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1 arXiv:1305.5487v1 [cond-mat.quant-gas] 1 arXiv:1305.5487v1 [cond-mat.quant-gas]

Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope to examine the novel electronic states that emerge from the uranium f states in URu 2 Si 2 . We find that, as the temperature is lowered, partial screening of the f electrons' spins gives rise to a spatially modulated Kondo-Fano resonance that is maximal between the surface U atoms. At T ¼ 17.5 K, URu 2 Si 2 is known to undergo a second-order phase transition from the Kondo lattice state into a phase with a hidden order parameter. From tunneling spectroscopy, we identify a spatially modulated, bias-asymmetric energy gap with a mean-field temperature dependence that develops in the hidden order state. Spectroscopic imaging further reveals a spatial correlation between the hidden order gap and the Kondo resonance, suggesting that the two phenomena involve the same electronic states.heavy fermion | scanning tunneling spectroscopy A remarkable variety of collective electronic phenomena have been discovered in compounds with partially filled f orbitals, where electronic excitations act as heavy fermions (1, 2). Like other correlated electronic systems, such as the high temperature superconducting cuprates, several of the heavy fermion compounds display an interplay between magnetism and superconductivity and have a propensity toward superconducting pairing with unconventional symmetry (1-5). However, unlike cuprates, or the newly discovered ferropnictides, the heavy fermion systems do not suffer from inherent dopant-induced disorder and offer a clean material system for the study of correlated electrons. The local f electrons interact both with the itinerant spd electrons as well as with each other, resulting in a rich variety of electronic phases. In many of these materials, screening of the local moments by the Kondo effect begins at relatively high temperatures resulting in a heavy fermion state at low temperatures. Exchange interactions between the local moments become more important at lower temperatures and can result in the formation of magnetic phases as well as superconductivity at even lower temperatures. Among the heavy fermion compounds perhaps the most enigmatic is the URu 2 Si 2 system, which undergoes a second-order phase transition with a rather large change in entropy (6-8) at 17.5 K from a paramagnetic phase with Kondo screening to a phase with an unknown order parameter (9). This material possesses low-energy commensurate and incommensurate spin excitations, which are gapped below the hidden order (HO) transition temperature (10-13). These features are believed to be signatures of a more complex order parameter, the identification of which has so far not been possible despite numerous investigations (12-18). Moreover, analogous to other correlated systems, this unusual conducting phase is transformed into an unconventional superconducting state at 1.5 K (6,8,19), the understanding of which hinges on fo...

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In few-body physics, Efimov states are an infinite series of three-body bound states that obey universal discrete scaling symmetry when pairwise interactions are resonantly enhanced. Despite abundant reports of Efimov states in recent cold atom experiments, direct observation of the discrete scaling symmetry remains an elusive goal. Here we report the observation of three consecutive Efimov resonances in a heteronuclear Li-Cs mixture near a broad interspecies Feshbach resonance. The positions of the resonances closely follow a geometric series 1, λ, λ 2 . The observed scaling constant λexp = 4.9(4) is in good agreement with the predicted value of 4.88.The emergence of scaling symmetry in physical phenomena suggests a universal description that is insensitive to microscopic details. Well-known examples are critical phenomena, which are universal and invariant under continuous scaling transformations [1]. Equally intriguing are systems with discrete scaling symmetry, which are invariant under scaling transformations with a specific scaling constant [2]; a classic example is the selfsimilar growth of crystals, as in snowflakes. Surprisingly, such discrete scaling symmetry also manifests in the infinite series of three-body bound states that Vitaly Efimov predicted in 1970 [3].In the Efimov scenario, while pairs of particles with short-range resonant interactions cannot be bound, there exists an infinite series of three-particle bound states. These bound states have universal properties that are insensitive to the details of the molecular potential and display discrete scaling symmetry; the size R n and binding energy E n of the Efimov state with the nth lowest energy scale geometrically as R n = λR n−1 and E n = λ −2 E n−1 , where λ is the scaling constant. An alternative picture to understand discrete scaling symmetry is based on renormalization group limit cycles [4]. Away from the two-body scattering resonance, Efimov states couple to the scattering continuum and induce a series of threebody scattering resonances at scattering lengths a (n) − < 0, which also follow the scaling law a (Fig. 1)