Recent experiments show the spontaneous breaking of rotational symmetry in the superconducting topological insulators $M_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($M$ represents Cu, Sr, or Nd), suggesting that the pairing belongs to a two-dimensional representation of the $D_{3d}$ symmetry group of the crystal. Motivated by this progress, we construct an exhaustive list of possible two-component pairings of the $M_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ superconductors, both for the odd-parity $E_u$ representation and for the even-parity $E_g$ representation. Starting from a tight-binding model for the normal phase of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and $M_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, we firstly construct the pairing channels in the spin-orbital basis, up to second-nearest-neighbor pairing correlations in the basal plane. We then infer the properties of these pairings by transforming them to the band (pseudospin) basis for the conduction band. A comparison with the experiments leads to several multichannel pairings as promising pairings for $M_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ superconductors. Besides a nematic and time-reversal symmetric pairing combination, the other pairings that we have identified are chiral and nematic at the same time, which may be nonunitary and have a spontaneous magnetization. A complementary set of experiments are proposed to identify the true pairing symmetries of these superconductors and their evolution with the doping concentration $x$.

The field of heavy-fermion physics emerged nearly four decades ago and has since remained one of the most prominent research directions in condensed-matter physics. Nonetheless, while significant progress has been made in unraveling heavy-fermion behavior and accompanying exotic phenomena, many questions remain. This issue can be advanced from two directions: comprehensive understanding of existing materials and discovery of novel systems. In this work, we propose a targeted method for discovery of uranium-based heavy-fermion materials by synthesis of complex intermetallic compounds with low mass percentage of uranium, high coordination number of uranium, and long overall shortest uranium bond length. We report the discovery and synthesis of the new complex uranium-based heavy-fermion material ${\mathrm{U}}_{23}{\mathrm{Hg}}_{88}$, which suggests this approach to be a reliable route for the targeted search of novel strongly correlated uranium-based materials. The Sommerfeld coefficient $\gamma =630\mathrm{mJ}{\mathrm{mol}}_{\text{U}}^{-1}{\mathrm{K}}^{-2}$ indicates extremely strong electronic correlations and places ${\mathrm{U}}_{23}{\mathrm{Hg}}_{88}$ among the heaviest uranium-based compounds. ${\mathrm{U}}_{23}{\mathrm{Hg}}_{88}$ orders antiferromagnetically below $T_{\text{N}}=2.2\mathrm{K}$ and displays a dual nature of the $5f$ electrons. This work will pave a way for a comprehensive understanding of heavy-fermion phenomena in general and uranium-based systems in particular.

We present a theoretical study of the effects of optical fields on a ferromagnetic model system of itinerant carriers that includes both magnetism at the level of a time-dependent mean-field and spin-orbit coupling. In the framework of this model, which contains a band gap and is similar to the one introduced by Qaiumzadeh et al. [Phys. Rev. B 88, 064416 (2013)] we investigate the inverse Faraday effect, i.e., how the magnetization of the ferromagnetic bands can be influenced by the helicity of off-resonant optical fields. The magnetization dynamics are calculated self-consistently by including a dynamic ferromagnetic splitting and the corresponding single-particle states. We study the magnetization dynamics for the case of a rapid ramping-up of an optical field that is off-resonant with respect to the gap and find that the magnetization switching occurs due to the interplay of the coherence between the spin-split ferromagnetic bands and incoherent scattering/dephasing processes.

The interplay of spin and charge degrees of freedom, introduced by doping mobile holes into a Mott insulator with strong antiferromagnetic (AFM) correlations, is at the heart of strongly correlated matter such as high-$T_c$ cuprate superconductors. Here, we capture this interplay in the strong coupling regime and propose a trial wave function of mobile holes in an AFM. Our method provides a microscopic justification for a class of theories which describe doped holes moving in an AFM environment as mesonlike bound states of spinons and chargons. We discuss a model of such bound states from the perspective of geometric strings, which describe a fluctuating lattice geometry introduced by the fast motion of the chargon, relative to the spinon. This is demonstrated to give rise to short-range hidden string order, signatures of which have recently been revealed by ultracold atom experiments at elevated temperatures. We present evidence for such short-range hidden string correlations also at zero temperature by performing numerical density-matrix renormalization-group simulations. To test our microscopic approach, we calculate the ground-state energy and dispersion relation of a hole in an AFM, as well as the magnetic polaron radius, and obtain good quantitative agreement with advanced numerical simulations at strong coupling. We discuss extensions of our analysis to systems without long-range AFM order to systems with short-range magnetic correlations.

We study isotropic antiferromagnetic Heisenberg chains coupled by antiferromagnetic Ising interaction as an effective spin model for the ytterbium aluminum perovskite ${\mathrm{YbAlO}}_3$. Using the density-matrix renormalization group (DMRG) method we calculate the magnetization curve, local spin, central charge, and dynamical spin structure factors in the presence of magnetic field. From the fitting of the experimental magnetization curve, the effective intrachain and interchain couplings are estimated as $J=2.3$ K and $J_{\mathrm{ic}}=0.8$ K, respectively. We can quantitatively explain the experimental observations: (i) phase transition from antiferromagnetic to incommensurate order at field 0.35 T, and (ii) quantum critical behaviors at the saturation field of 1.21 T. Furthermore, the low-energy excitations in the experimental inelastic neutron scattering spectra can be well described by our DMRG results of the dynamical structure factors.

The antiferromagnetic order in the heavy-fermion compound ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$ can be suppressed by Co-doping, and at critical composition $x_c=0.6$ ($T_N\to 0$ K) a quantum critical point has been observed. We have performed zero-field (ZF) and longitudinal-field muon spin relaxation ($\mu \mathrm{SR}$) measurements on polycrystalline samples of $\mathrm{Ce}{\left({\mathrm{Cu}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{Ge}}_2$ ($x=0,0.2,0.6,1$) over a temperature range of 100 mK to 10 K and in applied fields from 0 up to 3000 G. Above any ordering temperature, the muon relaxation spectra can be described by a Gaussian-Kubo-Toyabe times exponential line shape. Below the magnetic ordering temperature (i.e., for $x<0.6$), an additional Gaussian relaxation is observed. The zero-field muon relaxation rate suggests the presence of antiferromagnetic ordering below 4 and 0.8 K for $x=0$ and 0.2 samples, respectively. For $x=0.6$, the magnetic order is completely suppressed, and the quantum critical point is accompanied by non-Fermi-liquid behavior, manifested in the power-law divergence of exponential depolarization, i.e., $\lambda \propto T^{0.55}$. The relaxation rate of $x=0.6$ obeys the time-field scaling relation $G_z(t,H)=G_z(t/H^{\gamma })$, which is considered to be a characteristic feature of quantum critical magnetic fluctuations. Furthermore, for $x=0.6$, the exponent of isotherm magnetization, $M\sim H^{\eta }$, and magnetization-field-temperature scaling is consistent with the ZF-$\mu \mathrm{SR}$ data. These results provide strong evidence for the formation of a quantum Griffiths phase near the antiferromagnetic quantum phase transition.

The interplay between interband and intraband pairing interactions in multiband systems can result in superconducting order parameter with the broken time-reversal symmetry (BTRS). Here we consider a slightly inhomogeneous superconductor with the BTRS order parameter in the framework of Ginzburg-Landau functional. We show that the Giznburg-Landau functional possesses a minimum with zero spontaneous internal magnetic fields in the absence of the external magnetic fields. This extension of the functional space is important for understanding of experimental situation in multiband superconductors.

A comprehensive angle-resolved photoemission spectroscopy study of the band structure in single-layer cuprates is presented with the aim of uncovering universal trends across different materials. Five different hole- and electron-overdoped cuprate superconductors (${\mathrm{La}}_{1.59}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_{0.21}{\mathrm{CuO}}_4$, ${\mathrm{La}}_{1.77}{\mathrm{Sr}}_{0.23}{\mathrm{CuO}}_4$, ${\mathrm{Bi}}_{1.74}{\mathrm{Pb}}_{0.38}{\mathrm{Sr}}_{1.88}{\mathrm{CuO}}_{6+\delta }$, ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{CuO}}_{6+\delta }$, and ${\mathrm{Pr}}_{1.15}{\mathrm{La}}_{0.7}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$) have been studied with special focus on the bands with a predominately $d$-orbital character. Using a light polarization analysis, the $e_g$ and $t_{2g}$ bands are identified across these materials. A clear correlation between the $d_{3z^2-r^2}$ band energy and the apical oxygen distance $d_{\mathrm{A}}$ is demonstrated. Moreover, the compound dependence of the $d_{x^2-y^2}$ band bottom and the $t_{2g}$ band top is revealed. A direct comparison to density functional theory (DFT) calculations employing hybrid exchange-correlation functionals demonstrates excellent agreement. We thus conclude that the DFT methodology can be used to describe the global band structure of overdoped single-layer cuprates on both the hole- and electron-doped side.

In multiband superconductors, multiple collective modes exist associated with the multiple order parameters. Oscillations of the amplitude and the relative phase of the order parameters are called Higgs and Leggett modes, respectively. Recently, it has been suggested that nonmagnetic impurity scattering would enhance nonlinear coupling between the Higgs mode and an electromagnetic wave with a frequency located in the superconducting gap region, while its effect on the Leggett mode is still unresolved. Here, we theoretically investigated the nonlinear optical response of multiband Bardeen-Cooper-Schrieffer-type superconductors in the presence of nonmagnetic impurities with a density matrix approach extending the Mattis-Bardeen model of linear response. We found that the drastic enhancement of nonlinear optical response due to the nonmagnetic impurity scattering occurs only for the Higgs modes and not for the Leggett mode. As a result, both the light-induced dynamics of the superconducting gaps and the resulting third-harmonic generation are dominated by the Higgs modes. We also examined the role of quasiparticle excitations to find that they give the subdominant contribution to the third-harmonic generation.

Nonlocal order parameters in space-time are proposed to characterize the unconventional orbital-selective conducting state in fulleride superconductors, called the Jahn-Teller metal. In previous works, it has been argued that this state can be interpreted as a spontaneous orbital-selective Mott state, in which the electrons in two of the three $t_{1u}$ molecular orbitals are localized, while those in the third one are metallic. Here, based on the realistic band structure for fullerides, we provide a systematic study of nonlocal order parameters and characterize the Jahn-Teller metal, for which there exists no one-body local order parameter in contrast to conventional orderings. It is shown that the Mottness, or integer filling nature for each orbital due to strong correlation effects, is a relevant feature of the present orbital order. The local orbital moment thus vanishes and the static distortion associated with a conventional orbital moment is absent. Transport characteristics are also investigated, and it is found that the dimensionality is effectively reduced from three to two at low energies, while the cubic nature is recovered at high energies. This accounts for the high upper critical field observed in the superconducting state of the fcc fullerides inside the Jahn-Teller metal regime.

From the Kubo formula for transport in a tilted Weyl semimetal, we calculate the absorptive part of the dynamic conductivity for both right- and left-handed circular polarized light. These depend on the real part of the longitudinal conductivity and the imaginary part of the transverse (Hall) conductivity. We include the effect of the chiral anomaly, which pumps charge from negative to positive chirality node when the usual $\mathit{E}·\mathit{B}$ term is included in the electrodynamics, and obtain analytic expressions. To calculate the Hall angle, we further provide expressions for the imaginary part of longitudinal and real part of the transverse conductivity and compare results with and without the pumping term. We also consider the case of a noncentrosymmetric Weyl semimetal in which the chiral nodes are displaced in energy by an amount $\pm {\mathcal{Q}}_0$. This leads to modification in dichroism and Hall angle which parallel the pumping case.

Low-frequency noise close to the carrier remains little explored in spin-torque nano-oscillators. However, it is crucial to investigate as it limits the oscillator's frequency stability. This work addresses the low offset frequency flicker noise of a spin-torque vortex oscillator in the regime of large-amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory, aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillator's $1/f$ flicker noise and discuss the results based on the theoretical predictions. Thereby, we connect the oscillator's nonlinear dynamics with the concept of flicker noise and furthermore refer to the influence of a standard $1/f$ noise description based on the Hooge formula, taking into account the nonconstant magnetic oscillation volume, which contributes to the magnetoresistance.

Electrical transport properties near an electronic Ising-nematic quantum critical point in two dimensions are of both theoretical and experimental interest. In this work, we derive a kinetic equation valid in a broad regime near the quantum critical point using the memory matrix approach. The formalism is applied to study the effect of the critical fluctuations on the dc resistivity through different scattering mechanisms, including umklapp, impurity scattering, and electron-hole scattering in a compensated metal. We show that electrical transport in the quantum critical regime exhibits a rich behavior that depends sensitively on the scattering mechanism and the band structure. In the case of a single large Fermi surface, the resistivity due to umklapp scattering crosses over from $\rho \sim T^2$ at low temperature to sublinear at high temperature. The crossover temperature scales as $q_0^3$, where $q_0$ is the minimal wave vector for umklapp scattering. Impurity scattering leads to $\rho -{\rho }_0\sim T^{\alpha }$ (${\rho }_0$ being the residual resistivity), where $\alpha$ is either larger than 2 if there is only a single Fermi sheet present, or $4/3$ in the case of multiple Fermi sheets. Finally, in a perfectly compensated metal with an equal density of electrons and holes, the low-temperature behavior depends strongly on the structure of “cold spots” on the Fermi surface, where the coupling between the quasiparticles and order parameter fluctuations vanishes by symmetry. In particular, for a system where cold spots are present on some (but not all) Fermi sheets, $\rho \sim T^{5/3}$. At higher temperatures, there is a broad crossover regime where $\rho$ either saturates or $\rho \sim T$, depending on microscopic details. We discuss these results in the context of recent quantum Monte Carlo simulations of a metallic Ising nematic critical point, and experiments in certain iron-based superconductors.

We study theoretically the time-domain dynamics of the spin-dependent Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between driven magnetic impurities localized in a spin-orbit-coupled two-dimensional system. Particular attention is given to the influence of the spin-orbit coupling (SOC) on the system's dynamical response to a time-dependent precessional motion of the localized magnetic moment. We show that, via the RKKY mechanism, a flip of the spin $z$ component of one localized moment affects all $x,y$, and $z$ spin components of the other localized moment. The Friedel oscillations and the transient spin current triggered by the time-varying localized spin depend strongly on the orientation of the spin with respect to the two-dimensional structure. Our results demonstrate how the dynamic interplay between SOC and the RKKY interaction can be used to manipulate and fine-tune the characteristics of impurity spin reversal and to control the generated spin current and the local magnetization.

The electronic and transport properties of a three-dimensional (3D) Dirac system are investigated theoretically, which is motivated by recent experimental measurements on quantum and transport mobilities in the 3D Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ by J. Xiong et al. [Science 350, 413 (2015); Europhys. Lett. 114, 27002 (2016)]. The electron Hamiltonian is taken from a simplified $\mathbf{k}·\mathbf{p}$ approach. From the obtained electronic band structure and the Fermi energy, we explain why the anomalous effect induced by the chiral anomaly and the Berry curvature in the energy band can be observed experimentally in magnetotransport coefficients in both low- and high-density samples. Moreover, the quantum and transport mobilities are calculated on the basis of the momentum-balance equation derived from a semiclassical Boltzmann equation with the electron-impurity interaction. The quantum and transport mobilities obtained from this study agree both qualitatively and quantitatively with those measured experimentally. We also examine the electron mobilities along different crystal directions in ${\mathrm{Na}}_3\mathrm{Bi}$ and find them largely anisotropic. The theoretical findings from this work can be helpful in gaining an in-depth understanding of the experimental results and of the basic electronic and transport properties of newly developed 3D Dirac systems.

Flat bands with extremely narrow bandwidths on the order of a few millielectron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flat bands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of 2 in the same parameter space of twist angle $\theta$ and interlayer coupling $\omega$, making it in principle simpler to tailor narrow bandwidth flat bands. Application of vertical pressure can enhance the first magic angle in minimal models at $\theta \sim 1.{05}^{\circ }$ to larger values of up to $\theta \sim 1.5^{\circ }$ when $P\sim 2.5$ GPa, where $\theta \propto \omega /{\upsilon }_F$. Narrow bandwidths are expected in bi-bilayers for a continuous range of small twist angles, i.e., without magic angles, when intrinsic bilayer gaps open by electric fields, or due to remote hopping terms. We find that moderate vertical electric fields can contribute in lifting the degeneracy of the low-energy flat bands by enhancing the primary gap near the Dirac point and the secondary gap with the higher energy bands. Distinct valley Chern bands are expected near $0^{\circ }$ or ${180}^{\circ }$ alignments.

The terahertz (THz) to visible irradiation induced current in zigzag and armchair graphene nanoribbons were investigated by focusing on the modulation of the photovoltaic effects by tuning the electric field ($E$) strength. The numerical results show that spin photovoltaic effects in zigzag-edged graphene nanoribbons can be significantly improved by enhancing the $E$ strength. In detail, an acceptable broadband photoresponsivity with a full optical spin polarization in a broad range of photon energies, including the THz region, can be obtained that can be preserved in the presence of the edge roughness. Furthermore, armchair-edged graphene nanoribbons could reveal a tunable photoresponsivity induced by THz to ultraviolet wavelengths. These results could lead to the enhancement of photovoltaic effects and especially the generation of a spin-polarized photocurrent in all-carbon junctions.

Two-dimensional Dirac fermions are subjected to two types of interactions, namely, the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $\alpha$ is larger than some critical value ${\alpha }_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value ${\alpha }_c$ is increased by weak short-range interaction. As $U$ increases to approach $U_c$, the quantum fluctuation of the antiferromagnetic order parameter becomes important and interacts with the Dirac fermions via the Yukawa coupling. After treating the Coulomb interaction and Yukawa coupling interaction on an equal footing, we show that ${\alpha }_c$ is substantially increased as $U\to U_c$. Thus, the excitonic pairing is strongly suppressed near the antiferromagnetic quantum critical point. We obtain a global phase diagram on the $U\text{−}\alpha$ plane and illustrate that the excitonic insulating and antiferromagnetic phases are separated by an intermediate semimetal phase. These results provide a possible explanation of the discrepancy between recent theoretical progress on excitonic gap generation and existing experiments in suspended graphene.

We report a detailed magnetotransport study on single crystals of PrBi. The presence of $f$ electrons in this material raises the prospect of realizing a strongly correlated version of topological semimetals. PrBi shows a magnetic-field-induced metal-insulator-like transition below $T\sim 20\mathrm{K}$ and a very large magnetoresistance ($\approx 4.4\times {10}^4\%$) at low temperatures ($T=2\mathrm{K}$). We have also probed the Fermi surface topology by de Haas–van Alphen and Shubnikov–de Haas quantum oscillation measurements complimented with density functional theory (DFT) calculations of the band structure and the Fermi surface. Angle dependence measurements of the Shubnikov–de Haas oscillations have been carried out to probe the possible signature of surface Dirac fermions. We find three frequencies corresponding to one electron ($\alpha$) and two hole ($\beta$ and $\gamma$) pockets in experiments, consistent with DFT calculations. The angular dependence of these frequencies is not consistent with a two-dimensional Fermi surface, suggesting that the transport is dominated by bulk bands. We estimate high mobility and small effective mass for carriers in PrBi that are comparable to those of other compounds in this series proposed as topologically nontrivial. A Lifshitz-Kosevich fitting of the quantum oscillation data as well as a Landau fan diagram analysis gave a Berry phase close to $\pi$, suggesting the presence of topological electrons in PrBi.