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Register a new userDetailed optical spectroscopy of the hybridization gap and the hidden order transition in high quality URu$_{2}$Si$_{2}$ single crystals
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We present a detailed temperature and frequency dependence of the optical conductivity measured on clean high quality single crystals of URu$_{2}$Si$_{2}$ of $ac$- and $ab$-plane surfaces. Our data demonstrate the itinerant character of the narrow 5f bands, becoming progressively coherent as temperature is lowered below a cross-over temperature $T^*{sim}75~K$. $T^*$ is higher than in previous reports as a result of a different sample preparation, which minimizes residual strain. We furthermore present the density-response (energy-loss) function of this compound, and determine the energies of the heavy fermion plasmons with $a$-and $c$-axis polarization. Our observation of a suppression of optical conductivity below 50~meV both along $a$ and $c$-axis, along with a heavy fermion plasmon at 18~meV, points toward the emergence of a band of coherent charge carriers crossing the Fermi energy and the emergence of a hybridization gap on part of the Fermi surface. The evolution towards coherent itinerant states is accelerated below the hidden order temperature $T_{HO}=17.5$~K. In the hidden order phase the low frequency optical conductivity shows a single gap at $sim 6.5$meV, which closes at $T_{HO}$.
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In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave-function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic, and still unsolved, example is the transition of the heavy fermion compound URu$_2$Si$_2$ (URS) into the so-called hidden-order (HO) phase when the temperature drops below $T_0 = 17.5$K. Here we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a non-rigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO-to-AFM phase transition.
Electrical resistivity measurements were performed on single crystals of URu$_2-x$Os$_x$Si$_2$ 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 $P_{ch}$($x$), (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 $P_{c}$ is required to induce the HO to LMAFM phase transition. We compare the $T(x)$, $T(P)$ phase behavior reported here for the URu$_2-x$Os$_x$Si$_2$ system with previous reports of enhanced HO in URu$_2$Si$_2$ upon tuning with $P$, or similarly in URu$_2-x$Fe$_x$Si$_2$ upon tuning with positive $P_{ch}$($x$). It is noted 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 URu$_2$Si$_2$. 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-5$f$- and transition metal $d$-electron states which leads to electronic instability in the paramagnetic phase and a concurrent stability of HO (and LMAFM) in URu$_2$Si$_2$. Calculations in the tight binding approximation are included to determine the strength of hybridization between the U-5$f$ electrons and each of the isoelectronic transition metal $d$-electron states of Fe, Ru, and Os.
We measured the polarized optical conductivity of URu$_2$Si$_2$ from room temperature down to 5 K, covering the Kondo state, the coherent Kondo liquid regime, and the hidden-order phase. The normal state is characterized by an anisotropic behavior between the ab plane and c axis responses. The ab plane optical conductivity is strongly influenced by the formation of the coherent Kondo liquid: a sharp Drude peak develops and a hybridization gap at 12 meV leads to a spectral weight transfer to mid-infrared energies. The c axis conductivity has a different behavior: the Drude peak already exists at 300 K and no particular anomaly or gap signature appears in the coherent Kondo liquid regime. When entering the hidden-order state, both polarizations see a dramatic decrease in the Drude spectral weight and scattering rate, compatible with a loss of about 50 % of the carriers at the Fermi level. At the same time a density-wave like gap appears along both polarizations at about 6.5 meV at 5 K. This gap closes respecting a mean field thermal evolution in the ab plane. Along the c axis it remains roughly constant and it fills up rather than closing.
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu$_2$Si$_2$.
A second-order phase transition is associated with emergence of an order parameter and a spontaneous symmetry breaking. For the heavy fermion superconductor URu$_2$Si$_2$, the symmetry of the order parameter associated with its ordered phase below 17.5 K has remained ambiguous despite 30 years of research, and hence is called hidden order (HO). Here we use polarization resolved Raman spectroscopy to specify the symmetry of the low energy excitations above and below the HO transition. These excitations involve transitions between interacting heavy uranium 5f orbitals, responsible for the broken symmetry in the HO phase. From the symmetry analysis of the collective mode, we determine that the HO parameter breaks local vertical and diagonal reflection symmetries at the uranium sites, resulting in crystal field states with distinct chiral properties, which order to a commensurate chirality density wave ground state.
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