Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the interquantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble employing a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach that maintains local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the variation of the electron $g$ factor on the spin-noise power spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the interdot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.

The time-dependent state of a classical spin locally exchange coupled to an edge site of a Kane-Mele model in the topologically nontrivial phase is studied numerically by solving the full set of coupled microscopic equations of motion for the spin and the electron system. Dynamics in the long-time limit is accessible thanks to dissipative boundary conditions, applied to all but the zigzag edge of interest. We study means to control the state of the spin via transport of a spin-polarization cloud through the helical edge states. The cloud is formed at a distant edge site using a local magnetic field to inject an electron spin density and released by suddenly switching off the injection field. This basic process, consisting of spin injection, propagation of the spin-polarization cloud, and scattering of the cloud from the classical spin, can be used to steer the spin state in a controlled way. We find that the effect of a single basic process can be reverted to a high degree with a subsequent process. Furthermore, we show that by concatenating several basic injection-propagation-scattering processes, the spin state can be switched completely and that a full reversal can be achieved.

Dynamic tuning of electromagnetic responses guarantees numerous applications in subwavelength optoelectronics. In this paper, by taking advantages strong field confinement of all-dielectric nanohole arrays and tunability of optical conductivity through changes to the Fermi level of graphene, we present variable electromagnetic responses of the graphene/silicon hybrid nanohole arrays in the near-infrared region through simulations and experiments. We demonstrate a high quality $\left(Q\right)$ factor of toroidal dipoles resonance change from 1660 to 910 with a 0.3-nm shift in resonant wavelength. In addition, we observe a hysteretic optical behavior at 1593 nm, which originates from the interface between graphene and the ion gel and a slow polarization response in ion gel at the kHz scale. This complementary metal-oxide-semiconductor compatible flat platform, with combined advantages of low power consumption and compact footprint, enables fruitful applications in modulators, photonic memory, artificial intelligence, and neuromorphic computing.

The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schrödinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schrödinger equation provides access to trions as well as a continuum of scattering states. The dynamics of coupled excitons, trions, and scattering continua is subsequently described by Heisenberg equations of motion including mean-field contributions and correlation effects due to the interaction of excitons with trions and scattering continuum states. Our calculations for optical excitation close to the band edge reveal the influence of doping on the exciton resonances in combination with the simultaneous identification of not only ground- but also excited-state trion resonances.

Semiconductor quantum dots embedded in optical cavities are promising on-demand sources of single photons. Here, we theoretically study single photon emission from an optically driven two-photon Raman transition between the biexciton and the ground state of a quantum dot. The advantage of this process is that it allows all-optical control of the properties of the emitted single photon with a laser pulse. However, with the presence of other decay channels and excitation-induced quantum interference, on-demand emission of the single Raman photon is generally difficult to achieve. Here we show that laser pulses with nontrivial shapes can be used to maintain excitation conditions for which, with increasing pulse intensities, the on-demand regime is reached. To provide a realistic picture of the achievable system performance, we include phonon-mediated processes in the theoretical calculations. While preserving both high photon purity and indistinguishability, we find that although based on a higher-order emission process, for realistic system parameters on-demand Raman photon emission is indeed achievable with suitably tailored laser pulses.

One- and two-dimensional twisted bilayer structures are examples of ultratunable quantum materials that are considered the basis for the next generation of electronic and photonic devices. Here, we develop a general theory of the electron band structure for such commensurate and incommensurate bilayer graphene structures within the framework of the tight-binding approximation. To model the band structure of commensurate twisted bilayer graphene (TBLG), we apply the classic zone folding theory. The latter leads us to the construction of TBLG Hamiltonians in the basis of shifted Bloch wave functions (SBWFs) which, in contrast to the usual Bloch functions, have the wave vector $\mathbf{q}$ shifted by a set of vectors ${\mathbf{Q}}_i$. The dimension of the considered Hamiltonians is equal to $4T$, where the factor $T$ is a number of vertices ${\mathbf{Q}}_i$ of the folded reciprocal space falling into the original first Brillouin zone of any of the layers. We propose and discuss a method for choosing a reduced set of SBWFs to construct effective Hamiltonians that correctly describe the low-energy spectrum of commensurate TBLG. The flattening of low-energy bands with a decrease in twist angle is discussed. As we show, this spectrum results from interactions between the lowest-energy modes of the folded dispersion curves. The effective Hamiltonians for calculating the low-energy band structure of incommensurate TBLG and double-walled carbon nanotubes (DWCNTs) are constructed in a similar way. To test the developed theory, we calculate the energies of 105 intratube optical transitions in 29 DWCNTs and compare them with experimental data. We also apply the theory to calculate the energies of recently discovered intertube transitions. Geometrical conditions allowing this type of transition are discussed. We show that these transitions occur in DWCNTs whose layers have close chiral angles and the same handedness or, in the structural context, in DWCNTs with a large unit cell of the periodic moiré pattern.

Quantum paramagnets are strongly correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations instead induce topological order, supporting fractionalized quasiparticles. In this Letter, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such a state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and nontrivial topology coexist. Through this interplay, we uncover excitations that would be absent otherwise, such as cornerlike bulk states bound to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet is also induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.

We show that line defects in a non-Abelian Kitaev spin liquid harbor gapless one-dimensional Majorana modes if the interaction across the defect falls below a critical value. Treating the weak interaction at the line defect within a mean-field approximation, we determine the critical interaction strength as a function of the external magnetic field. In the gapless regime, we use the low-energy effective field theory to calculate the spin-lattice relaxation rate for a nuclear spin near the defect and find a cubic temperature dependence that agrees with experiments in the Kitaev material $\alpha {\text{-RuCl}}_3$.

Strong Coulomb interactions in atomically thin semiconductors like monolayer ${\mathrm{WSe}}_2$ induce not only tightly bound excitons, but also make their optical properties very sensible to doping. By utilizing a microscopic theory based on the excitonic Heisenberg equations of motion, we systematically determine the influence of doping on the excitonic linewidth, line shift, and oscillator strength. We calculate trion resonances and demonstrate that the Coulomb coupling of excitons to the trionic continuum generates a non-Markovian interference, which, due to a time retardation, builds up a phase responsible for asymmetric exciton line shapes and increased excitonic linewidths. Our calculated doping dependence of exciton and trion linewidths, line shifts, and oscillator strengths explains recent experiments. The gained insights provide the microscopic origin of the optical fingerprint of doped atomically thin semiconductors.

Interlayer magnetic coupling in emerging two-dimensional layered magnets holds great potential for manipulating layered magnetic structures for cross-layer transport or tunneling phenomena. In this paper, we employed first-principles calculations to show enhanced ferromagnetic (FM) interlayer exchange coupling for ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ by reducing stacking symmetry or reducing the layer number. Electronic structure analysis reveals that the former is mainly due to low-symmetry enhanced interlayer orbital hopping, and the latter originates from reduced Pauli potential for out-of-plane metallic electrons with respect to thicker layers. Interlayer FM coupling could also be weakened by substrates due to the screened Coulomb interactions, simulated by reducing the onsite Coulomb repulsion for Fe $d$ electrons. In this paper, we provide guidance to rationally control interlayer magnetic coupling via engineering stacking configuration and dielectric environment.

Magnetic nanoelements attract great interest due to their prospects for data storage and signal processing. Spin-wave confinement in these elements implies wave-number quantization, discrete frequency spectra and thus complex resonance patterns, strongly dependent on the elements' geometry and static magnetic configuration. Here we report experimental observation of unconventional single-frequency resonance response of flat circular Permalloy nanodots, which is achieved via the application of a magnetic field at a certain critical angle ${\tilde{\theta }}_B$ with respect to the dot normal. This observation is explained as the merging of spin-wave eigenmodes under the transition of the spin-wave dispersion from the forward-volume to the backward-volume type, as elucidated by micromagnetic simulations in conjunction with an analytical theory. Our results offer a way for the creation of spin-wave systems with spectrally narrow magnetic noise.

A generalized phenomenological model for the mixed state of type-II superconductors with magnetic field parallel to the superconducting plate is proposed. This model considers the global magnetization including both the equilibrium magnetization from surface screening current and the nonequilibrium magnetization from bulk pinning in a self-consistent way. Our model can be used to simulate the magnetization hysteresis loops (MHLs) and flux penetrating process of different type-II superconductors, from low- to high-$\kappa$ values. Here we take a ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystal and pure Nb plate as testing examples. The model can fit the data quite well and several important parameters can be extracted from the fitting. Thus the model can be extended to a general case for studying the magnetization and flux penetration in other type-II superconductors.

This paper solves a longstanding debate: Raman measurements on double-walled carbon nanotubes appear to show that significantly more pressure than expected can be transmitted to the inner tube. We reinterpret those Raman spectra consistently reported in the literature, by assigning the Raman peaks to coupled vibrational modes of both walls, instead of individual contributions from the inner and outer tubes. These coupled vibrational modes are important for the correct interpretation of the Raman shift from strained layered 2D materials (we demonstrate it on bilayer graphene as an example), for researching the mechanical properties, thermal expansion, and strain engineering of two-dimensional materials.

Using ab initio band structure calculations we show that mineral cubanite, ${\mathrm{CuFe}}_2{\mathrm{S}}_3$, demonstrates an orbital-selective behavior with some of the electrons occupying molecular orbitals of $x^2-y^2$ symmetry and others localized at atomic orbitals. This is a rare situation for $3d$ transition metal compounds that explains the experimentally observed absence of charge disproportionation, anomalous Mössbauer data, and ferromagnetic ordering in between nearest-neighbor Fe ions.

We study the pairing and superconducting properties of the attractive Hubbard model in two quasi-one-dimensional topological lattices—the Creutz and sawtooth lattices—which share two peculiar properties: each of their band structures exhibits a flat band with a nontrivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, due to a chiral (sublattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use a multiband mean field and exact density matrix renormalization group in our work. Our three main results are as follows: (a) For both lattice systems, the superconducting weight, $D_s$, is linear in the coupling strength, $U$, for low values of $U$. (b) For small $U, D_s$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent. We have therefore extended the approach to this more complex situation and found an excellent agreement with the numerical results. (c) At moderate and large $U$, the conventional BCS mean field is no longer appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multiband mean-field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean-field parameters.

Symmetry-protected topological superconductors (TSCs) can host multiple Majorana zero modes (MZMs) at their edges or vortex cores, while whether the Majorana braiding in such systems is non-Abelian in general remains an open question. Here, we uncover in theory the unitary symmetry-protected non-Abelian statistics of MZMs and propose the experimental realization. We show that braiding two vortices with each hosting $N$ MZMs protected by commutative or noncommutative unitary symmetries generically reduces to $N$ independent sectors, with each sector braiding two different Majorana modes. This renders the unitary symmetry-protected non-Abelian statistics. We demonstrate the proposed non-Abelian statistics in a spin-triplet TSC which hosts two MZMs at each vortex and, interestingly, can be precisely mapped to a quantum anomalous Hall insulator. Thus the unitary symmetry-protected non-Abelian statistics can be verified in the latter insulating phase, with the application to realizing various topological quantum gates being studied, and an experimental scheme of observation being proposed. This work suggests that there are a much broader range of symmetry-protected topological superconductors which host non-Abelian Majorana modes.

The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners $K$ and $K^{\prime }$, analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$, without spin-orbit coupling, we identify two energetically split helical nodal lines winding along $z$ in the vicinity of $K$ and $K^{\prime }$ resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. We identify the latter to be one order of magnitude weaker than the former owing to the underlying $d$-orbital degrees of freedom. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ as a model Dirac kagome metal by clarifying the roles played by interplane coupling, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.

In the recent advancement in graphene heterostructures, it is possible to create a double-layer tunnel decoupled graphene system that has a strong interlayer electronic interaction. In this work, we restrict the parameters in the low energy effective Hamiltonian using simple symmetry arguments. Then, we study the ground state of this system in the Hartree-Fock approximation at ${\nu }_1^{}={\nu }_2^{}=0$. In addition to the phases found in monolayer graphene, we found an existence of layer-coherent phase which breaks the layer $U\left(1\right)$ symmetry. At nonzero Zeeman coupling strength $\left(E_z\right)$, this layer-coherent state has a small magnetization that vanishes when $E_z$ tends to zero. We discuss the bulk gapless modes using the Goldstone theorem. We also comment on the edge structure for the layer-coherent phase.

We propose an operatorially exact formalism for describing the equilibrium and quantum-dynamical properties of many-electron systems interacting locally on a lattice, called “ghost rotationally invariant slave-boson theory” (g-RISB). We demonstrate that our theoretical framework reduces to the recently developed ghost Gutzwiller approximation (g-GA) at the mean-field level. Furthermore, we introduce the time-dependent mean-field g-RISB action, generalizing the time-dependent GA theory. Since the g-RISB is based on exact reformulation of the many-body problem, it may pave the way to the development of practical implementations for adding systematically quantum-fluctuation corrections towards the exact solution, in arbitrary dimension.