The optical spectra of two-dimensional (2D) materials exhibit sharp absorption peaks that are commonly identified with exciton and trions (or charged excitons). In this paper, we show that excitons and trions in doped 2D materials can be described by two coupled Schrödinger-like equations—one two-body equation for excitons and another four-body equation for trions. In electron-doped 2D materials, a bound trion state is identified with a four-body bound state of an exciton and an excited conduction-band electron-hole pair. In doped 2D materials, the exciton and trion states are the not the eigenstates of the full Hamiltonian and their respective Schrödinger equations are coupled due to Coulomb interactions. The strength of this coupling increases with the doping density. Solutions of these two coupled equations can quantitatively explain all the prominent features experimentally observed in the optical absorption spectra of 2D materials, including the observation of two prominent absorption peaks and the variation of their energy splittings and spectral shapes and strengths with the electron density. The optical conductivity obtained in our paper satisfies the optical conductivity sum rule exactly. A superposition of exciton and trion states can be used to construct a solution of the two coupled Schrödinger equations and this solution resembles the variational exciton-polaron state, thereby establishing the relationship between our approach and Fermi polaron physics.

Using density functional theory based electronic structure calculations, we carry out detailed investigation on geometric and electronic properties of group-III atom (B, Al, and Ga) based monolayers, namely borophene, aluminene, and gallinene, in ${\beta }_{12}$ configuration which is one of the stable structures for borophene. The results of our calculations indicate that all these monolayers form energetically stable systems and these are all metallic in nature since they possess finite density of states at the Fermi level. Analysis of optimized geometric structures reveals that while borophene in ${\beta }_{12}$ structure stabilizes in planar structure, the geometries of the remaining monolayers are nonplanar. In the case of borophene, there is a signature of crossing of two linear bands (which form Dirac cones) at about 2 eV and 0.5 eV above the Fermi level. Similar features have also been observed in electronic band structures of both aluminene and gallinene. Interestingly, one of the Dirac cones in these monolayers lies much closer to the Fermi level compared to the borophene case. The Fermi velocities around these Dirac cones are also higher and comparable to that in graphene. We further study the effect of isoelectronic substitution at one of the inequivalent sites (C site) of the ${\beta }_{12}$ configuration for these three monolayers. Our results show that borophene still retains its planar geometry following the substitution. Interestingly, in all these cases, crossing of linearly dispersing bands (Dirac cones) is observed nearer to the Fermi level compared to the pristine systems. Our study suggests that isoelectronic substitutions may be useful in tuning the electronic properties, in particular linear dispersion, of monolayer systems.

We calculate the quasiparticle properties of $\mathrm{Mo}{\mathrm{S}}_2$ monolayer at $T=0$ considering the dynamical electron-electron interaction effect within random-phase-approximation (RPA). The calculations are carried out for an electron-doped slab of $\mathrm{Mo}{\mathrm{S}}_2$ monolayer using a minimal massive Dirac Hamiltonian and the quasi-two-dimensional nature of the Coulomb interaction in this system is taken into account considering a modified interaction of Keldysh type. Having calculated the real and imaginary parts of the retarded self-energy, we find the spectral function and discuss the impact of extrinsic variables such as the dielectric medium and the charge carrier density on the appearance and position of the quasiparticle peaks. We also report the results of the renormalization constant and the effective Fermi velocity calculations in a broad range of the coupling constant and carrier density. We show that the effective Fermi velocity obtained solving the self-consistent Dyson equation has an absolutely different behavior from the one found from the on-shell approximation. Our results show that the nonlocal dielectric screening of the monolayer tends to stabilize the Fermi liquid picture in $\mathrm{Mo}{\mathrm{S}}_2$ monolayer and that the interaction strength parameter of this system is a multivariable function of the coupling constant, carrier density, and also the screening length.

We performed inelastic x-ray scattering experiments on solid and liquid Li to determine the static density response function $\chi (q,0)$, where $q$ is wave vector. The experimentally determined $\chi (q,0)$ allows meaningful comparison of the response function with that of the electron gas model; $\chi (q,0)$ exhibits the $2k_F$ singularity predicted in the electron gas model. The screening electron density induced by a positive point charge is calculated, and it shows Friedel oscillations both in solid and liquid Li. Moreover, we found that the Friedel oscillations become weak upon melting.

The effects on the rare-earth crystal-field-splitting schemes of incorporation of large spin-orbit coupling ($5d$) ions, such as ${\text{Ir}}^{\text{4}}+$, into the rare-earth pyrochlores are largely unknown. We report on the preparation, specific heat, magnetization, and inelastic neutron-scattering study of ${\text{Er}}_{\text{2}}{\text{Ir}}_{\text{2}}{\text{O}}_{\text{7}}$ pyrochlore. An anomaly in specific heat and bifurcation of zero-field cooled and field cooled magnetization indicates an ordering of the Ir sublattice below 140 K, in good agreement with other rare-earth pyrochlore iridates. The Er sublattice ordering below 2 K can be considered short range as well, following the development of specific-heat and magnetization data down to low temperatures. The inelastic neutron scattering allowed us to unambiguously determine the crystal-field (CF) eigenenergies and parameters of ${\text{Er}}_{\text{2}}{\text{Ir}}_{\text{2}}{\text{O}}_{\text{7}}$, which are dictated dominantly by nearest-neighbor anions (the oxygen cage around the Er cation). The influence of the magnetic iridium cations on the erbium CF scheme is rather moderate despite the strong spin-orbit coupling expected in a $5d$ metal, which is evident when comparing the energy spectra of this iridate and other $3d$- or $4d$-metal containing erbium pyrochlores. The determined CF parameters were subsequently utilized for calculations of magnetization and specific-heat CF contributions, leading to an excellent agreement with experimental data.

The existence of orbital-dependent electronic correlations has been recognized as an essential ingredient to describe the physics of iron-based superconductors. NaFeAs, a parent compound of iron-based superconductors, exhibits a tetragonal-to-orthorhombic lattice distortion below $T_s\approx 60$ K, forming an electronic nematic phase with two ${90}^{\circ }$ rotated (twinned) domains, and orders antiferromagnetically below $T_N\approx 42$ K. We use inelastic neutron scattering to study spin waves in uniaxial pressure-detwinned NaFeAs. By comparing the data with combined density functional theory and dynamical mean-field theory calculations, we conclude that spin waves up to an energy scale of $E_{\text{crossover}}\approx 100$ meV are dominated by $d_{yz}\text{−}{d}_{yz}$ intraorbital scattering processes, which have the twofold ($C_2$) rotational symmetry of the underlying lattice. On the other hand, the spin wave excitations above $E_{\text{crossover}}$, which have approximately fourfold ($C_4$) rotational symmetry, arise from the $d_{xy}\text{−}{d}_{xy}$ intraorbital scattering that controls the overall magnetic bandwidth in this material. In addition, we find that the low-energy ($E\approx 6$ meV) spin excitations change from approximate $C_4$ to $C_2$ rotational symmetry below a temperature $T^{*}$ ($>T_s$), while spin excitations at energies above $E_{\text{crossover}}$ have approximate $C_4$ rotational symmetry and are weakly temperature dependent. These results are consistent with angle-resolved photoemission spectroscopy measurements, where the presence of a uniaxial strain necessary to detwin NaFeAs also raises the onset temperature $T^{*}$ of observable orbital-dependent band splitting to above $T_s$, thus supporting the notion of orbital selective spin waves in the nematic phase of iron-based superconductors.

We use scanning tunneling microscopy/spectroscopy to elucidate the Cooper pairing of the iron pnictide superconductor ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$. By a cold-cleaving technique, we obtain atomically resolved termination surfaces with different layer identities. Remarkably, we observe that the low-energy tunneling spectrum related to superconductivity has an unprecedented dependence on the layer identity. By cross referencing with the angle-revolved photoemission results and the tunneling data of LiFeAs, we find that tunneling on each termination surface probes superconductivity through selecting distinct $\mathrm{Fe}\text{−}3d$ orbitals. These findings imply the real-space orbital features of the Cooper pairing in the iron pnictide superconductors, and propose a general concept that, for complex multiorbital material, tunneling on different terminating layers can feature orbital selectivity.

The vortex ice system has been proposed as a promising platform to study the geometrical frustration and the emergent exotic phenomena, mainly because of the availability of tunable vortex-vortex interactions and the feasibility to manufacture a variety of nanoscale pinning potential geometries. In this paper, we designed and fabricated a kagome lattice of paired antidots with geometrical frustration. By changing the magnetic field to tune the number of interaction units, the vortex ice pattern formation and its evolution are revealed. We have found that only local topological charge order is formed at low magnetic fields, while the vortex pattern enters a disordered paramagnetic state with no long-range order of chirality or topological charge at relatively high magnetic fields. Instead of the expected half matching field in a vortex ice, the vertices fulfill the ice rule, reaching the maximum proportion at $0.7H_1$ due to the appearance of interstitial vortices. The correlation of vortex interaction also confirms such nontrivial matching field.

The appearance of a plateau in the magnetization of a quantum spin system subject to continuously varying magnetic field invites the identification of a topological quantization. Indeed, the magnetization plateaus at $1/8$ and $1/2$ of saturation in ${\mathrm{TmB}}_4$ have been suggested to be intrinsic, resulting from such a topological quantization, or, alternatively, to be metastable phases. By means of neutron- and x-ray-scattering experiments and magnetization measurements, we show that the 1/8 plateau is metastable, arising because the spin dynamics are frozen below $T\approx 4.5$ K. Our experiments show that in this part of the phase diagram of ${\mathrm{TmB}}_4$, many long-ranged orders with different propagation vectors may appear and coexist, particularly as the applied field drives the system from one plateau to another. The magnetic structures accommodating a magnetization of $\approx 1/8$ seem to be particularly favorable, but still only appear if the system has sufficient dynamics to reorganize into a superstructure as it is driven toward the expected plateau. This work demonstrates that ${\mathrm{TmB}}_4$ represents a model material for the study of slow dynamics, in and out of equilibrium.

Based on reliable ab initio computations and the numerical renormalization group method, systematic studies on a two-dimensional GaSe monolayer with Co adatoms have been carried out. It is shown that the stable lowest-energy configuration of the system involves the Co adatom located over a Ga atom. For such a configuration, it is demonstrated that the electronic and magnetic properties of the system can be effectively controlled by means of external factors, such as magnetic field, gate voltage, or temperature. Moreover, if properly tuned, the GaSe-Co system can also exhibit the Kondo effect. The development of the Kondo phenomenon is revealed in the local density of states of the Co adatom, its magnetic field dependence, which presents the splitting of the Kondo peak, as well as in the temperature dependence of the conductance, which exhibits scaling typical of the spin-$\frac{1}{2}$ Kondo effect.

We report the observation of an intense anomalous peak at 1608 ${\mathrm{cm}}^{-1}$ in the Raman spectrum of graphene associated with the presence of chromium nanoparticles in contact with graphene. Bombardment with an electron beam demonstrates that this peak is distinct from the well-studied $D^{\prime }$ peak appearing as defects are created in graphene; this peak is found to be nondispersive. We argue that the bonding of chromium atoms with carbon atoms softens the out-of-plane optical (ZO) phonon mode, in such a way that the frequency of its overtone decreases to $2{\omega }_{\mathrm{ZO}}\sim {\omega }_{\mathrm{G}}$, where ${\omega }_{\mathrm{G}}=1585$ ${\mathrm{cm}}^{-1}$ is the frequency of the Raman-active $E_{2\mathrm{g}}$ mode. Thus, the observed peak is attributed to the 2ZO mode which becomes Raman active following a mechanism known as Fermi resonance. First-principles calculations of the vibrational and anharmonic properties of the graphene/Cr interface support this scenario.

Semiconductors in the proximity of superconductors have been proposed to support phases hosting Majorana bound states. When the systems undergo a topological phase transition towards the Majorana phase, the spectral gap closes, then reopens, and the quasiparticle band spin polarization is inverted. We focus on two paradigmatic semiconductor-superconductor heterostructures and propose an all-electrical spectroscopic probe sensitive to the spin inversion at the topological transition. Our proposal relies on the indirect coupling of a time-dependent electric field to the electronic spin due to the strong Rashba spin-orbit coupling in the semiconductor. We analyze within linear response theory the dynamical correlation functions and demonstrate that some components of the susceptibility can be used to detect the nontrivial topological phases.

In bilayer $\mathrm{Cr}{\mathrm{I}}_3$, experimental and theoretical studies suggest that the magnetic order is closely related to the layer staking configuration. In this work, we study the effect of dynamical lattice distortions, induced by nonlinear phonon coupling, in the magnetic order of the bilayer system. We use density functional theory to determine the phonon properties and group theory to obtain the allowed phonon-phonon interactions. We find that the bilayer structure possesses low-frequency Raman modes that can be nonlinearly activated upon the coherent photoexcitation of a suitable infrared phonon mode. This transient lattice modification in turn inverts the sign of the interlayer spin interaction for parameters accessible in experiments, indicating a low-frequency light-induced antiferromagnet-to-ferromagnet transition.

We report a comprehensive investigation of the structural, magnetic, transport, and thermodynamic properties of single crystal PrAlSi, in comparison to its nonmagnetic analog LaAlSi. PrAlSi exhibits a ferromagnetic transition at $T_C=17.8$ K which, however, is followed by two weak phase transitions at lower temperatures. The two reentrant magnetic phases can be suppressed by a small magnetic field of about 0.4 T and are proposed to be spin glasses or ferromagnetic cluster glasses based on dc and ac magnetic susceptibilities. Both the two compounds reveal large, nonsaturating magnetoresistance as a function of field. While Shubnikov-de Haas oscillations are absent in LaAlSi, they are clearly observed below about 25 K in PrAlSi, with an unusual temperature dependence of the dominating oscillation frequency $F$. It increases from $F=18$ T at 25 K to $F=33$ T at 2 K, hinting at an emerging Fermi pocket upon cooling into the ordered phase. Specific-heat measurements indicate a non-Kramers magnetic doublet ground state and a small overall crystal electric field splitting of the ${\mathrm{Pr}}^{3+}$ multiplets of less than 100 K; Hall-effect measurements show a large anomalous Hall conductivity amounting to $\sim 2000{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ below $T_C$. These results suggest that PrAlSi is a new system where a small Fermi pocket is strongly coupled to local-moment magnetism. Whether topological state is also involved remains an intriguing open problem.

The emergent Weyl fermions in condensed matter generally break the Lorentz invariance, resulting in a tilted (type-I) or overtilted (type-II) energy dispersion. The tilting energy spectra can lead to exotic quantum interference effects in a junction setup. Here, we theoretically investigate the Josephson current in a Weyl superconductor–Weyl (semi)metal–Weyl superconductor junction of a time-reversal (TR) broken type-I Weyl semimetal. We reveal a Josephson current 0-$\pi$ transition and zero-bias supercurrent for BCS-like pairing with inversion-symmetric tilt in the Weyl nodes. The zero-bias current is the manifestation of the tilt-assisted anomaly in this model. In contrast, these anomalous effects remain absent in the case of inversion-breaking tilt and for Fulde-Ferrell-Larkin-Ovchinnikov-like pairing in the Weyl superconductor. We further chart qualitative differences between the two distinct types of pairings by studying the critical current dependency on junction length. Our study opens an avenue to probe these two types superconducting pairings in TR-broken Weyl semimetals. It is also quite interesting that the tilting in Weyl nodes naturally leads to anomalous current phase relations in this model without any magnetic manipulation.

We investigate the nature of strain in $\mathrm{Mo}{\mathrm{S}}_2$ and correlate it to defect types and densities, while systematically assessing the tolerance of this low dimensional material to He and Au ion irradiations. Through a series of theoretical predictions and experimental observations, we establish the onset of the crystalline-to-amorphous transition in $\mathrm{Mo}{\mathrm{S}}_2$ and identify sulfur vacancies as the most favorable defects introduced during irradiation. We note the presence of both tensile and compressive strains, which depend on the types of defects introduced into the lattice and vary with increasing fluence. The results show that defects can be used to tune strain in two-dimensional materials and provide an exciting pathway for using external stimuli to control properties of low dimensional materials.

Photon scattering and the ensuing excitation of surface plasmons in single rings, single composite rings, and many-ring systems was recently shown to provide dispersion and field distributions [K. V. Garapati et al., J. Phys. Commun. 2, 015031 (2018)] of potential for specific applications in particle and molecular trapping [R. Alaee et al., Appl. Phys. Lett. 109, 141102 (2016); M. Salhi et al., Phys. Rev. A 92, 033416 (2015)], in addition to metamaterials and sensing. Following photon or electron interactions with metallic nanorings, both radiative and nonradiative decay channels are important in the consideration of the nanoparticle as a photon or phonon source, and in related applications. Here, we quantize the electronic normal modes of the ring torus and obtain the radiative decay of plasmons. Due to a geometry-related complexity, we employ a perturbation approach to obtain analytical expressions for the radiative decay channel for a vacuum bounded single solid nanoring. In quantizing the fields, the frequency spectrum of the charge density normal modes of the nanoring is obtained and shown to agree with the exact quasistatic plasmon dispersion relations. Higher-order corrections beyond the presented zero- and first-order calculations may be obtained following the presented results. The results are of potential interest in quantum sensing such as entangling photons and plasmons, or plasmons and trapped molecules.

We report on line-width analysis of optical transitions in InAs/GaAs coupled quantum dots as a function of bias voltage, temperature, and tunnel coupling strength. A significant line broadening up to 100 $\mu \mathrm{eV}$ is observed at hole tunneling resonances where the coherent tunnel coupling between spatially direct and indirect exciton states is maximized, corresponding to a phonon-assisted transition rate of $150{\mathrm{ns}}^{-1}$ at 20 K. With increasing temperature, the linewidth shows broadening characteristic of single-phonon transitions. The linewidth as a function of tunnel coupling strength tracks the theoretical prediction of line-width broadening due to phonon-assisted transitions, and is maximized with an energy splitting between the two exciton branches of $0.8-0.9\mathrm{meV}$. This report highlights the line-width broadening mechanisms and fundamental aspects of the interaction between these systems and the local environment.