Heavy-fermion Superconductor URu2Si2 Research Articles

Quantum-well states at the surface of a heavy-fermion superconductor

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 bands2,5–10. 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 states12,13. 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 URu2Si2, 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.

Nodal gap structure of the heavy-fermion superconductor URu2Si2 revealed by field-angle-dependent specific-heat measurements

URu2Si2 is a promising candidate for a chiral d-wave superconductor whose gap is composed of a horizontal line node at equator and point nodes at the north and south poles. However, previous measurements of the specific heat and the thermal conductivity did not detect quasiparticle excitations from a horizontal line node in heavy-mass bands. Here, we have provided strong evidence for the presence of a horizontal line node from field-angle-dependent specific-heat measurements by using a high-quality single crystal of URu2Si2. We observed the behavior of the specific heat at low fields which does not depend on inplane field angle ϕ but shows a shoulder-like anomaly in the polar-angle θ dependence around θ ∼ 45°. This feature is more clearly seen at lower temperatures, suggesting the detection of low-energy quasiparticle excitations reflecting the gap structure. From theoretical analyses based on microscopic calculations, we have demonstrated that this anomaly can be explained by the existence of a horizontal line node at kz = 0. Thus, the gap structure of URu2Si2 matches well with the Eg chiral kz(kx + iky) symmetry.

Colossal thermomagnetic response in the exotic superconductor URu2Si2

The Nernst coefficient is a measure of the transverse thermoelectric effect in a conductor. Superconducting fluctuations magnify this effect but in URu2Si2, the million-fold enhancement suggests that the fluctuations have an exotic origin. The superconducting fluctuation effect, due to preformed Cooper pairs above the critical temperature Tc, has been generally understood by the standard Gaussian fluctuation theories in most superconductors1. The transverse thermoelectric (Nernst) effect is particularly sensitive to the fluctuations, and the large Nernst signal found in the pseudogap regime of the underdoped cuprates2,3 has raised much debate. Here we report on the observation of a colossal Nernst signal due to the superconducting fluctuations in the heavy-fermion superconductor URu2Si2. The Nernst coefficient is anomalously enhanced (by a factor of ∼106) as compared with the theoretically expected value of the Gaussian fluctuations. Moreover, contrary to the conventional wisdom, the enhancement is more significant with a reduction of the impurity scattering rate. This unconventional Nernst effect intimately reflects the highly unusual superconducting state of URu2Si2. The results invoke possible chiral or Berry-phase fluctuations associated with the broken time-reversal symmetry4,5,6,7 of the superconducting order parameter.

Scaling relation found in anomalous electrical transport and superconductivity of heavy fermion superconductor URu2Si2

The pressure dependent electrical resistivity of URu2Si2 has been studied at high pressure across the first order phase boundary of Px where the ground state switches under pressure from “hidden order” (HO) to large moment antiferromagnetic (LAFM) states. We have measured an ultra-clean single crystal whose quality is the highest among those used in previous studies. We have previously analyzed the resistivity data with the generalized power law ρ = ρ0 + AnTn. It was found that the electric transport property deviates from Fermi liquid theory in the HO phase but obeys the theory well above Px. In this paper, we re-analyze the data using the polynomial in T expression ρ = ρ0 + α1T + α2T2. The analysis finds the relation α1/α2 α Tsc in the HO phase. While the pressure dependence of α2 is very weak, α1 is roughly proportional to Tsc. This suggests a strong correlation between the anomalous quasiparticle scattering and the superconductivity and that both have a common origin. The present study clarifies a universality of the HO phase inherent in strongly correlated electron superconductors near quantum criticality.

Search for hidden order parameter of URu2Si2 by neutron-scattering experiment under uniaxial stress

Elastic neutron-scattering experiment was performed on the heavy-fermion superconductor URu2Si2 under uniaxial stress in order to search a sign of a hidden order parameter. Contour maps of neutron-scattering at 1.5 K were achieved by mesh scanning. No additional magnetic signal exists in (h0l) and (hhl) planes except for a well-known weak antiferromagnetic signal with magnetic-propagation vector of Q = (100) within the present experimental accuracy and scanned area.

The pressure-temperature phase diagram of URu2Si2 under hydrostatic conditions

AbstractThe pressure dependence of the hidden order phase of the heavy fermion superconductor URu2Si2 has been a subject of intense research since shortly after the discovery of the compound decades ago. Applied pressure increases the critical temperature of the paramagnetic / hidden order transition and brings about a transition to long-range antiferromagnetism. The reported pressures and temperatures of these phase boundaries vary between studies: 4 – 7 kbar at low temperature and 12 – 15 kbar at high temperature. We review experimental evidence that the measured values of pressure and temperature are very sensitive to the chosen pressure transmitting medium. Recent x-ray diffraction measurements suggest that the relative position of the silicon atom in the unit cell is changing as a function of pressure. Recent neutron diffraction measurements show that the zero-temperature limit of the hidden order / antiferromagnetic transition occurs at pressures greater than 7.5 kbar.

Novel mixed-state thermal transport properties in ultra-clean URu2Si2

The heavy-fermion superconductor URu2Si2 shows an intriguing increase of the thermal conductivity in the mixed-state immediately below the upper critical field Hc2 which is in a sharp contrast to common experience. A brief description of the origin of this behavior is given by focusing on the role of the semi-metallic Fermi surface reconstruction induced by the hidden order phase transition.

Vortex lattice melting in the ultraclean heavy-fermion superconductor URu2Si2

The vortex states and the quasiparticle dynamics in the ultraclean heavy-fermion superconductor URu2Si2 (Tc0=1.45 K) are studied by the electronic and thermal transport measurements. We find that a distinct vortex lattice melting transition, which is similar to that in high-Tc cuprates, occurs well below the mean-field upper critical field. The thermal fluctuations are exceptionally enhanced by very low carrier number with heavy mass even at sub-Kelvin temperatures. Additionally, we find a thermal conductivity anomaly below the melting transition, indicating enhancement of the quasiparticle mean free path possibly due to the formation of a novel quasiparticle Bloch state.

Thermal Transport in the Hidden-Order State ofURu2Si2

We present a study of thermal conductivity in the normal state of the heavy-fermion superconductor URu2Si2. Ordering at 18 K leads to a steep increase in thermal conductivity and (in contrast with all other cases of magnetic ordering in heavy-fermion compounds) to an enhancement of the Lorenz number. By linking this observation to several other previously reported features, we conclude that most of the carriers disappear in the ordered state and this leads to a drastic increase in both the phononic and electronic mean free path.

Inflection point in the magnetic field dependence of the ordered moment of URu2Si2 observed by neutron scattering in fields up to 17 T.

We have measured the magnetic field dependence of the ordered antiferromagnetic moment and the magnetic excitations in the heavy-fermion superconductor URu2Si2 for fields up to 17 T applied along the tetragonal c axis, using neutron scattering. The decrease of the magnetic intensity of the tiny moment with increasing field does not follow a simple power law, but shows a clear inflection point, indicating that the moment disappears first at the metamagnetic transition at approximately 40 T. This suggests that the moment m is connected to a hidden order parameter psi which belongs to the same irreducible representation breaking time-reversal symmetry. The magnetic excitation gap at the antiferromagnetic zone center Q = (1,0,0) increases continuously with increasing field, while that at Q = (1.4,0,0) is nearly constant. This field dependence is opposite to that of the gap extracted from specific-heat data.

Nonstationary Josephson effect for superconductors with spin-density waves

The nonstationary Josephson I, interference I, and quasiparticle J current amplitudes through symmetrical and nonsymmetrical ~ns! tunnel junctions involving partially dielectrized ~partially gapped! superconductors with spin-density waves ~SDW’s! and described by the dielectric order parameter S were calculated. Riedeltype singularities and jumps for all currents are determined by superconducting order parameter D , as well as S . It was shown that each current for symmetrical junctions, made up of thermodynamically identical SDW superconductors ~with uS leftu5uS rightu), can exhibit three possible current-voltage characteristics ~CVC’s! depending on the relationship between the electrodes’ S signs in the course of experiment: ~i! one symmetrical CVC for genuinely symmetrical configuration ~s! when the dielectric order parameters S left and S right have the same sign for both electrodes and ~ii! two nonsymmetrical ones for symmetrical junction in the state of broken symmetry ~bs! when S left and S right are opposite in sign. The actual setup choice is at random. Thus, the symmetrical junctions can serve as phase-sensitive indicators for the SDW’s. The ns junctions which include SDW and ordinary BCS superconductors are also studied. The current amplitudes Ins 1,2 and Jns are asymmetrical functions of the voltage V and depend on the sign of S . Our calculations reveal main features appropriate to CVC’s of tunnel junctions involving the heavy-fermion SDW superconductor URu2Si2. @S0163-1829~99!03742-X#

Neutron spin-echo study of URu2Si2

Abstract We have studied the magnetic correlations in the heavy-fermion superconductor URu2Si2 using high-resolution neutron spin-echo techniques. The measurements confirm previous results that the weak ordered moment flips the neutron spin, and hence is of dipolar origin. The spin-echo signal, with an energy resolution two orders of magnitude better than earlier neutron experiments, confirms the static nature of the moment, in agreement with muon measurements. In addition, we found evidence for the presence of rapidly fluctuating magnetic moments in the ordered phase, which are most likely at the origin of the enhancement of the linear term in the specific heat at low temperatures.

Unusual temperature dependence of the ordered moment in URu2Si2

Abstract We have performed neutron-scattering experiments in order to study the tiny magnetic moment in a heavy-fermion superconductor URu2Si2. The (1 0 0) magnetic Bragg peak intensity is found to be reduced by about 2% in magnitude below the superconducting transition temperature of about 1 K. This result indicates the interplay between magnetism and superconductivity in URu2Si2.

Anisotropy of Susceptibility and Optical investigation of the Antiferromagnetic phase Transition in U1-xCexRu2Si2

Temperature dependence of magnetic susceptibility of U 1 _x Ce.xRu2 Si2 single crystals (x = 0, 0.025, 0.05, 0.075) has been studied at temperatures from 4.2 K up to room temperature and in magnetic fields applied along and perpendicular to the c-axis. The attention was paid to anomalies connected with the antiferromagnetic phase transition, which are present in crystals with x < 0.05. Far-infrared measurements of U0,99 Ce0,01 Ru e Sit single crystal have been studied for the first time. The measurements support the assumption that the origin of magnetic ordering in U0.99 Ce0.01 Rue Sit is the same as in heavy-fermion superconductor URu2Si2 and can be interpreted as being due to a spin-density-wave gap.

Non-trivial magnetic order in URu2Si2?

We have searched for the hidden multispin order parameters that have been proposed to explain the weak ordered moment observed in the heavy-fermion superconductor URu2Si2. Since the exotic spin order is predicted to cause broken-symmetry Bragg peaks that develop rapidly with applied magnetic field, we have measured their strength in fields up to 8 T, for which a large easily observable moment is predicted. The Bragg neutron scattering is found to decrease rather than increase when a field is applied along the easy tetragonal c-axis, while there is no change for a field at right angles. The results rule out the proposed symmetric multispin order parameters. The zero-field transition is found to exhibit critical softening of the spin gap and a cusp in the susceptibility at TN, as expected for the ordering of magnetic dipoles.

Andreev reflections and Josephson effects in point contacts between the heavy fermion superconductor URu2Si2 and conventional superconductors

We have studied thedV/dI vs.V characteristics of point contacts between the heavy fermion superconductor URu2Si2 and the conventional superconductors Zn and NbTi. Contacts between URu2Si2 and Zn do not show Josephson effects; instead Andreev reflection type structures occur, which are related to both, the heavy fermion and the conventional superconductor. In contrast, contacts between URu2Si2 and NbTi become superconducting at low currents. A closed-loop setup with two NbTi contacts on URu2Si2 showed SQUID oscillations in a small magnetic field. Our data give evidence that the contacts should be described as superconductor/normal/superconductor junctions with a thick normal layer on the URu2Si2 side of the contact with proximity induced superconductivity in theN-layer in the case of NbTi. With such a model the occurrence or absence of superconductivity can be explained and also the suppression of Andreev-scattering which is frequently observed for contacts between heavy fermion superconductors and normal metals.

On the Néel temperature of URu2Si2 in high magnetic fields

Abstract Measurements of the magnetic force and torque acting on a polycrystalline sample of the heavy-fermion superconductor URu2Si2 are presented. These measurements are made with a capacitive magnetometer in the vicinity of the antiferromagnetic transition near 17 K, in magnetic fields to 100 kOe. The temperature-dependent susceptibility derived from the magnetic torque is in reasonable agreement with measurements made on a commercial superconducting-quantum-interference-device-based magnetometer. As the field is increased, a depression of the antiferromagnetic transition to lower temperatures is observed, a depression which is consistent with that expected for a spin-density wave.

Thermal conductivity of F-electron systems ErO4Ho0.6Rh4B4 and URu2Si2

We have measured the thermal conductivity of the reentrant ferromagnetic superconductor Er0.4Ho0.6Rh4B4 and the heavy fermion superconductor URu2Si2. For these two materials thermal conduction behaves in a very different form. We can explain the thermal conductivity of Er0.4Ho0.6Rh4B4 in terms of BCS theory, but in URu2Si2 we find a behaviour that clearly suggest unconventional superconductivity. A comparison with results in UPt3 allows us to speculate with the possibility of p-wave or d-wave superconductivity.

Anisotropy of the upper critical field in the magnetic heavy-fermion superconductor URu2Si2

Measurements have been performed of the upper critical field Hc2 anisotropy in the magnetic heavy-fermion superconductor URu2Si2. The dHc2/dT value is constant within 5% when H is rotated in the basal plane, whereas ‖dHc2/dT‖ decreases by about 35% for H rotated by 20°–30° out of the basal plane. Contrary to CeCu2Si2 the Hc2 anisotropy in URu2Si2 is enhanced as temperature decreases below Tc. This disparity can be attributed to the different strengths of paramagnetic and spin-orbit effects responsible for the suppression of superconductivity by a magnetic field in CeCu2Si2 and URu2Si2.