The decay of quantum systems through a potential barrier is ubiquitous in many fields of physics and chemistry, occurring in electron conduction within devices and quantum dots as well as chemical reactions, and nuclear fission. The usual framework for describing the barrier crossing is the "transition-state" theory, which was invented long ago to investigate chemical reactions and nuclear fission. The main assumption of this theory is that the decay rate is entirely determined at the highest point of the barrier and does not depend on what occurs afterward. This remarkable theory has been part of reaction theory since the 1930s and has been used in disciplines as widely distinct as chemistry and nuclear physics. However, this theory has not been validated for the quantum mechanics of many interacting particles.

In this study, a model was proposed to study reactions in systems with many interacting particles. The model allowed us to test whether the assumptions of the transition state theory could be satisfied in a full quantum theory. The model contains two reservoirs of internal states connected to each other by additional barrier-top states, and the reservoir states were considered using random matrix theory.

For the first time, we demonstrated that a main assumption of the transition-state theory can be easily satisfied by a more detailed theory, that is, the overall decay rate going through the far-side reservoir is largely determined by the barrier region and internal properties of the reservoirs, and is insensitive to the individual decay rates of the states out of the far-side reservoir.

In a subsequent paper (K. Hagino and G.F. Bertsch, Phys. Rev. E104, L052104(2021)), we applied the same model to discuss the variation of the decay rates between states. There is a well-established theory known as the Porter-Thomas distribution that has been validated for many systems, including atomic spectra, chemical reaction spectra, and nuclei. Surprisingly, our transition-state model revealed that this distribution differed depending on how large the individual rates were. The new distribution followed a different random matrix model, namely the Gaussian Unitary Ensemble, proposed by Dyson in 1960.

(Written by K. Hagino on behalf of all authors)

In quantum field theory (or QFT), perturbation theory is a mathematical approximation used to describe a complex quantum system with a simpler one. However, this approach is not valid for strongly coupled systems or phase transitions, for which the perturbative expansions are not convergent.

A technique called “resurgence theory” could, however, allow us to understand non-perturbative effects from information concealed within a perturbative series. This approach has been used to describe a wide range of systems in quantum mechanics, hydrodynamics, and string theory. But so far, there has been little focus on describing systems with phase transitions.

Against this backdrop, physicists from Japan studied the resurgence structure of a three-dimensional supersymmetric quantum electrodynamics (or SQED) model with a second-order quantum phase transition to explore the relations between resurgence and phase transitions.

The team used two approaches in their study: one involved a “Lefschetz thimble analysis,” in which the path integral representations of physical observables were decomposed in terms of Lefschetz thimbles. The thimble decomposition, in turn, could either change discontinuously to give rise to “Stokes phenomena” or remain unchanged but switch dominant saddle points to give “anti-Stokes phenomena.” The other was “Borel resummation technique,” which could decode these phenomena from a purely perturbative expansion.

The team interpreted the second-order phase transition as a simultaneous Stokes and anti-Stokes phenomena and showed that the order of phase transition was governed by the number of saddles colliding and by their collision angle at the critical point. In addition, supersymmetry led to an infinite number of Stokes phenomena. Finally, they showed that Borel resummation can be used to understand phase transitions.

These findings could open up potential applications of resurgence in QFT along with opportunities to explore problems such as hadron dynamics.

]]>Cuprate superconductors, discovered in 1986, still confront researchers of condensed matter physics with unresolved challenges. On top of this, superconductivity research is now booming again—thanks to recent studies that demonstrate how phenomena like charge order and fluctuations can coexist and interact with high-temperature superconductivity.

To help researchers approach the daunting amount of literature on this subject, the Special Topics issue of the Journal of the Physical Society of Japan includes 12 papers on recent experimental and theoretical research on remarkable new phenomena in high-temperature superconductors.

First, Uchida provides an overview of the field and future prospects, while Tranquada and colleagues pursue the relationship between charge order and superconductivity using scattering and transport techniques in cuprate families.

Fujita and colleagues provide an atomic-scale visualization of Cooper-pair density waves using scanning tunneling microscopy techniques. Meanwhile, Lee summarizes recent findings on the charge density wave in superconducting cuprates using X-ray scattering.

Also employing X-ray scattering techniques, Arpaia and Ghiringhelli explore high temperature and high energy charge fluctuations, whereas Le Tacon and colleagues investigate charge order and phonon anomalies under uniaxial stress.

Abbamonte and colleagues search for a new ordered state using X-ray diffraction, and Kawasaki and colleagues employ nuclear magnetic resonance to probe charge order and fluctuations.

On the theoretical side, Imada explores the relationships between charge order and superconductivity and how to measure them using spectroscopic methods.

Devereaux and colleagues analyze charge-spin fluctuations using large-scale numerical calculation of the Hubbard model, while Yamase delves into the theory of bond charge order, collective charge fluctuations, and nematic order. Finally, Kontani and colleagues explore the theory of various liquid crystal orders in cuprate superconductors and related materials.

The sheer amount of knowledge that has been accumulated on high-temperature superconductivity makes it hard for new researchers to approach the subject, but this issue will hopefully be a useful source of information so that anyone can approach and grasp the hottest spots of the field.

]]>Research on photoinduced phase transitions has progressed recently accelerated because of the rapid development of laser technology. Irradiation by circularly polarized light was theoretically proven to induce a photoinduced topological phase transition to the Chern insulator phase in a tight-binding model on the honeycomb lattice via a special kind of band structure resembling those predicted by Haldane. According to this prediction, the possible emergence of the photoinduced topological phase in graphene has been explored, and an observation of photoinduced Hall currents in graphene was argued in this context.

Since these pioneering studies, photoinduced topological phase transitions have undergone extensive theoretical investigations. However, the further development of this growing research field requires proposals of novel target materials and theoretical predictions of interesting physical phenomena. In this study, we theoretically predicted the occurrence of photoinduced topological phase transitions and the emergence of the topologically nontrivial Chern insulator phase as a nonequilibrium steady state in the organic salt α-(BEDT-TTF)_{2}I_{3} under irradiation with elliptically polarized light.

We constructed rich nonequilibrium phase diagrams in the plane of the x-axis and y-axis components of the amplitude of elliptically polarized light by calculating the band structures, Chern numbers, and Hall conductivity in a photodriven α-(BEDT-TTF)_{2}I_{3}
system using the Floquet theory. These include the Chern insulator phases, non-topological insulator phases, and semimetal phases. In addition, calculations of the Hall conductivity using the Floquet–Keldysh scheme predicted that the quantization of Hall conductivity can be observed in this nonequilibrium Chern insulator phase at low temperatures, just as it is observed in equilibrium Chern insulators. Furthermore, we revealed that the present photoinduced Chern insulator phase possesses another feature of the equilibrium Chern insulators, namely, the gapless state localized at the edges. The predicted quantized Hall conductivity and edge current owing to the predicted edge states in the photoinduced Chern insulator phase are expected to be observed in future experiments for α-(BEDT-TTF)_{2}I_{3}. Our results expand a range of target materials and contribute to the research on the optical manipulation of electronic states in matter.

(Written by M. Mochizuki on behalf of all authors)

]]>The first-ever gravitational waves were directly observed when two massive black holes in close orbit around each other collided to create a ripple in the fabric of space-time. The detection of these waves at LIGO/Virgo facilities marked a new dawn in gravitational wave physics and astronomy where theoretical predictions met actual observational data. This event also opened up new opportunities to test the theory of gravity beyond general relativity and gain a deeper understanding of the evolution of stars, short gamma-ray bursts, and the formation of heavy elements.

Two years after this event, on August 17, 2017, another event occurred: the merging of two binary neutron stars. The observation of this new event led to a paradigm shift in gravitational wave astronomy. It sparked a collaborative project called “Gravitational Wave Physics and Astronomy: Genesis,” where scientists from various fields of physics, working on various instruments, came together to conduct follow-up observations, and shared their insights into what happened during and after the event. This quest into the unknown received a huge boost from the expanding international network of highly sensitive ground-based gravitational interferometers and will receive a further boost from gravitational wave antennas in space.

Over the years, by combining advanced observation techniques with theoretical predictions, new sources of gravitational waves, such as binary neutron stars and massive black holes, have been discovered. Exploration of such gravitational wave events and their sources could be used to probe strong gravity, the physical properties of nuclear matter, the origin of heavy elements, and even potentially rewrite our perception of the universe.

Dirac electrons, which are relativistic particles, appear when the linear bands have intersections in the band structure of solids. Materials with band intersections near the Fermi level, such as monatomic layers of graphite (graphene), have attracted much attention for their ultra-high mobility and significantly large magnetoresistance due to Dirac electrons. However, when the spin-orbit interaction is turned on, a gap opens at the band crossing point, and the properties of the Dirac electrons vanishes. Recently, Dirac electrons originating from the "hourglass" band structure, which is protected by non-symmorphic crystal symmetry, have attracted particular attention because the gap does not open, and their properties do not disappear in the presence of the spin-orbit interaction. Several candidates for materials with hourglass-shaped band structures have been proposed from theoretical studies; however, the experimental verification has been limited.

In 2017, a theoretical group in China pointed out an hourglass-shaped band dispersion near the Fermi level in ReO_{2}, a simple rhenium oxide. They predicted that the Dirac points at the neck-crossing point of the hourglass bands draw loops (forming nodal lines); they have a special electronic structure called a "Dirac loop chain," in which two types of loops are connected like a chain. ReO_{2}
has been known for a long time. The temperature dependence of resistivity was reported more than 50 years ago. However, the purity of the sample was not good; no experimental results suggesting the existence of Dirac electrons were obtained.

The authors grew high-quality single crystals of ReO_{2} by the chemical vapor transport method and observed giant magnetoresistance and quantum oscillations. From the electronic structure calculations, it was obtained that an hourglass-shaped band structure exists near the Fermi level and that the Dirac loop chain potentially causes these unusual observed.

This study show that even in transition metal compounds with large atomic numbers such as ReO_{2}, which have strong spin-orbit coupling, the Dirac electrons originating from the hourglass-shaped band structure are not vanished; in addition, unique properties such as giant magnetoresistance appear. Further studies are expected to reveal novel properties derived from the Dirac loop chain, such as special surface states and angular dependence of transport properties. These results provide a guideline for searching new Dirac fermionic materials focusing on the non-symmorphic crystal symmetry.

(Written by D. Hirai on behalf of all authors)

]]>Topological semimetals are materials distinct from conventional metals and insulators and are characterized by the touching of valence and conduction bands in momentum space, which occurs at discrete point nodes (Dirac and Weyl points) or closed loops (nodal lines), which emerge robustly against disorder. There has been a growing interest in such topological semimetals owing to unconventional electron transport phenomena (e.g., the anomalous Hall effect (AHE) and the spin Hall effect) arising from band topology.

Recently, topological semimetals having ferromagnetic or antiferromagnetic orders have been theoretically predicted and experimentally synthesized. Numerous theoretical and experimental studies have considered the effect of magnetism on Weyl points, whereas the idea of magnetic nodal lines is still limited. We hence need to understand how the nodal structures, especially nodal lines, and the consequent electronic properties are related to magnetic orders. Understanding such magnetic topological semimetals would also be useful for spintronics applications to realize the efficient control of electron transport in nanoscale structures and devices via magnetism.

In this study, we theoretically investigate the characteristics of nodal structures including nodal lines in magnetic topological semimetals by using a topological Dirac semimetal (TDSM)-based model. While a nonmagnetic TDSM has a pair of Dirac points with twofold spin degeneracy (up/down), we demonstrate that a ferromagnetic order introduced in this system breaks the degeneracy and converts the Dirac points into either Weyl points or nodal lines, depending on the direction of magnetization. This behavior may enable efficient switching of electron transport related to the nodal structures, such as the AHE, by controlling the magnetization, which may be applicable for low-current magnetic sensors.

In addition to the electronic structure in the bulk, we observe that magnetic nodal lines give rise to a characteristic feature at magnetic domain walls. Flat-band states with zero energy (“drumhead” states) emerge at localized regions on the domain wall. These states have band structures similar to the drumhead surface states in nonmagnetic nodal-line semimetals. The drumhead states found here contribute to electric charging of the magnetic domain walls, which facilitates the efficient manipulation of magnetic domains using electric fields and may be useful for magnetic memories and neuromorphic computing devices.

Our work highlights a close correspondence among the magnetic order, nodal structure in the bulk, and boundary modes at magnetic domain walls. Our theoretical proposals may be experimentally verified by adding magnetic dopants or constructing magnetic heterostructures with TDSM materials (e.g., Cd_{3}As_{2}).

(Written by Yasufumi Araki on behalf of all authors)

]]>The physics of exotic nuclei, or nuclei with short lifetimes, is often governed by beta decay, a process in which a neutron decays into a proton, an electron, and an antineutrino. The decay rate is estimated by calculating the product of the electron and nuclear current densities. A widely used formula for calculating this rate relies on a leading-order approximation of the electron wave functions distorted by the Coulomb potential. However, for heavy nuclei with large atomic numbers, this simple approximation may no longer be valid.

To address this issue, physicists from Japan developed a simple approach for improving the conventional formula to apply for the case of heavy nuclei. They treated the neutrino wave function as an exact plane wave and numerically solved for the electron wave functions to obtain both leading-order (or LO) and next-to-leading-order (or NLO) approximations. The physicists then showed that the LO approximation led to an overestimation of the decay rate while the NLO approximation better reproduced the exact result for a schematic transition density as well as for the transition densities obtained by a nuclear energy-density functional method.

The proposed formula could significantly impact our understanding of the origin and formation of heavy elements in our universe and perhaps open a window into yet-undiscovered physics lying beyond the standard model of particle physics.

]]>Mesoscopic physics is the study of systems ranging in size from nanoscale to microns. A major focus in mesoscopic physics is studying the quantum nature of electrons and associated correlated effects. One way to do that is by measuring “shot noise,” a noise originating from the discrete nature of electrons. Recently, researchers from The University of Tokyo and NTT Corporation published a review in the *Journal of the Physical Society of Japan,* detailing advances in shot noise measurements in mesoscopic systems.

Shot noise is often too small to be measured using commercial ammeters, and therefore, requires special experimental techniques for its quantitative evaluation. In their review, the researchers introduce and discuss the characteristics of several measurement techniques as well as explain the theoretical framework to calculate the shot noise.

Shot noise studies have revealed unique information about a system modeled within a single-particle picture. For example, the measurements enable us to evaluate the spin polarization of an electronic current flowing through a mesoscopic solid-state device, such as a quantum point contact. Furthermore, they can be used to explore the quantum Hall effect breakdown, tunnel junction devices, correlated electron transport through quantum dots, and Fermion quantum optics.

Another fascinating aspect of shot noise measurements is that they can also be used to study quantum liquids. In fact, physical phenomena such as the Kondo effect, the fractional quantum Hall effect, and superconductivity show their peculiarity in shot noise properties as well as conductance. Additionally, shot noise could help detect exotic particles like Majorana fermions and non-Abelian anyons that could help us create a fault-tolerant topological quantum computer.

All in all, understanding shot noise is critical not only to the development of quantum physics but also to new technologies.

]]> Thomas Johann Seebeck discovered the thermoelectric (TE) conversion from heat to electrical energy just 200 years ago. Recently, high-performance TE materials have attracted research interest as energy-harvesting technologies. Most of the experimentally discovered TE materials are impurity-doped semiconductors *i.e.*, disordered systems. High-TE effects are expected near the band edge in the impurity-doped semiconductors, where the electronic states are under the influence of strong impurity scattering not properly treated by the conventional Boltzmann transport theory (BTT). Therefore, it is necessary to develop a sophisticated theory beyond BTT. Recently, the authors (T.Y. and H.F.) have alleviated this drawback using the linear response theory (Kubo–Luttinger formula) in conjunction with the thermal Green's function technique [1–3].

The TE linear response theory was successfully applied to nitrogen-doped semiconducting carbon nanotubes (N-CNTs) in the present study. The N-CNTs functioned as lightweight, flexible, and high-performance TE materials. The power factor, *PF* (=*L*_{11}*S*^{2}), was dependent on the nitrogen concentration, *c* (up to 10^{-2}), per unit cell of a CNT at various temperatures. The electrical conductivity and Seebeck coefficient were designated as *L*_{11} and *S*, respectively. The *PF* increased with a decrease in *c* at 300 K. When *c*
decreased to less than the optimal impurity concentration, *c*_{opt }(= 3.1×10^{-5}), the* PF *started to decrease. This behavior was explained based on *L*_{11} and *S*, considering the *c*-dependence of the chemical potential, *μ*. The *μ* at *c* = 10^{-3}
located below the donor level formed via nitrogen doping, and the electrons were thermally excited from the donor level to conduction band. The *μ* level shifted downward with a decrease in *c* owing to a decrease in the net carrier density of the N-CNTs. Here, |*S*| increased with a decrease in *c*. A decrease in *c*, corresponding to a decrease in the rate of scattering by the impurities, was accompanied by an increase in *L*_{11}
owing to the electrons in the conduction band. Consequently, the *PF*
increased with a decrease in *c*. A further lowering of *c* promoted the asymptotic approach of *μ* toward the center of the band gap owing to the thermally excited holes. The holes contributed to an increase in *L*_{11}; however, |*S*| decreased rapidly because the hole contribution to *S* cancels out the electron contribution to *S*. Therefore, the *PF* started to decrease below* c*_{opt}. These results facilitated successful estimation of the optimal nitrogen concentration to maximize the *PF* at various temperatures. A *PF* of 0.30 W/K^{2}m was obtained for *c*_{opt} at 300 K, which is significantly higher than the *PF* of commercial Bi_{2}Te_{3}
alloys. These theoretical predictions will facilitate the development of new materials with optimal TE performances.

(written by M. Matsubara on behalf of all authors)

[1] T. Yamamoto and H. Fukuyama, J. Phys. Soc. Jpn. **87**, 024707 (2018).

[2] T. Yamamoto and H. Fukuyama, J. Phys. Soc. Jpn. **87**, 114710 (2018).

[3] M. Ogata and H. Fukuyama, J. Phys. Soc. Jpn. **88**, 074703 (2019).