Table of contents

Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects. We discuss how these combine to yield a rich phase structure, and their implications for transport and spectroscopy measurements. In parallel, we discuss relevant experimental systems. We close with an outlook on future directions.

In this review, we will focus on the recent development of the order-disorder transition in metallic materials. The past decades have witnessed fast development in the first-principles methodologies and their applications to ordering transitions in multi-component alloys, particularly the high-entropy alloys. The driving force for the proceedings comes from (i) the advance of algorithms and increasingly cheaper hardware, and also (ii) the great passion to model alloys with increasing number of components.

The review starts with a brief introduction of the history for the ordering transitions. More detailed scientific proceedings prior to the 1970s had been well summarized in Krivoglaz and Smirnov (1965 The Theory of Order-Disorder in Alloys (New York: Elsevier)) and Stoloff and Davies (1968 Prog. Mater. Sci. 13 1–84). In the second part, the methods to study the ordering transitions, primarily on the theoretic methods are introduced. These will include (i) KKR-CPA method and supercell methods for energetic calculations; and (ii) thermodynamic and statistical methods to compute the transition temperatures. The third part will focus on representative applications in alloys, including our own work and many others. This part supplies the primary information of this review to the readers. The fourth part will summarize the connections between ordering transitions and broader physical properties (e.g. the mechanical properties). In the last part, some concluding remarks and perspectives will be given.

With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo–Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo–Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon–phonon and other scatterings is summarized.

We study the competition between the Kondo effect and the exchange interaction in the parallel double quantum dot (DQD) system within an effective action field theory. The strong on-site Coulomb interactions in DQDs are treated by using the Hubbard–Stratonovich transformation and the introduction of scalar potential fields. We show that a self-consistent perturbation approach, which takes into account the statistical properties of the potential fields acting on electrons in DQDs, describes well the crossover from the Kondo regime to the spin-singlet state in this system. The linear conductance and the intradot/interdot spin excitation spectra of this system are obtained.

Excitons in two-dimensional nanomaterials are studied by solving the many-electron Hamiltonian with a configuration-interaction approach. It is shown that graphene or phosphorene nanoflakes can not accommodate any excitonic bound states if the long-range Coulomb interaction is suppressed when the systems are placed in a high-k dielectric environment or on a metal substrate. Hence it is revealed that an electron–hole pair created by an optical excitation does not always form an exciton even in a confined nanostructure. The negative exciton binding energy is found to exhibit distinct dependence on the strength of short-range Coulomb interaction as the system undergoes a phase transition from non-magnetic to anti-ferromagnetic. It is further shown that the electron–hole pair may form an exciton state only when the long-range Coulomb interaction is recovered in the nanoflakes.

We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose–Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman's universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross–Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state.

We employed femtosecond pump-probe technique to investigate the dynamics of coherent optical phonons in iron garnet. A phenomenological symmetry-based consideration reveals that oscillations of the terahertz T_2g mode are excited. Selective excitation by a linearly polarized pump and detection by a circularly polarized probe confirm that impulsive stimulated Raman scattering (ISRS) is the driving force for the coherent phonons. Experimental results obtained from ISRS measurements reveal excellent agreement with spontaneous Raman spectroscopy data, analyzed by considering the symmetry of the phonon modes and corresponding excitation and detection selection rules.

Cooper instability (CI) associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion–fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead CI can be generated only if the absolute strength of fermion–fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the CI at zero chemical potential, which in principle are harmful to CI although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the CI is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.

Room temperature optical absorption spectroscopy (OAS) and Raman spectroscopy measurements have been carried out in order to understand the effect of structural disorder on the electronic and phononic states. For this purpose, polycrystalline samples of Cr doped PrFeO₃ have been prepared via wet chemical route. OAS analysis suggests the systematic scaling of electronic disorder with Cr doping; whereas, shifting in Raman line shapes and an increase in Raman line width has been observed with Cr doping. X-ray diffraction analysis clearly suggests the increase in structural disorders in the form of crystallographic strain with Cr doping, which is consistent with the broadening in Raman line shapes. The major contribution to Raman line width has been understood in terms of temperature independent terms i.e. structural disorder induced by doping. The generation of a new phonon mode at ~510 cm⁻¹ has been observed and understood as a disorder phonon mode due to strain induced structural disorder. Moreover, a systematic correlation between crystallographic strain, Raman line width, disordered parameter (σ) and Urbach energy has been observed, which implies that structural disorder affects phononic as well as electronic states of the system. Such comparative study allows us to find the correlation between densities of tail states, structural disorders and anharmonic effects probed by Raman spectroscopy.

Epitaxial 200 nm BiFe_0.95Mn_0.05O₃ (BFO) film was grown by pulsed laser deposition (PLD) on (1 1 1) oriented SrTiO₃ substrate buffered with a 50 nm thick SrRuO₃ electrode. The BFO thin film shows a rhombohedral structure and a large remnant polarization of Pr  =  104 µC cm⁻². By comparing I(V) characteristics with different conduction models we reveal the presence of both bulk limited Poole–Frenkel and Schottky interface mechanisms and each one dominates in a specific range of temperature. At room temperature (RT) and under 10 mW laser illumination, the as grown BFO film presents short-circuit current density (J_sc) and open circuit voltage (V_oc) of 2.25 mA cm⁻² and  −0.55 V respectively. This PV effect can be switched by applying positive voltage pulses higher than the coercive field. For low temperatures a large V_oc value of about  −4.5 V (−225 kV cm⁻¹) is observed which suggests a bulk non-centrosymmetric origin of the PV response.

ZrCo₂Sn is a potential candidate as a Weyl semimetal with a ferromagnetic ground state, and Nb-doping is expected to shift the Weyl points to the vicinity of Fermi level. We successfully synthesized a series of Zr_1−xNb_xCo₂Sn single crystals with various concentrations of Nb (x  =  0, 0.1, 0.2, 0.275, 0.4, 0.5). All samples have a spinel structure and the lattice constant decrease as the Nb doping level increases. The magnetization and transport measurements suggest that the ferromagnetic ordering temperature can be strongly modified by the Nb doping. When x increases, the Curie temperature decreases significantly, accompanied by a change from metal-like to semiconductor-like behavior. There is a crossover for positive to negative MR at a temperature between 30 K to 50 K. In constant, the magnitude of the anomalous Hall resistance increases monotonously with decreasing temperature.

Magnetism of Cu₂(OH)₃Br single crystals based on a triangular lattice is studied by means of magnetic susceptibility, pulsed-field magnetization, and specific heat measurements. There are two inequivalent Cu²⁺ sites in an asymmetric unit. Both Cu²⁺ sublattices undergo a long-range antiferromagnetic (AFM) order at K. Upon cooling, an anisotropy crossover from Heisenberg to XY behavior is observed below 7.5 K from the anisotropic magnetic susceptibility. The magnetic field applied within the XY plane induces a spin-flop transition of Cu²⁺ ions between 4.9 T and 5.3 T. With further increasing fields, the magnetic moment is gradually increased but is only about half of the saturation of a Cu²⁺ ion even in 30 T. The individual reorientation of the inequivalent Cu²⁺ spins under field is proposed to account for the magnetization behavior. The observed spin-flop transition is likely related to one Cu site, and the AFM coupling among the rest Cu spins is so strong that the 30 T field cannot overcome the anisotropy. The temperature dependence of the magnetic specific heat, which is well described by a sum of two gapped AFM contributions, is a further support for the proposed scenario.

Electronic structure of Pr₂CoFeO₆ (at 300 K) was investigated by x-ray photoemission spectroscopy (XPS) and x-ray absorption spectroscopy techniques. All three cations, i.e. Pr, Co and Fe were found to be trivalent in nature. XPS valance band analysis suggested the system to be insulating in nature. The analysis suggested that Co³⁺ ions exist in low spin state in the system. Moreover, Raman spectroscopy study indicated the random distribution of the B-site ions (Co/Fe) triggered by same charge states. In temperature-dependent Raman study, the relative heights of the two observed phonon modes exhibited anomalous behaviour near magnetic transition temperature T_N ~ 270 K, thus indicating towards interplay between spin and phonon degrees of freedom in the system. Furthermore, clear anomalous softening was observed below T_N which confirmed the existence of strong spin–phonon coupling occurring for at least two phonon modes of the system. The line width analysis of the phonon modes essentially ruled out the role of magnetostriction effect in the observed phonon anomaly. The investigation of the lattice parameter variation across T_N (obtained from the temperature-dependent neutron diffraction measurements) further confirmed the existence of the spin–phonon coupling.

The appearance of Hall sign change in perovskite SrRuO₃ thin films at Curie temperature was confirmed from our fabricated samples and the result was simulated by our proposed theoretical model. In particular, our simulation results are consistent with experimental results mainly due to the introduction of an impurity band in a two-band model. We found the other important factors in our theory responsible for observed consistency Hall measurements are the itinerant carrier density and its intrinsic carrier type. Eventually the theory possibly interprets the mechanism of Hall sign change.

We investigate the influence of the magnon–phonon relaxation processes in the magnon transport under thermal gradient in the ferrimagnetic insulator yttrium iron garnet (YIG). Based on the Boltzmann equation we calculate the magnon contribution in the thermal conductivity in YIG and the longitudinal spin Seebeck effect in YIG/Pt films, including the influence of the magnon relaxation to the lattice through a phenomenological damping parameter. Our results are in good agreement with reported experimental data showing that besides the magnon–magnon relaxation processes, the magnon–phonon relaxation plays an important role in the thermal properties in YIG films.