The presence or absence of certain symmetries in the normal state (NS) also determines the symmetry of the Cooper pairs. Here, we show that parity ($\mathcal{P}$-) and time-reversal ($\mathcal{T}$-) odd Dirac insulators (trivial or topological) or metals, sustain a local or intraunit cell pairing that supports corner (in $d=2$) or hinge (in $d=3$) modes of Majorana fermions and stands as a higher-order topological superconductor (HOTSC), when the NS additionally breaks discrete fourfold ($C_4$) symmetry. Although these outcomes do not rely on the existence of a Fermi surface, around it (when the system is doped) the HOTSC takes the form of a mixed parity, $\mathcal{T}$-odd (due to the lack of $\mathcal{P}$ and $\mathcal{T}$ in the NS, respectively) $p+id$ pairing, where the $p(d$)-wave component stems from the Dirac nature of quasiparticles (lack of $C_4$ symmetry) in the NS. Thus, when strained, magnetically ordered Dirac materials, such as doped magnetic topological insulators (${\mathrm{MnBi}}_2{\mathrm{Te}}_4$), can harbor HOTSCs, while the absence of an external strain should be conducive for the axionic $p+is$ pairing.

Available experimental data about static and dynamic critical behaviors of ${\text{Sn}}_2{\text{P}}_2{\text{S}}_6$-type ferroelectrics and $({\mathrm{Pb}}_y{\mathrm{Sn}}_{1-y}{)}_2{\mathrm{P}}_2{\left({\mathrm{Se}}_x{\mathrm{S}}_{1-x}\right)}_6$ mixed crystals with a line of tricritical points and a line of Lifshitz points on the $T-x-y$ phase diagram, which meet at the tricritical Lifshitz point, are described in a combined Blume-Capel anisotropic next-nearest-neighbor Ising model. Such spin-1 Ising models with anisotropic competing first- and second-neighbor interactions is applied for the considered ferroelectrics with mixed displacive versus order/disorder character of phase transitions within the framework of a microscopic model with three-well total energy surface for ferroelectric distortion that was earlier built in an ab initio effective Hamiltonian approach. It was found that below the temperature of the tricritical Lifshitz point, the “chaotic” state accompanied by the coexistence of ferroelectric, metastable paraelectric, and modulated phases is expected. In addition to the frustration of polar fluctuations near the Brillouin zone center, in ${\mathrm{Sn}}_2{\mathrm{P}}_2{\mathrm{S}}_6$ crystals the antipolar fluctuations also strongly develop in the paraelectric phase on cooling to the continuous phase-transition temperature $T_0$. Here, the critical behavior can be described as a crossover between Ising and XY universality classes, which is expected near bicritical points with coupled polar and antipolar order parameters and competing instabilities in $q$ space.

We study the one-dimensional nearest-neighbor tight-binding model of electrons with independently distributed random hopping and no on-site potential (i.e., off-diagonal disorder with particle-hole symmetry, leading to sublattice symmetry, for each realization). For nonsingular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $\rho \left(E\right)\sim 1/|E{ln}^3\left|E\right||$ and of the localization length $\xi \left(E\right)\sim |ln|E\left|\right|$, near the band center $E=0$. (This singular behavior is also applicable to random XY and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain.) Simultaneously, the state at $E=0$ shows a universal, subexponential decay at large distances $\sim exp[-\sqrt{r/r_0}]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $t$ is of the form $\sim 1/\left[t{ln}^{\lambda +1}(1/t)\right]$, characterized by a single, continuously tunable parameter $\lambda >0$. We find, using a combination of analytic and numerical methods, that while the universal result applies for $\lambda >2$, it no longer holds in the interval $0<\lambda <2$. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the nonuniversal parameter $\lambda$; simultaneously, the localization length shows a less divergent form at low energies and ceases to diverge below $\lambda =1$. For $\lambda <2$, the fall-off of the $E=0$ state at large distances also deviates from the universal result and is of the form $\sim exp[-{(r/r_0)}^{1/\lambda }]$, which decays faster than an exponential for $\lambda <1$.

Kondo metal $\mathrm{CePtA}{\mathrm{l}}_4\mathrm{G}{\mathrm{e}}_2$ exhibits long-range antiferromagnetic order below 2.3 K. Neutron powder-diffraction experiments reveal that Ce moments order antiferromagnetically with an incommensurate ordering wave vector $\mathit{k}=\left(1.39,0,0.09\right)$. Inelastic neutron powder scattering experiments show a magnetic excitation at 14.5 meV, which corresponds to the first excited state due to the crystalline electric field splitting of the ground-state multiplet of $\mathrm{C}{\mathrm{e}}^{3+}$. The temperature and field dependence of the magnetization of $\mathrm{CePtA}{\mathrm{l}}_4\mathrm{G}{\mathrm{e}}_2$ is consistent with a doublet ground state with a dominant $|j_{\mathrm{z}}=1/2\rangle$ character and a first excited doublet $|j_{\mathrm{z}}=3/2\rangle$ at 14.5 meV.

Magnetic ordering breaks the time-reversal symmetry, greatly impacting material topological properties. We report the investigation of the magnetic properties of the layered $\mathrm{EuMnS}{\mathrm{b}}_2$, which has two sets of magnetic sublattices. Both the magnetization and electrical resistivity reveal two phase transitions with one at $T_{\mathrm{N},\mathrm{Eu}}\sim 21\mathrm{K}$ and the other at $T_{\mathrm{N},\mathrm{Mn}}\sim 346\mathrm{K}$. Single crystal neutron diffraction refinement indicates that both transitions are originated from magnetic ordering. Below $T_{\mathrm{N},\mathrm{Mn}},$ the Mn sublattice forms the C-type antiferromagnetic (AFM) structure with moments [$(4.5\pm 0.6){\mu }_B$ at 7 K] pointing along the $a$ axis. Below $T_{\mathrm{N},\mathrm{Eu}}$, the Eu sublattice forms the canted A-type AFM structure with moments [$(5.9\pm 0.8){\mu }_{\mathrm{B}}$ at 7 K] lying in the $ac$ plane but pointing (41 ± 1)° away from the $a$ axis. Quantitative analysis indicates that the spin-spin correlation length, while anisotropic, has long-range characteristic in all directions for both the Eu and Mn sublattices.

We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\pi ,\pi )$, $(0,\pi )$, and (0,0) we find incommensurate phases where the ordering wave vectors $\mathbf{Q}=(Q,Q)$ and $(Q,\pi )$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the $(Q,Q)$ and $(Q,\pi )$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.

We present an infrared reflectivity study of the $E_{1u}$ in-plane phonons of hexagonal BN as a function of temperature in the 40–680 K range. The infrared reflectance spectra of high-quality lamellar single crystals are accurately fitted using Lowndes' factorized form of the dielectric response, where the longitudinal-optic (LO) frequency is an independent adjustable parameter. From this analysis we obtain reliable values for the phonon damping of the IR-active $E_{1u}$ phonons which couple to light and give rise to the phonon-polariton excitations in this hyperbolic material. Anharmonic coupling potentials are estimated from the temperature dependence of the damping parameters. The $E_{1u}\left(\text{LO}\right)$ mode exhibits a substantially longer lifetime than its transverse-optic counterpart, as it is basically unaffected by isotopic-disorder scattering owing to the low density of phonon states around the $E_{1u}\left(\text{LO}\right)$ frequency.

Semiconductor quantum dots in photonic cavities are strongly coupled light-matter systems with prospective applications in optoelectronic devices and quantum information processing. Here we present a theoretical study of the coupled exciton–light field dynamics of a planar quantum dot ensemble, treated as two-level systems, embedded in a photonic cavity modeled by Maxwell's equations. When excited by coupling an external short laser pulse into the cavity, we find an exciton-polariton-like behavior for weak excitation and Rabi oscillations for strong excitation with a sharp transition between these regimes. In the transition region, we find highly nonlinear dynamics involving high harmonics of the fundamental oscillation. We perform a numerical study based on the finite-difference-time-domain method for the solution of Maxwell's equations coupled to Bloch equations for the quantum dots and also derive an analytical model to describe the coupled cavity-quantum dot system, which allows us to describe the light field dynamics in terms of a Newton-like dynamics in an effective anharmonic potential. From the shape of this potential combined with the initial conditions, the transition can be well understood. The model is then extended to a broadened ensemble of quantum dots. For weak excitation, the polariton spectrum broadens and the lines slightly shift, however, the sharp transition to the Rabi oscillation regime is still present. Furthermore, we find a second, lower threshold with additional lines in the spectra which can be traced back to Rabi oscillations driven by the polariton modes. Our approach provides new insights in the dynamics of both quantum dot and light field in the photonic structure.

Graphene is a natural material platform for experimental realization of triangular fractals. Hence, forming triangular holes in the hexagonal lattice following a self-similar recipe leads to fractal Sierpinski triangles. Two subclasses characterized by armchair and zigzag edges are investigated using a mean-field Hubbard approach. We find that zigzag-edged fractals support a significant spin polarization whereas the armchair subclass is spin balanced. Despite this difference, the energy gap between like-spin states is large for both types. A self-similar distribution of energy levels is found in late-generation fractals. In an external magnetic field, the energy gaps tend to decrease, and an intricate dispersion of individual levels is found. This leads to optical Hall conductivities with a seemingly chaotic field dependence in late-generation fractals.

Suspended graphene exhibits ripples of size ranging from 50 to 100 Å and height $\sim 10$ Å, however, their origin remains undetermined. Previous theoretical works have proposed that rippling in graphene might be generated by the coupling between the bending modes and the density of electrons. These theoretical studies proposed that, in the thermodynamic limit, a membrane of single layer graphene becomes unstable for large enough electron-phonon coupling, which signals a phase transition from a flat phase to a rippled one. Here, we find the stable configuration of a suspended monolayer of graphene at $T=0$ by minimizing the average energy of a membrane where the Dirac electrons of graphene couple to elastic classical deformation fields. We find that the electron-phonon coupling controls a transition from a stable flat configuration to a stable rippled phase. We propose a scaling procedure that allows us to effectively reach larger system sizes. We find that the critical value of the coupling $g_c$ rapidly decays as the system increases its size, in agreement with the experimental observation of an unavoidable stable rippled state for suspended graphene membranes. This decay turns out to be controlled by a power law with a critical exponent $\sim 1/2$. Consistent arguments based on bifurcation theory indicate that the phase transition is discontinuous at large scaling parameter $k$, that the jump in the order parameter decreases as $k^{-1/2}$, and that the phase transition becomes continuous at $k=\infty$, with the order parameter scaling as ${(g-g_{c,\infty })}^{1/4}$.

We predict an anomalous thermal Hall effect (ATHE) mediated by photons in networks of Weyl semimetals. Contrary to the photon thermal Hall effect in magneto-optical systems which requires the application of an external magnetic field the ATHE in a Weyl semimetals network is an intrinsic property of these systems. Since the Weyl semimetals can exhibit a strong nonreciprocal response in the infrared over a broad spectral range, the magnitude of thermal Hall flux in these systems can be relatively large compared to the primary flux. This ATHE paves the way for a directional control of heat flux by locally tuning the magnitude of temperature field without changing the direction of temperature gradient.

We predict that spatially modulated Zeeman splitting resulting in the formation of a Zeeman lattice can be used for creation of localized self-sustained excitations in spinor polariton condensates with dominant repulsive interactions. In such lattices, the phenomenon of TE-TM splitting, playing the role of effective spin-orbit interaction, leads to the emergence of the stripe phase and formation of stable gap-stripe solitons with a complex intrinsic structure resulting from the presence of two characteristic spatial scales, one of which is set by the period of the Zeeman lattice, while the other is set by the momentum in the depth of the Brillouin zone, at which such solitons bifurcate from the linear spectrum. Gap-stripe polariton solitons can be excited by a suitable resonant pump.

We study Landau-Zener-Stückelberg (LZS) interferometry in a cQED architecture under the effects of dissipation. To be specific, we consider a superconducting qubit driven by a $\mathrm{dc}+\mathrm{ac}$ signal and coupled to a transmission line resonator, but our results are valid for general qubit-resonators devices. To take the environment into account, we assume that the resonator is coupled to an Ohmic quantum bath. The Floquet-Born-Markov master equation is numerically solved to obtain the dynamics of the system for an arbitrary amplitude of the drive and different timescales. We unveil important differences in the resonant patterns between the strong coupling and ultrastrong coupling regimes in the qubit-resonator interaction, which are mainly due to the magnitude of photonic gaps in the energy spectrum of the system. We identify in the LZS patterns the contribution of the qubit gap and the photonic gaps, showing that for large driving amplitudes the patterns present a weaving structure due to the combined intercrossing of the different gaps contributions.

By using density-functional theory-based GW method, we studied the valley degree of freedom of Janus monolayer VSSe. The GW corrections lead to a doubling of the band gap and change the band dispersion considerably, indicating significant many-body effects. VSSe is confirmed to be ferromagnetic, which breaks the time-reversal symmetry and the odd parity of the Berry curvature in momentum space. The dissimilar magnitudes of Berry curvatures of the inequivalent valleys give rise to appreciable anomalous Hall conductivity (AHC). The calculated valley optical response of VSSe exhibits a clear valley-selective circular dichroism. The ferromagnetism induces large valley-Zeeman splitting, making it possible to realize the selective valley excitation even by unpolarized light. The Janus VSSe is more tunable by external fields because of symmetry breaking. Due to the relief of time-reversal symmetry, the valley-Zeeman splitting can be continuously tuned by varying the magnetization direction. The loss of mirror symmetry in VSSe enables a bidirection modulation of the band gap by changing the direction of electric field. The strain can linearly tune the valley gap in a considerable range. The Berry curvature and AHC can be effectively regulated in the external fields.

Excitons in two-dimensional (2D) transition metal dichalcogenides (TMDC) are stable at room temperature because of high exciton binding energies. They can be selectively addressed based on the unique optical selection rules from angular momentum conservation for the $K/K^{\prime }$ valley state and the helicity of circularly polarized light. When coupled with the optical modes in optical cavities, excitons can form exciton-polaritons, exploiting which in 2D TMDC may lead to optoelectronic devices for room temperature operation. The valley degree of freedom of the excitons, however, is mostly lost when forming exciton-polaritons because the cavity mode usually does not have a well-defined spin angular momentum. Here, we theoretically demonstrate that the valley information of exciton-polaritons can be preserved and resolved in a photonic cavity made of birefringent materials. Because of the optical anisotropy, the guided resonance modes have a net transverse spin angular momentum and selectively couple to exciton-polaritons with the corresponding valley state. In the strong-coupling regime, the exciton-polariton behaves in a way like the Rashba effect in the solid. The dispersion of the $K/K^{\prime }$ exciton-polariton splits in momentum space based on its valley state, similar to electron spins in Rashba systems. Realizing valley-dependent exciton-polaritons affords a possibility to explore valley exciton dynamics in a strongly coupled system and will contribute to the study of excitonic, polaritonic devices, Bose-Einstein condensation, and superfluidity in semiconductors.

Scientists have long studied the physics of highly disordered conducting systems, seeking to understand the multitude of quantum phenomena that govern how electrons move through material systems. Recently, research into silicon-based quantum computing has made disordered conducting systems, such as Si:P monolayers embedded in isotopically pure Si, technically relevant. Consequently, applying and advancing the theoretical frameworks developed to describe electron behavior in disordered systems is a necessary objective in this field of research. This study investigates key components of dopant-based Si quantum computing devices: embedded regions of highly doped delta layers (δ layers). We examine the transport behavior and the electron-electron interaction (EEI) physics in embedded Si:P δ layers by means of self-consistent magnetotransport measurements. Parameters associated with the electronic transport offer a meaningful quantitative characterization of δ-layer quality and dopant diffusion. In addition, by examining EEI behaviors in a set of samples with embedded Si:P δ layers produced with different $\mathrm{P}{\mathrm{H}}_3$ exposure procedures prior to Si encapsulation, we show how details of material synthesis affect the dimensionality of charge carrier interactions in embedded Si:P δ layers. The relationship between δ-layer confinement and EEI screening lengths is established here. This understanding will help validate important models used for device simulation and design and lead to improvements in the control of electrostatic gating of and tunneling transport through Si:P single atom transistors.