The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework for the description of the electronic structure, spectroscopy, and dynamics of strongly correlated systems. However, the underlying Kadanoff-Baym equations (KBE) for the two-time Keldysh Green's functions involve a memory kernel, which results in a high computational cost for long simulation times $t_{\text{max}}$, with a cubic scaling of the computation time with $t_{\text{max}}$. Truncation of the memory kernel can reduce the computational cost to linear scaling with $t_{\text{max}}$, but the required memory times will depend on the model and the diagrammatic approximation to the self-energy. We explain how a truncation of the memory kernel can be incorporated into the time-propagation algorithm to solve the KBE, and investigate the systematic truncation of the memory kernel for the Hubbard model in different parameter regimes, and for different diagrammatic approximations. The truncation is easier to control within dynamical mean-field solutions, where it is applied to a momentum-independent self-energy. Here, simulation times up to two orders of magnitude longer are accessible both in the weak and strong coupling regime, allowing for a study of long-time phenomena such as the crossover between prethermalization and thermalization dynamics.

We investigate the temperature $\left(T\right)$ evolution of orbital anisotropy and its effect on spectral function and optical conductivity in ${\mathrm{Ce}}_2{\mathrm{IrIn}}_8$ using a first-principles dynamical mean-field theory combined with density functional theory. The orbital anisotropy develops by lowering $T$ and it is intensified below a temperature corresponding to the crystalline-electric field (CEF) splitting size. Interestingly, the depopulation of CEF excited states leaves a spectroscopic signature, “shoulder,” in the $T$-dependent spectral function at the Fermi level. From the two-orbital Anderson impurity model, we demonstrate that CEF splitting size is the key ingredient influencing the emergence and the position of the “shoulder.” Besides the two conventional temperature scales $T_K$ and $T^{*}$, we introduce an additional temperature scale to deal with the orbital anisotropy in heavy fermion systems.

We present a study of even-parity Rydberg exciton states in cuprous oxide using second harmonic generation (SHG) spectroscopy. Excitonic states with principal quantum number $n=5-12$ were excited by nanosecond pulses around $1143\mathrm{n}\mathrm{m}$. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at $1.993\mathrm{e}\mathrm{V}$ associated with a long lifetime of $641\pm 7\mathrm{\mu }\mathrm{s}$. The near transform-limited excitation bandwidth enabled high-resolution measurements of the exciton lineshape and position, from which we obtained values for the quantum defects of the S and D excitonic states associated with the appropriate crystal symmetries. Odd-parity P and F excitonic states were also observed, in accordance with predicted quadrupole-allowed two-photon excitation processes. We compared our measurements to conventional one-photon spectroscopy in the same sample, and find that the SHG spectrum is cut off at a lower principal quantum number ($n=12$ vs $n=15$). We attribute this effect to a combination of spatial inhomogeneities and local heating, and discuss the prospects for observing higher principal quantum number even-parity states in future experiments.

Based on the transmission coefficient of tunneling electrons, we have presented tunneling current and conductivity across a square-potential barrier for both graphene and $\alpha \text{−}{\mathcal{T}}_3$ lattices under a linearly polarized off-resonant dressing field. The presence of such a dressing field introduces an anisotropy factor in the energy dispersion of tunneling electrons so that the cross section of a Dirac cone appears as elliptical. Consequently, the field-polarization controlled major axis of the ellipse will be misaligned with the normal direction of a barrier layer in the tunneling system, which exhibits an asymmetric Klein paradox for an off-normal-direction tunneling. The resulting tunneling current in this system is calculated by using a transmission coefficient and a longitudinal group velocity (different from a longitudinal momentum) of electrons. By presenting numerically calculated tunneling conductivity modified by a laser dressing field, we demonstrate a significant enhancement of electrical conductivity by external laser-field intensity, which is expected to be crucial in the application of ultrafast optical modulation of optoelectronic devices for photodetection and fiber-optic communication.

The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing us to write the Hamiltonian in terms of a $2\times 2$ matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential, and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle of rotation as well as in terms of the wave-function localization properties. It is proved that the non-Abelian operator represents interlayer currents between each layer of triangular sublattices, i.e., a second-neighbor interlayer current between bipartite sublattices. A crossover is seen between such contributions, and thus, the first magic-angle is different from other higher-order magic-angles. Such angles are determined by a balance between the negative energy contribution from interlayer currents and the positive contributions from the kinetic and confinement energies. A perturbative analysis performed around the first magic-angle allows us to explore analytically the details of such an energy balance.

We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient, and the frequency of the Rabi oscillations are obtained in an explicit form. We trace the dependencies of the above quantities on the ribbon width and electric field strength for both the multiphoton assisted and tunneling regimes relevant to the time-oscillating and practically constant electric field, respectively. A significant enhancement effect of the oscillating character of the electric field on the intersubband transitions is encountered. Our analytical results are in qualitative agreement with those obtained for the graphene layer by numerical methods. Estimates of the expected experimental values for the typically employed AGNR and laser parameters show that both the Rabi oscillations and multiphoton absorption are accessible in the laboratory. The data relevant to the intersubband tunneling makes the AGNR a one-dimensional condensed matter analog in which the quantum electrodynamic vacuum decay can be detected by applying an external laboratory electric field.

In metals in the vicinity of a polar transition, interactions between electrons and soft phonon modes remain to be determined. Here we explore the consequences of spin-orbit assisted electron-phonon coupling on the collective modes of such nearly polar metals in the presence of magnetic field. We find that the soft polar phonon hybridizes with spin-flip electronic excitations of the Zeeman-split bands leading to an anticrossing. The associated energy splitting allows for an unambiguous determination of the strength of the spin-orbit mediated coupling to soft modes in polar metals by spectroscopic experiments. The approach to the polar transition is reflected by the softening of the effective $g$ factor of the hybridized spin-flip mode. Analyzing the static limit, we find that the polar order parameter can be oriented by magnetic field. This provides possibilities for alternative switching protocols in polar metallic materials. We demonstrate that the effects we predict can be observed with current experimental techniques and discuss promising material candidates.

We report on the implementation of the Bogoliubov-de Gennes method into the JuKKR code, an implementation of the relativistic all-electron, full-potential Korringa-Kohn-Rostoker Green function method, which allows a material-specific description of inhomogeneous superconductors and heterostructures on the basis of density functional theory. We describe the formalism and report on calculations for the $s$-wave superconductor Nb, a potential component of the materials platform enabling the realization of the Majorana zero modes in the field of topological quantum computing. We compare the properties of the superconducting state both in the bulk and for (110) surfaces. We compare slab calculations for different thicknesses, the effect of surface relaxations, and the influence of a softening of phonon modes on the surface for the resulting superconducting gap.

Within generalized density functional theory, recent developments of functionals which depend upon the kinetic energy density, such as the r2SCAN form, show significant improvement in the computational representation of real material properties. In order to implement these forms within plane-wave codes, it is necessary to use pseudopotentials, ideally constructed with the same exchange-correlation functional as has been implemented for the projector augmented-wave (PAW) formalism in the atompaw code. This was accomplished with the help of an efficient solver for the self-consistent radial bound states of each atom, based on cubic spline interpolation. Details of the formalism are presented, and preliminary results for several simple materials are encouraging.

Synthesis of single-crystalline NaMnAs is reported, and we confirm its high quality by x-ray photoemission spectra. Magnetometry results are consistent with previous findings of antiferromagnetic order. The electronic structure was further studied using optical transmittance and by theoretical modeling using local-density approximation (LDA) extended to LDA $+ U$ for the purpose of determining the Heisenberg model parameters. Optical transmittance measurements confirm theoretical predictions that NaMnAs is a semiconductor. The Néel temperature was determined from temperature dependence of susceptibility, in agreement with our Monte Carlo simulations.

The presence of disorder in semiconductors can dramatically change their physical properties. Yet, models faithfully accounting for it are still scarce and computationally inefficient. We present a mathematical and computational model able to simulate the optoelectronic response of semiconductor alloys of several tens of nanometer sidelength, while at the same time accounting for the quantum localization effects induced by the compositional disorder at the nanoscale. The model is based on a Wigner-Weyl analysis of the structure of electron and hole eigenstates in phase space made possible by the localization landscape theory. After validation against eigenstate-based computations in 1D and 2D, our model is applied to the computation of light absorption in 3D InGaN alloys of different compositions. We obtain the detailed structures of the absorption tail below the average band gap and the Urbach energies of all simulated compositions. Moreover, the Wigner-Weyl formalism allows us to define and compute 3D maps of the effective locally absorbed power at all frequencies. Finally, the proposed approach opens the way to generalize this method to all energy-exchange processes such as radiative and nonradiative recombination in realistic devices.

We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type, that is, interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed by G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath [Phys. Rev. Lett. 122, 106405 (2019)]. We also find that if AB-type interlayer-hopping processes are turned off, the resulting model is chiral but differs from the model discussed mentioned above. Therefore TBG has two separate chiral limits: One of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a nonrelaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly spectrum. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy $E=0$. This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide, in a slightly simplified model. Here, we find that no additional terms that break chiral symmetry are introduced. Therefore it is found to lead to no increase in asymmetry of the energy spectrum. In fact, we identify specific experimentally accessible driving regimes in which the TBG achieves any of the two chiral limits.

Structured light mechanically interacts with matter via optical forces and torques. Optical torque is traditionally calculated via the flux of total angular momentum (AM) into a volume enclosing an object. In the work published in [Phys. Rev. A 92, 043843 (2015)], a powerful method was suggested to calculate the optical torque separately from the flux of the spin and the orbital parts of optical AM, rather than the total, providing useful physical insight. However, the method predicted a new type of dipolar torque dependent on the gradient of the helicity density of the optical beam, inconsistent with prior torque calculations. In this work, we first intend to clarify this discrepancy and clear up the confusion. We rederive, from first principles and with detailed derivations, both the traditional dipolar torque using total AM flux, and the spin and orbital torque components based on the corresponding AM contributions, ensuring that their sum agrees with the total torque. We also test our derived analytical expressions against numerical integration, with the exact agreement. We find that “helicity gradient” torque terms indeed exist in the spin and orbital components separately, but we present corrected prefactors, such that upon adding them, they cancel out, and the helicity gradient term vanishes from the total dipolar torque, reconciling literature results. In the second part of the work, we derive the analytical expression of the quadrupolar torque, showing that it is proportional to the spin of the EM field gradient, rather than the local EM field spin, as sometimes wrongly assumed in the literature. We provide examples of counter-intuitive situations where the spin of the EM field gradient behaves very differently from the local EM spin. Naively using the local EM field spin leads to wrong predictions of the torque on large particles with strong contributions of quadrupole and higher-order multipoles, especially in a structured incident field.

We study the subgap transport through a ferromagnet/Ising superconductor/ferromagnet (F/ISC/F) junction by solving the Bogoliubov–de Gennes equations. It is found that the crossed Andreev reflection (CAR) and local Andreev reflection (LAR) depend strongly on the spin-polarized F, the magnetization direction, and the Ising superconducting phase. For the same magnetization directions of the two F leads, the equal-spin CAR could take place due to the spin-flip mechanism induced by the Ising spin-orbit coupling and equal-spin-triplet pairing. Both equal-spin CAR and equal-spin LAR exhibit a remarkable magnetoanisotropy with period $\pi$ and show oscillatory behavior with a chemical potential. The equal-spin CAR is more prominent for half-metal F and double-band ISC while the normal CAR is completely suppressed. When the magnetization directions of the two F leads are different, the oblique-spin CAR occurs and its magnetoanisotropic period generally becomes $2\pi$ instead of $\pi$. In the oblique-spin CAR process, the spins of the electron and hole are neither parallel nor antiparallel. Furthermore, the property of oblique-spin CAR is very sensitive to the spin and valley degrees of freedom. The spin- and valley-polarized CAR can be achieved and controlled by the chemical potentials and the magnetization directions.

The effect of non-Hermiticity in band topology has sparked many discussions on non-Hermitian topological physics. It has long been known that non-Hermitian Hamiltonians can exhibit real energy spectra under the condition of parity-time ($PT$) symmetry—commonly implemented with balanced loss and gain—but only when non-Hermiticity is relatively weak. Sufficiently strong non-Hermiticity, on the other hand, will destroy the reality of energy spectra, a situation known as spontaneous $PT$-symmetry breaking. Here, based on nonreciprocal coupling, we show a systematic strategy to construct non-Hermitian topological systems exhibiting bulk and boundary energy spectra that are always real, regardless of weak or strong non-Hermiticity. Such nonreciprocal-coupling-based non-Hermiticity can directly drive a topological phase transition and determine the band topology, as demonstrated in a few non-Hermitian systems from one dimensional to two dimensional. Our work develops a theory that can guarantee the reality of energy spectra for non-Hermitian Hamiltonians, and offers an avenue to explore non-Hermitian topological physics.

We explore a phenomenological phase diagram for the magnetic helical state with ${90}^{\circ }$ turn angle between neighboring spins in the external magnetic field. Such a state is formed by the Eu spin layers in the superconducting iron arsenide ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$. The peculiarity of this spin configuration is that it is not realized in the standard Heisenberg model with bilinear exchange interactions. A minimum model allowing for such a state requires the biquadratic nearest-neighbor interaction term. In addition, in tetragonal materials, the ${90}^{\circ }$ helix state may be stabilized by the in-plane fourfold anisotropy term, which also fixes helix orientation with respect to the crystal lattice. Such a system has a very rich behavior in the external magnetic field. The magnetic field induces the metamagnetic transition to the double-periodic state with the moment angles ($\alpha$, $\alpha$, $-\alpha$, $-\alpha$) with respect to the field for the four subsequent spins. The transition field to this state from the deformed helix is determined by the strength of biquadratic interaction. The transition is second-order for small biquadratic coupling and becomes first-order when this coupling exceeds the critical value. On the other hand, the aligned state at high magnetic field becomes unstable with respect to the formation of an incommensurate fan state, which transforms into the double-periodic state with decreasing magnetic field. The range of this incommensurate state near the saturation field is proportional to square of the biquadratic coupling. In addition, when the magnetic field is applied along one of four the equilibrium moment directions, the deformed helix state experience the first-order rotation transition at the field determined by the fourfold anisotropy.

Detection and manipulation of the Néel vector in antiferromagnetic materials are promising for more stable, faster, and much higher-density spintronic devices. However, the electrical manipulation of the antiferromagnetic Néel vector remains challenging and controversial due to the difficulty in the detection of the zero net magnetization and the unavoidable complications from thermal artifacts. In this work, by utilizing the uniaxial antiferromagnet (AFM) ${\mathrm{Cr}}_2{\mathrm{O}}_3$, we demonstrate the detection and manipulation of the antiferromagnetic Néel vector. We reveal unambiguously the spin-dependent electrical responses of the coherent ${\mathrm{Cr}}_2{\mathrm{O}}_3$ Néel vector switching, where a symmetric Hall signal and a fourfold angular-dependent magnetoresistance are captured. We also demonstrate the in-plane arbitrary manipulation of the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ Néel vector when the magnetocrystalline anisotropy energy is compensated. Our work for detecting and manipulating Néel vectors offers a critical guide for antiferromagnetic-based Néel vector switching exploration.

Here we report the magnetic and electronic properties of recently discovered ${\mathrm{Ce}}_3{\mathrm{Cd}}_2{\mathrm{As}}_6$. At ambient pressure, ${\mathrm{Ce}}_3{\mathrm{Cd}}_2{\mathrm{As}}_6$ presents a semiconducting behavior with an activation gap of 74(1) meV. At 136 K, a sudden increase of the electrical resistivity and a peak in specific heat are consistent with a charge density wave transition. At low temperatures, antiferromagnetic order of the ${\mathrm{Ce}}^{3+}$ ions occurs below $T_{\mathrm{N}}=4.0$ K with a magnetic hard axis along the $c$ axis and a ${\mathrm{\Gamma }}_6=|\pm 1/2\rangle$ doublet ground state. The application of external pressure strongly suppresses the charge density wave order, which is completely suppressed above 0.8(1) GPa, and induces a metallic ground state. No evidence for superconductivity is detected above 2 K. Conversely, the antiferromagnetic state is favored by pressure, reaching a transition temperature of 5.3 K at 3.8(1) GPa. Notably, the resistivity anomaly characterizing the antiferromagnetic order changes with increasing pressure, indicating that two different magnetic phases might be present in ${\mathrm{Ce}}_3{\mathrm{Cd}}_2{\mathrm{As}}_6$ under pressure. This change in ordering appears to be associated to the crossing of the $T_{\mathrm{CDW}}$ and $T_{\mathrm{N}}$ lines.