There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity-which cannot be explained by weak electron-phonon interactions-in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°-the first 'magic' angle-the electronic band structure of this 'twisted bilayer graphene' exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature-carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

Unconventional superconductivity in magic-angle graphene superlattices

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

Magnetic ordering of CePt5

One of the most successful paradigms of many-body physics is the concept of quasiparticles: excitations in strongly interacting matter behaving like weakly interacting particles in free space. Quasiparticles in metals are very robust objects. Nevertheless, when a system’s ground state undergoes a qualitative change at a quantum critical point (QCP)1, the quasiparticles may disintegrate and give way to an exotic quantum-fluid state of matter. The nature of this breakdown is intensely debated2–5, because the emergent quantum fluid dominates material properties up to high temperatures and might even be related to the occurrence of superconductivity in some compounds6. Here we trace the dynamics of heavy-fermion quasiparticles in CeCu6−xAux and monitor their evolution towards the QCP in time-resolved experiments, supported by many-body calculations. A terahertz pulse disrupts the many-body heavy-fermion state. Under emission of a delayed, phase-coherent terahertz reflex the heavy-fermion state recovers, with a coherence time 100 times longer than typically associated with correlated metals7,8. The quasiparticle weight collapses towards the QCP, yet its formation temperature remains constant—phenomena believed to be mutually exclusive. Coexistence in the same experiment calls for revisions in our view on quantum criticality. Using terahertz pulses, the quasiparticle dynamics of the heavy-fermion compound CeCu6−xAu are investigated in the vicinity of its quantum critical point.

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Time-resolved collapse and revival of the Kondo state near a quantum phase transition

While CeCu6 does not show long-range magnetic order, the intersite magnetic correlations in CeCu6 developing below 1 K are destroyed in a magnetic field of B ≈ 2 T as evidenced by distinct maximum in the derivative of the magnetization M, d M d B versus B, which vanishes for T > 0.6 K. This metamagnetic-like transition thus appears to be a common feature of heavy-fermion systems without long-range magnetic order. CeCu6−xAux alloys show long-range antiferromagnetic order for x > 0.1, e.g., TN = 0.48 K for x = 0.3 and 0.95 K for x = 0.5. The increase in the CeCe distance with x stabilizes the Ce moments against formation of local Kondo singlets. The alloys have a similar easy-axis anisotropy as pure CeCu6. TN is suppressed strongly for B∥c, while it hardly changes for B∥b. Likewise, the reduction of the specific heat C below TN shows the same directional dependence. Even for x = 0.5, the Kondo compensation affects the magnetization ( M ⋍1 μ B Ce atom in 6 T at 0.15 K) and the specific heat ( C T ≃2.3 J/mol K 2 for T→0).

Magnetic correlations and magnetic ordering in CeCu6−xAux single crystals

We have observed interaction effects in the differential conductance $G$ of short, disordered metal bridges in a well-controlled non-equilibrium situation, where the distribution function has a double Fermi step. A logarithmic scaling law is found both for the temperature and for the voltage dependence of $G$ in all samples. The absence of magnetic field dependence and the low dimensionality of our samples allow us to distinguish between several possible interaction effects, proposed recently in nanoscopic samples. The universal scaling curve is explained quantitatively by the theory of electron-electron interaction in diffusive metals, adapted to the present case, where the sample size is smaller than the thermal diffusion length.

Hilbert von Löhneysen

Papers

Magnetic ordering of CePt5

Time-resolved collapse and revival of the Kondo state near a quantum phase transition

Magnetic correlations and magnetic ordering in CeCu6−xAux single crystals

Nonequilibrium electronic transport and interaction in short metallic nanobridges

Electrical resistance and magnetoresistance of pyrocarbon at low temperatures in fields up to 14 Tesla