetic fields. In the field of 2 T, the total magnetization almost saturates and the measured excitation spectrum is well reproduced by the spin-wave calculations taking into account solely the dipole-dipole interactions. The small positive Curie-Weiss temperature derived from the susceptibility measurements is also accounted for by the dipolar spin model. Altogether, our results suggest that Yb3Ga5O12 is a quantum dipolar magnet.

W. Knafo, G. Knebel, P. Steffens, K. Kaneko, A. Rosuel, J.-P. Brison, J. Flouquet, D. Aoki, G. Lapertot, and S. Raymond LNCMI-EMFL, CNRS UPR3228, Univ. Grenoble Alpes, Univ. Toulouse, Univ. Toulouse 3, INSA-T, 143 Avenue de Rangueil, 31400 Toulouse, France Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, 38000, Grenoble, France Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble, France Materials Sciences Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan Institute for Materials Research, Tohoku University, Ibaraki 311-1313, Japan Univ. Grenoble Alpes, CEA, IRIG, MEM, MDN, 38000 Grenoble, France (Dated: June 25, 2021)

Since the mid-80s, new classes of superconductors have been discovered in which the origin of superconductivity cannot be attributed to the electron–ion interactions at the heart of conventional superconductivity. Most of these unconventional superconductors are strongly correlated electron systems, and identifying (or even more difficult, predicting) the precise superconducting state has been, and sometimes remains, an actual challenge. However, in most cases, it has been demonstrated that in these materials the spin state of the Cooper pairs is a singlet state, often associated with a ‘d-wave’ or ‘ s +/- ’ orbital state. For a few systems, a spin-triplet state is strongly suspected, like in superfluid ^3 He; this leads to a much more complex superconducting order parameter. This was long supposed to be the case for the d-electron system Sr _2 RuO _4 , and is very likely realized in some uranium-based (f-electron) ‘heavy fermions’ like UPt _3 (with multiple superconducting phases) or UGe _2 (with coexisting ferromagnetic order). Beyond the interest for these materials, p-wave superconductivity is presently quite fashionable for its topological properties and the prediction that it could host Majorana-like low energy excitations, seen as a route towards robust (topologically protected) qubits. The aim of these notes is to make students and experimentalists more familiar with the d-vector representation used to describe p-wave (spin triplet) superconductivity. The interest of this formalism will be illustrated on some systems where p-wave superconductivity is the prime suspect.

We investigate the spin dynamics in the superconducting phase of UTe$_{2}$ by triple-axis inelastic neutron scattering on a single crystal sample. At the wave-vector $\bf{k_1}$=(0, 0.57, 0), where the normal state antiferromagnetic correlations are peaked, a modification of the excitation spectrum is evidenced, on crossing the superconducting transition, with a reduction of the relaxation rate together with the development of an inelastic peak at $\Omega$ $\approx$ 1 meV. The low dimensional nature and the the $a$-axis polarization of the fluctuations, that characterise the normal state, are essentially maintained below $T_{sc}$. The high ratio $\Omega/k_{B}T_{sc}$ $\approx$ 7.2 contrasts with the most common behaviour in heavy fermion superconductors.