Thermal transport in the hidden-order state of URu2Si2

Directional ballistic transport in the two-dimensional metal PdCoO2

In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO₂ yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.

Isoelectronic perturbations to f-d-electron hybridization and the enhancement of hidden order in URu2Si2

Electrical resistivity measurements were performed on single crystals of URu2-x Os x Si2 up to x = 0.28 under hydrostatic pressure up to P = 2 GPa. As the Os concentration, x, is increased, 1) the lattice expands, creating an effective negative chemical pressure Pch(x); 2) the hidden-order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase; and 3) less external pressure Pc is required to induce the HO→LMAFM phase transition. We compare the behavior of the T(x, P) phase boundary reported here for the URu2-x Os x Si2 system with previous reports of enhanced HO in URu2Si2 upon tuning with P or similarly in URu2-x Fe x Si2 upon tuning with positive Pch(x). It is noteworthy that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first-order transition to the LMAFM phase in URu2Si2 We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5f-electron and transition metal d-electron states which leads to electronic instability in the paramagnetic phase and the concurrent formation of HO (and LMAFM) in URu2Si2 Calculations in the tight-binding approximation are included to determine the strength of hybridization between the U-5f-electron states and the d-electron states of Ru and its isoelectronic Fe and Os substituents in URu2Si2.

Evidence for a nematic component to the hidden-order parameter in URu2Si2 from differential elastoresistance measurements

For materials that harbour a continuous phase transition, the susceptibility of the material to various fields can be used to understand the nature of the fluctuating order and hence the nature of the ordered state. Here we use anisotropic biaxial strain to probe the nematic susceptibility of URu2Si2, a heavy fermion material for which the nature of the low temperature 'hidden order' state has defied comprehensive understanding for over 30 years. Our measurements reveal that the fluctuating order has a nematic component, confirming reports of twofold anisotropy in the broken symmetry state and strongly constraining theoretical models of the hidden-order phase.

Symmetry of the excitations in the hidden order state of URu2Si2

We perform polarized electronic Raman scattering on URu2Si2 single crystals at low temperature down to 8 K in the hidden-order state and under a magnetic field up to 10 T. The hidden-order state is characterized by a sharp excitation at 1.7 meV and a gap in the electronic continuum below 6.8 meV. Both Raman signatures are of pure A2g symmetry. By comparing the behavior of the Raman sharp excitation and the neutron resonance at Q0=(0,0,1), we provide new evidence, constrained by selection rules of the two probes, that the hidden-order state breaks the translational symmetry along the c axis such that Γ and Z points fold on top of each other. The observation of these distinct Raman features with a peculiar A2g symmetry as a signature of the hidden-order phase places strong constraints on current theories of the hidden-order in URu2Si2.

Momentum-resolved hidden-order gap reveals symmetry breaking and origin of entropy loss in URu2Si2

Spontaneous symmetry breaking in physical systems leads to salient phenomena at all scales, from the Higgs mechanism and the emergence of the mass of the elementary particles, to superconductivity and magnetism in solids. The hidden-order state arising below 17.5 K in URu2Si2 is a puzzling example of one of such phase transitions: its associated broken symmetry and gap structure have remained longstanding riddles. Here we directly image how, across the hidden-order transition, the electronic structure of URu2Si2 abruptly reconstructs. We observe an energy gap of 7 meV opening over 70% of a large diamond-like heavy-fermion Fermi surface, resulting in the formation of four small Fermi petals, and a change in the electronic periodicity from body-centred tetragonal to simple tetragonal. Our results explain the large entropy loss in the hidden-order phase, and the similarity between this phase and the high-pressure antiferromagnetic phase found in quantum-oscillation experiments.

Momentum-resolved evolution of the Kondo lattice into "hidden order" in URu2Si2

We study, using high-resolution angle-resolved photoemission spectroscopy, the evolution of the electronic structure in URu2Si2 at the Γ, Z, and X high-symmetry points from the high-temperature Kondo-screened regime to the low-temperature hidden-order (HO) state. At all temperatures and symmetry points, we find structures resulting from the interaction between heavy and light bands related to the Kondo-lattice formation. At the X point, we directly measure a hybridization gap of 11 meV already open at temperatures above the ordered phase. Strikingly, we find that while the HO induces pronounced changes at Γ and Z, the hybridization gap at X does not change, indicating that the hidden-order parameter is anisotropic. Furthermore, at the Γ and Z points, we observe the opening of a gap in momentum in the HO state, and show that the associated electronic structure results from the hybridization of a light electron band with the Kondo-lattice bands characterizing the paramagnetic state.

Cyclotron resonance in the hidden-order phase of URu2Si2

We report the first observation of cyclotron resonance in the hidden-order phase of ultraclean URu2Si2 crystals, which allows the full determination of angle-dependent electron-mass structure of the main Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance line under in-plane magnetic-field rotation. This is most naturally explained by the domain formation, which breaks the fourfold rotational symmetry of the underlying tetragonal lattice. The results reveal the emergence of an in-plane mass anisotropy with hot spots along the [110] direction, which can account for the anisotropic in-plane magnetic susceptibility reported recently. This is consistent with the "nematic" Fermi liquid state, in which itinerant electrons have unidirectional correlations.

Gross violation of the Wiedemann-Franz law in a quasi-one-dimensional conductor

When charge carriers are spatially confined to one dimension, conventional Fermi-liquid theory breaks down. In such Tomonaga-Luttinger liquids, quasiparticles are replaced by distinct collective excitations of spin and charge that propagate independently with different velocities. Although evidence for spin-charge separation exists, no bulk low-energy probe has yet been able to distinguish successfully between Tomonaga-Luttinger and Fermi-liquid physics. Here we show experimentally that the ratio of the thermal and electrical Hall conductivities in the metallic phase of quasi-one-dimensional Li(0.9)Mo(6)O(17) diverges with decreasing temperature, reaching a value five orders of magnitude larger than that found in conventional metals. Both the temperature dependence and magnitude of this ratio are consistent with Tomonaga-Luttinger liquid theory. Such a dramatic manifestation of spin-charge separation in a bulk three-dimensional solid offers a unique opportunity to explore how the fermionic quasiparticle picture recovers, and over what time scale, when coupling to a second or third dimension is restored.

Modulated spin liquid: a new paradigm for URu2Si2

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.

Rotational symmetry breaking in the hidden-order phase of URu2Si2

A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden-order" phase transition in the heavy-fermion compound URu(2)Si(2), at transition temperature T(h) = 17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below T(h), which breaks the four-fold rotational symmetry of the tetragonal URu(2)Si(2). Two-fold oscillations in the magnetic torque under in-plane field rotation were sensitively detected in small pure crystals. Our findings suggest that the hidden-order phase is an electronic "nematic" phase, a translationally invariant metallic phase with spontaneous breaking of rotational symmetry.

The suppression of hidden order and the onset of ferromagnetism in URu2Si2 via Re substitution

Substitution of Re for Ru in the heavy fermion compound URu(2)Si(2) suppresses the hidden order transition and gives rise to ferromagnetism at higher concentrations. The hidden order transition of URu(2 - x)Re(x)Si(2), tracked via specific heat and electrical resistivity measurements, decreases in temperature and broadens, and is no longer observed for x > 0.1. A critical scaling analysis of the bulk magnetization indicates that the ferromagnetic ordering temperature and ordered moment are suppressed continuously towards zero at a critical concentration of x ≈ 0.15, and this is accompanied by the additional suppression of the critical exponents γ and δ - 1 towards zero. This unusual trend appears to reflect the underlying interplay between Kondo and ferromagnetic interactions, and perhaps the proximity of the hidden order phase.

Possible phase transition deep inside the hidden order phase of ultraclean URu2Si2

To elucidate the underlying nature of the hidden order (HO) state in heavy-fermion compound URu(2)Si(2), we measure electrical transport properties of ultraclean crystals in a high field, low temperature regime. Unlike previous studies, the present system with much less impurity scattering resolves a distinct anomaly of the Hall resistivity at H;{*} = 22.5 T, well below the destruction field of the HO phase = or approximately 36 T. In addition, a novel quantum oscillation appears above a magnetic field slightly below H;{*}. These results indicate an abrupt reconstruction of the Fermi surface, which implies a possible phase transition well within the HO phase caused by a band-dependent destruction of the HO parameter.

Hidden order in URu2Si2 originates from Fermi surface gapping induced by dynamic symmetry breaking

Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter driving the transition. The notion of a 'hidden order' has recently been used for a variety of materials where a clear phase transition occurs without a known order parameter. The prototype example is the heavy-fermion compound URu(2)Si(2), where a mysterious hidden-order transition occurs at 17.5 K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Here, we provide a microscopic explanation of the hidden order using density-functional theory calculations. We identify the Fermi surface 'hot spots' where degeneracy induces a Fermi surface instability and quantify how symmetry breaking lifts the degeneracy, causing a surprisingly large Fermi surface gapping. As the mechanism for the hidden order, we deduce spontaneous symmetry breaking through a dynamic mode of antiferromagnetic moment excitations.

Flux line lattice melting and the formation of a coherent quasiparticle Bloch state in the ultraclean URu2Si2 superconductor

We find that in the ultraclean heavy-fermion superconductor URu(2)Si(2) (T_{c0}=1.45 K) a distinct flux line lattice melting transition with outstanding characters occurs well below the mean-field upper critical fields. We show that a very small number of carriers with heavy mass in this system results in exceptionally large thermal fluctuations even at sub-Kelvin temperatures, which are witnessed by a sizable region of the flux line liquid phase. The uniqueness is further highlighted by an enhancement of the quasiparticle mean free path below the melting transition, implying a possible formation of a quasiparticle Bloch state in the periodic flux line lattice.

Competing ordered phases in URu2Si2: hydrostatic pressure and rhenium substitution

A persistent kink in the pressure dependence of the "hidden order" (HO) transition temperature of URu(2-x)RexSi2 is observed at a critical pressure P(c)=15 kbar for 0 <or= x <or= 0.08. In URu2Si2, the kink at P(c) is accompanied by the destruction of superconductivity, a change in the magnitude of a spin excitation gap, determined from electrical resistivity measurements; and a complete gapping of a portion of the Fermi surface (FS), inferred from a change in scattering and the competition between the HO state and superconductivity for FS fraction.

Exotic superconducting properties in the electron-hole-compensated heavy-fermion "Semimetal" URu2Si2

We show that the charge and thermal transport measurements on ultraclean crystals of URu2Si2 reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first-order transition at Hc2 with a reduction of entropy flow. This is a consequence of multiband superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.

Field-induced Fermi surface reconstruction and adiabatic continuity between antiferromagnetism and the hidden-order state in URu2Si2

Shubnikov-de Haas oscillations reveal at high fields an abrupt reconstruction of the Fermi surface within the hidden-order (HO) phase of URu2Si2. Taken together with reported Hall effect results, this implies an increase in the effective carrier density and suggests that the field suppression of the HO state is ultimately related to destabilizing a gap in the spectrum of itinerant quasiparticles. While hydrostatic pressure favors antiferromagnetism in detriment to the HO state, it has a modest effect on the complex H-T phase diagram. Instead of phase separation between HO and antiferromagnetism our observations indicate adiabatic continuity between both orderings with field and pressure changing their relative weight.

Nernst effect in semimetals: the effective mass and the figure of merit

We present a study of electric, thermal, and thermoelectric transport in elemental bismuth, which presents a Nernst coefficient much larger than what was found in correlated metals. We argue that this is due to the combination of an exceptionally low carrier density with a very long electronic mean-free path. The low thermomagnetic figure of merit is traced to the lightness of electrons. Heavy-electron semimetals, which keep a metallic behavior in the presence of a magnetic field, emerge as promising candidates for thermomagnetic cooling at low temperatures.

Interplay between fermi surface topology and ordering in URu2Si2 revealed through abrupt hall coefficient changes in strong magnetic fields

Temperature- and field-dependent measurements of the Hall effect of pure and 4% Rh-doped URu2Si2 reveal low density (0.03 hole/U) high mobility carriers to be unique to the "hidden order" phase and consistent with an itinerant density-wave order parameter. The Fermi surface undergoes a series of abrupt changes as the magnetic field is increased. When combined with existing de Haas-van Alphen data, the Hall data expose a strong interplay between the stability of the "hidden order," the degree of polarization of the Fermi liquid, and the Fermi surface topology.

Phonon thermal transport of URu2Si2: broken translational symmetry and strong-coupling of the "hidden order" to the lattice

A dramatic increase in the total thermal conductivity (kappa) is observed in the hidden order (HO) state of single crystal URu2Si2. Through measurements of the thermal Hall conductivity, we explicitly show that the electronic contribution to kappa is extremely small, so that this large increase in kappa is dominated by phonon conduction. An itinerant BCS or mean-field model describes this behavior well: the increase in kappa is associated with the opening of a large energy gap at the Fermi surface, thereby decreasing electron-phonon scattering. Our analysis implies that the "hidden order" parameter is strongly coupled to the lattice, suggestive of a broken symmetry involving charge degrees of freedom.

Drastic change in transport of entropy with quadrupolar ordering in

The antiferroquadrupolar ordering of is explored by probing thermal and thermoelectric transport. The lattice thermal conductivity drastically increases with the ordering, as a consequence of a large drop in carrier concentration and a strong electron-phonon coupling. The low level of carrier density in the ordered state is confirmed by the anomalously large values of the Seebeck and Nernst coefficients. The results are reminiscent of and suggest that both belong to the same class of partial metal-insulator transitions. The magnitude of the Nernst coefficient, larger than in any other metal, indicates a new route for Ettingshausen cooling at Kelvin temperatures.

Irreversible dynamics of the phase boundary in U(Ru0.96Rh0.04)2Si2 and implications for ordering

We report measurements and analysis of the specific heat and magnetocaloric effect-induced temperature changes at the phase boundary into the single magnetic field-induced phase (phase II) of U(Ru0.96Rh0.04)2Si2, which yield irreversible properties similar to those at the valence transition of Yb(1-x)Y(x)InCu4. To explain these similarities, we propose a bootstrap mechanism by which lattice parameter changes caused by an electric quadrupolar order parameter within phase II become coupled to the 5f-electron hybridization, giving rise to a valence change at the transition.