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

Investigation of the quantum phase transition in CeCu6-xAux

We report the DC magnetisation of the easy-plane ferrimagnet CeSi 1.81 for magnetic field in the range ± 0.5  T as a function of temperature T down to 2.3 K and hydrostatic pressure p up to 14.4 kbar. We observe that the magnetic moment for the crystallographic a-axis vanishes continuously at p c ≈ 13 ± 0.2 kbar . The variation of the ordered moment as function of pressure at low T is qualitatively similar to its variation as function of temperature at p = 0 , hinting at the possible existence of a ferromagnetic quantum critical point at p c .

Pressure-induced magnetic quantum phase transition in CeSi1.81

The magnetic properties of ${\mathrm{BaNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ are studied by electron paramagnetic resonance (EPR) and $^{51}\mathrm{V}$ nuclear magnetic resonance (NMR). The divergence of the $^{51}T_{1}$ rate on approaching ${T}_{\mathrm{N}}$ in the paramagnetic phase displays the exponential correlation length expected for the Berezinskii-Kosterlitz-Thouless transition. The critical power-law behavior can be restored by applying a strong magnetic field perpendicular to the hexagonal axis, destroying the $XY$ anisotropy. The comparison of the EPR and NMR measurements at several magnetic fields yields a consistent description in terms of the Berezinskii-Kosterlitz-Thouless scenario in the temperature range above the antiferromagnetic phase transition of ${\mathrm{BaNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$.

Determining the Berezinskii-Kosterlitz-Thouless coherence length in BaNi 2 V 2 O 8 by V 51 NMR

Heavy-fermion alloys at a magnetic instability

YBa 2 Cu 3 O 7-δ single crystals obtained from different laboratories and highly c -axis oriented films sputtered on sapphire have been investigated with specific heat measurements in the temperature range from 70 mK to 2 K. The specific heat C shows large variations in the absolute magnitude and temperature dependence even for samples with similar transition temperatures and transition widths. These apparently impurity-associated contributions to C can be modelled by a power-law dependence on T over a considerable range, with exponent n between 0.3 and 1. In an external magnetic field the impurity contribution decreases and n systematically increases in a way reminiscent of magnetic clusters or spin glasses.

Hilbert von Löhneysen

Papers

Investigation of the quantum phase transition in CeCu6-xAux

Pressure-induced magnetic quantum phase transition in CeSi1.81

Determining the Berezinskii-Kosterlitz-Thouless coherence length in BaNi 2 V 2 O 8 by V 51 NMR

Heavy-fermion alloys at a magnetic instability

Impurity contributions to the specific heat of YBa2Cu3O7−δ-single crystal below 1 K in magnetic fields up to 6 T