Topological Physics: Hot Quantum Spin Hall Effect

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TOPOLOGICAL PHYSICS It can smear or even qualitatively change the found its way into general physics curricula Hot quantum spin Hall effect expected experimental signatures, such as and textbooks quite yet. Science 359, 76–79 (2018). the divergence of the correlation length close Gittes’s contribution might help to change to phase transitions. This has motivated the that. It shows that the Jarzynski equality The quantum spin Hall effect is a unique phase search for homogeneous gases, a goal that implies both Einstein’s classical relation of matter in which the bulk of the material is has been achieved previously for fermions in between diffusion and drag coefficients an insulator, but topological quantum states three dimensions. in Brownian motion and his results on exist at the edges — carrying up spins and Now, Klaus Hueck and colleagues have absorption and emission in quantum two- down spins in opposite directions. If these reduced the dimension to two, by making a state systems. Adding to the scope, the latter edge states can be controlled, they may have homogeneous sheet of Fermi gas well suited connection is obtained without explicit applications in spintronic devices. to investigating the interplay between reduced reference to the bosonic nature of photons, This phase was recently confirmed in dimensionality and strong interactions whereas the former leads to apparently a two-dimensional crystal by Sanfeng Wu in quantum many-body systems. As a paradoxical, but explained, behaviour in the and collaborators in an experiment that first benchmark experiment, Hueck et al. macroscopic limit. AHT measured the properties of the edge states in measured the two-dimensional equation of APPLIED MATHEMATICS monolayer WTe2. In particular, they saw the state and the momentum distribution in the quantized electronic conductance associated non-interacting case, showing a textbook The discovery of skewness with the edge states, which vanished when a example of statistical physics. Introducing eLife 6, e30212 (2017). magnetic field was applied and the edge states an attractive interaction, atoms form tightly were destroyed. bound dimers and a macroscopic occupation The edge states persisted at temperatures of low-momentum modes compatible up to 100 K, which is much easier to with Berezinskii–Kosterlitz–Thouless achieve in the laboratory than the liquid superfluidity. YL helium temperatures that were previously needed to observe them in semiconductor STATISTICAL MECHANICS heterostructures. That, and the fact that the Einstein by implication naturally two-dimensional nature of WTe2 Am. J. Phys. 86, 31–35 (2018). makes it easier to synthesize and process in devices, indicates that the quantum spin There is something irresistible about

Hall effect can be employed in more exotic Albert Einstein — no matter how often his / PHOTOGRAPHY PLACES CHRIS HOWES/WILD PHOTO STOCK ALAMY contexts in the near future. DA results are confirmed or revisited in fresh contexts, having a theoretical or experimental Most of us remember the frustration of trying ULTRA-COLD GASES finding anchored to Einstein’s works lets to complete a collection of cards or stamps — A homogeneous sheet us rest, it seems, a tad easier. But such you can never find the last one. In probability Phys. Rev. Lett. (in the press); preprint at connections can be rather inspiring, too, as theory, this is known as the coupon collector’s https://arxiv.org/abs/1704.06315 Fred Gittes has proven. problem: owing to those long waits, the Gittes derived two distinctly different probability of completing a collection after a Ultracold atomic gases have long served as a results from Einstein’s opus using the certain number of random draws is skewed textbook paradigm of many-body physics, Jarzynski equality, a general relation between to the right. Now it seems that the very same allowing studies of, say, Bose–Einstein the change in free energy of a system and process may be at the origin of the incubation condensation and superfluidity, in clean and the amount of irreversible work performed time for many diseases. well-controlled environments. However, on it. That equality, introduced in 1997, has Take measles, polio or leukemia: extremely the spatial inhomogeneity caused by the become central in several branches of non- different diseases, and yet their incubation external harmonic trap can be problematic. equilibrium thermodynamics, but has not periods all follow an approximately log- normal distribution. Clinical experiments LASERS have ruled out the heterogeneity of conditions, such as patients’ resilience, as the Scalable vortices ACS Nano https://doi.org/ch7x (2018) reason for this phenomenon. Instead, Bertrand Ottino-Loffler One promising way of controlling light waves is by topologically structuring laser beams with and colleagues modelled the disease vortices. A helical wavefront and a central phase singularity then make the light amenable progression as that of a pathogen invading to ultrahigh-resolution microscopy, and its optical angular momentum can be used to store a network-structured population of cells. and transfer information — offering scope for holographic applications and 3D displays. But A right-skewed, approximately log-normal existing implementations operate in the unfavourable infrared frequency range and claim incubation time would naturally appear if limited control over the angular momentum. Now, Thomas Krauss and co-workers have symptoms were assumed to emerge just as developed an integrated approach that provides access to miniaturization and a facile scaling. a share of the network had been taken over. Krauss et al. realized an organic semiconductor laser emitting in the visible frequency This explanation relies on the fundamental range with a controllable optical vortex. The key element is an Archimedean spiral grating, stochastic dynamics of the incubation process, which gives access to the phase, handedness and angular momentum of the beam through afflicted by the same long waits experienced the number of spiral arms. This effectively transfers the concept of optical vortices to the by the stamp collector. FL microscale and makes it possible to construct two-dimensional arrays of cheap, easy-to- fabricate and spectrally tunable emitters in a single lightweight device. JPK Written by David Abergel, Jan Philip Kraack, Federico Levi, Yun Li and Andreas H. Trabesinger.