We study the energy levels and transport properties of an extended Kitaev chain with a phase gradient. It is demonstrated that the hopping phase difference can effectively induce the generation of Majorana bound states, which are located at the nonendpoint sites of the chain. The number and position of the nonendpoint Majorana bound states can be modulated by the hopping phase difference and initial hopping phase, respectively. In addition, we propose a protocol to realize topological braiding operation by exchanging the positions of two Majorana bound states in the extended Kitaev ring. Furthermore, we also implement the braiding of any two of the multiple Majorana bound states in the extended Kitaev double rings.

The topological properties are investigated for strongly correlated materials having honeycomb lattice structures and spin texture $\vec{S}=S[sin\left({\vec{q}}_1\vec{r}\right)cos\left({\vec{q}}_2\vec{r}\right),sin\left({\vec{q}}_1\vec{r}\right)sin\left({\vec{q}}_2\vec{r}\right),cos\left({\vec{q}}_1\vec{r}\right)]$; here, ${\vec{q}}_1$ (polar) and ${\vec{q}}_2$ (azimuthal) are the spin modulating vectors and $S$ is the spin (total angular momentum) of the magnetic atoms. The results can be applied to materials showing the Kondo lattice behavior within the strong Kondo coupling regime. The explicit dependence of the Chern number on ${\vec{q}}_1$, ${\vec{q}}_2$ for $S=1,2,3$ and $S=1/2,3/2,5/2$ (in limiting cases) is derived. We find that for $S=1,2,3,$ the Chern number depends strongly on ${\vec{q}}_2$ and $S$; and for $S=1/2,3/2,5/2,$ the same dependence is expected. The main physical effect of our result is the change in the direction of the topological Hall resistivity ($+{\rho }_{xy}^{\mathrm{THE}}\to -{\rho }_{xy}^{\mathrm{THE}}$ or vice versa, THE stands for the topological Hall effect) when $S>2$ as the wave vectors are modulated. We propose heterostructures involving the iron based van der Waals magnet ${\mathrm{Fe}}_{N=3,4,5}{\mathrm{GeTe}}_2$, because in this material both the investigated spin texture and Kondo lattice behavior were observed. Our method can also be applied to materials with higher spin $S>3$ to investigate topological properties.

The Doppler effect plays a fundamental role in a vast array of applications, spanning from the quantum domain to cosmic scales. Nevertheless, its manifestation in the context of phonon excitation during the friction between two objects with relative motion remains unexplored. In this study, we predict and investigate the occurrence of the phononic Doppler effect within sliding friction, employing a phononic dynamics model derived through the atomistic Green's function method. As the friction-excited phonons propagate both forward and backward relative to the moving object, we predict frequency high-shift and low-shift phenomena, respectively. We propose a phonon excitation rule, grounded in the phonon dispersion relation, to elucidate the frequency-shift behavior, essentially capturing the Doppler effect on friction-excited phonons. The predicted frequency shift, as determined by the phonon excitation rule, finds validation through molecular dynamics simulations. The observation of the phononic Doppler effect in sliding friction opens a range of potential applications, providing innovative tools for detecting energy-dissipation mechanisms at interfaces caused by friction.

Helical twisted trilayer graphene exhibits zero-energy flat bands with large degeneracy in the chiral limit. The flat bands emerge at a discrete set of magic twist angles and feature properties intrinsically distinct from those realized in twisted bilayer graphene. Their degeneracy and the associated band Chern numbers depend on the parity of the magic angles. Two degenerate flat bands with Chern numbers $C_A=2$ and $C_B=-1$ arise at odd magic angles, whereas even magic angles display four flat bands, with Chern number $C_{A/B}=\pm 1$, together with a Dirac cone crossing at zero energy. All bands are sublattice polarized. We demonstrate the structure behind these flat bands and obtain analytical expressions for the wave functions in all cases. Each magic angle is identified with the vanishing of a zero-mode wave function at high-symmetry position and momentum. The whole analytical structure results from whether the vanishing is linear or quadratic for the, respectively, odd and even magic angles. The $C_{3z}$ and $C_{2y}T$ symmetries are shown to play a key role in establishing the flat bands. In contrast, the particle-hole symmetry is not essential, except from gapping out the crossing Dirac cone at even magic angles.

We perform a detailed study on the consequences of the nonsymmorphic symmetries in the Luttinger phase of the one-dimensional (1D) spin-$\frac{1}{2}$ Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Although the low-energy Hamiltonian has an emergent U(1) symmetry, the bosonization formulas for the spin operators contain ten nonuniversal coefficients which only respect the discrete nonsymmorphic symmetries and can be determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, the response to weak magnetic field is analyzed, and the zigzag phase in the 2D Kitaev-Heisenberg-Gamma model is recovered by weakly coupling an infinite number of 1D chains. Furthermore, we find a line of critical points with an emergent $\mathrm{SU}{\left(2\right)}_1$ conformal symmetry located on the boundary of the Luttinger liquid phase. Our work reveals the rich physics related to nonsymmorphic symmetries in strongly correlated quantum magnetic models, and demonstrates the usefulness of 1D analysis for understanding the 2D Kitaev physics.

Antiferromagnetic FeSn is considered to be a close realization of the ideal two-dimensional (2D) kagome lattice, hosting Dirac cones, van Hove singularities, and flat bands, as it comprises ${\mathrm{Fe}}_3\mathrm{Sn}$ kagome layers well separated by Sn buffer layers. We observe a pronounced optical anisotropy, with the low-energy optical conductivity being surprisingly higher perpendicular to the kagome planes than along the layers. This finding contradicts the prevalent picture of dominantly 2D electronic structure for FeSn. Our material-specific theory reproduces the measured conductivity spectra remarkably well. A site-specific decomposition of the optical response to individual excitation channels shows that the optical conductivity for polarizations both parallel and perpendicular to the kagome plane is dominated by interlayer transitions between kagome layers and adjacent Sn-based layers. Moreover, the matrix elements corresponding to these transitions are highly anisotropic, leading to larger out-of-plane conductivity. Our results evidence the crucial role of interstitial layers in charge dynamics even in seemingly 2D systems.

We investigate a generalized interpolating Aubry-André-Fibonacci (IAAF) model with p-wave superconducting pairing, focusing on its localization and topological properties. Within the Aubry-André limit, we demonstrate that the system experiences transitions from a pure phase, either extended or critical, to a variety of intermediate phases and ultimately enters a localized phase with increasing potential strength. These intermediate phases include those with coexisting extended and localized states, extended and critical states, localized and critical states, and a mix of extended, critical, and localized states. Each intermediate phase exhibits at least one type of mobility edge separating different states. As the system approaches the Fibonacci limit, both the extended and localized phases diminish, and the system tends towards a critical phase. Furthermore, the model undergoes a transition from topologically nontrivial to trivial phase as potential strength increases.

We propose a hybrid quantum-classical method to investigate the equilibrium physics and the dynamics of strongly correlated fermionic models with spin-based quantum processors. Our proposal avoids the usual pitfalls of fermion-to-spin mappings thanks to a slave-spin method which allows to approximate the original Hamiltonian into a sum of self-correlated free fermions and spin Hamiltonians. Taking as an example a Rydberg-based analog quantum processor to solve the interacting spin model, we avoid the challenges of variational algorithms or Trotterization methods. We explore the robustness of the method to experimental imperfections by applying it to the half-filled, single-orbital Hubbard model on the square lattice in and out of equilibrium. We show, through realistic numerical simulations of current Rydberg processors, that the method yields quantitatively viable results even in the presence of imperfections: it allows to gain insights into equilibrium Mott physics as well as the dynamics under interaction quenches. This method thus paves the way to the investigation of physical regimes, whether out of equilibrium, doped, or multiorbital, that are difficult to explore with classical processors.

Néel ordered antiferromagnets exhibit two-mode squeezing such that their ground state is a nonclassical superposition of magnon Fock states. Here we theoretically demonstrate that antiferromagnets can couple to spin qubits via direct dispersive interaction stemming from, e.g., interfacial exchange. We demonstrate that this kind of coupling induces a magnon number-dependent level splitting of the excited state resulting in multiple system excitation energies. This series of level splittings manifests itself as nontrivial excitation peaks in qubit spectroscopy thereby revealing the underlying nonclassical magnon composition of the antiferromagnetic quantum state. By appropriately choosing the drive or excitation energy, the magnonic state can be controlled via the qubit, suggesting that Fock states of magnon pairs can be generated deterministically. This enables achieving states useful for quantum computing and quantum information science protocols.

The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological ${\mathbb{Z}}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is at present, a subject of intense scrutiny due to recent experimental signatures pointing to a ${\mathbb{Z}}_2$ topological phase in certain materials, as well as theoretical studies predicting the emergence of a quantum spin liquid phase of debated nature. In this work, we employ hierarchical mean-field theory, a method based on the use of clusters preserving relevant symmetries and short-range quantum correlations, to investigate the quantum phase diagram of the antiferromagnetic Kitaev's model in a [111] magnetic field. By using clusters of 24 sites, we predict that the Kitaev spin liquid transits through two intermediate phases, characterized by emerging stripe and chiral orders, respectively, before entering the trivial partially polarized phase, differing from previous studies. We assess our results by performing exact diagonalization and computing the scaling of different observables, including the many-body Chern number and other topological quantities, thus establishing hierarchical mean-field theory as a method to study models of frustrated quantum magnetism potentially hosting topological quantum spin liquids.

The magnon frequency comb provides opportunities for exploring magnon nonlinear effects and measuring the transmission magnon frequency in magnets, whose controllability becomes vital for modulating the operating frequency and improving measurement accuracy. Nevertheless, this controllable frequency comb remains unexplored. In this work, we investigate theoretically and numerically the skyrmion-induced magnon frequency comb effect generated by the interaction between the magnon excitation mode and the skyrmion breathing mode in synthetic ferrimagnets. It is revealed that both the skyrmion breathing mode and the magnon frequency gap are closely dependent on the net angular momentum ${\delta }_s$, emphasizing the pivotal role of ${\delta }_s$ as an effective control parameter in governing the comb teeth. With the increase of ${\delta }_s$, the skyrmion size decreases, which results in an enlargement of the breathing frequency and the distance between the comb teeth. Moreover, the dependences of the magnon frequency gap on ${\delta }_s$ and the interlayer coupling allow one to modulate the lowest coherent frequency of the comb via structural control. Consequently, the coherent modes generated by the comb may range from gigahertz to terahertz frequencies, serving as a bridge between microwave and terahertz waves. This work represents a substantial advance in the understanding of the magnon frequency comb effect in ferrimagnets.

The pairing interactions between electrons play an essential role in determining the properties in superconducting states. Recently, a plethora of unconventional superconducting states has been extensively explored, which often emerge owing to multipole fluctuations in the vicinity of multipole orders. We classify such superconducting states from the viewpoint of the multipole degrees of freedom by extending its representation to Nambu space. We clarify that under the crystallographic point group, arbitrary Cooper pairs between electrons with any angular momenta are systematically classified by four types of multipoles: electric, magnetic, magnetic toroidal, and electric toroidal. As examples, we apply our formulation to an $sp$-orbital electron system, which potentially exhibits exotic Cooper pairs under polar and axial point groups. Our systematic classification will be useful in characterizing unconventional superconducting states in multiorbital systems.

We theoretically explore the Josephson diode effect (JDE) in superconductor/quantum dot (QD)/superconductor junction in the presence of a magnetic field and Rashba spin-orbit interaction (RSOI). We calculate the Josephson current in our QD junction using the Keldysh nonequilibrium Green's function technique. We show that JDE is induced in our chiral QD junction with a large rectification coefficient (RC) in the presence of RSOI and external magnetic field simultaneously. Interestingly, the sign and magnitude of the RC are highly controllable by the magnetic field and RSOI. For realistic RSOI strength in the presence of magnetic field and chirality, the RC can be tuned to be as high as $70\%$ by an external gate potential, indicating a giant JDE in our QD junction. Our proposed QD-based Josephson diode (JD) may serve as a potential superconducting device component.

Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals, and fractal lattices are the most prominent ones. By contrast, topological superconductors beyond the realm of quantum crystals are yet to be harnessed, as their nucleation takes place around a well-defined Fermi surface with a Fermi momentum, the existence of which rests on the underlying translational symmetry. Here we identify a family of noncrystalline Dirac materials, devoid of time-reversal ($\mathcal{T}$) and translational symmetries, on which a suitable local or on-site pairing yields topological superconductors. We showcase this outcome on all the abovementioned noncrystalline platforms embedded in a two-dimensional flat space. The resulting noncrystalline topological superconductors possess quantized topological invariants (Bott index and local Chern marker) and harbor robust one-dimensional Majorana edge modes, analogs of $\mathcal{T}$-odd $p+ip$ pairing in noncrystalline materials.

We propose a simple approach to simulating the phonon sector in electron energy-loss spectroscopy (EELS), as implemented in scanning transmission electron microscopy. Simplification of the problem is obtained by working with the phonon density of states (PDOS), a function of phonon energy, which is an integral over the details of the dispersion relations due to the correlated motions of the atoms. For a given PDOS, we derive a spectral distribution function, to distribute the total inelastic scattering, as calculated within the quantum excitation of phonons model, into an energy-loss/gain spectrum. The spectral distribution is obtained assuming a linear relationship between inelastic phonon scattering and atomic mean-squared displacements, a good approximation for phonon EELS with a detector covering only moderate scattering angles. We provide examples of the usefulness of the proposed approach in the modeling and interpretation of experimental phonon EELS data.

The van der Waals (vdW) layered multiferroics, which host simultaneous ferroelectric and magnetic orders, have attracted attention not only for their potentials to be utilized in nanoelectric devices and spintronics, but also offer alternative opportunities for emergent physical phenomena. To date, the vdW layered multiferroic materials are still very rare. In this work, we have investigated the magnetic structure and magnetoelectric (ME) effects in ${\mathrm{Co}}_5{\left(\mathrm{Te}{\mathrm{O}}_3\right)}_4{\mathrm{Cl}}_2$, a promising multiferroic compound with antiferromagnetic (AFM) Néel point $T_N\sim 18$ K. The neutron-powder diffraction reveals the noncoplanar AFM state with preferred Néel vector along the $c$ axis, while a spin reorientation occurring between 8 and 15 K is identified, which results from the distinct temperature dependence of the nonequivalent Co site's moment in ${\mathrm{Co}}_5{\left(\mathrm{Te}{\mathrm{O}}_3\right)}_4{\mathrm{Cl}}_2$. Moreover, it is found that ${\mathrm{Co}}_5{\left(\mathrm{Te}{\mathrm{O}}_3\right)}_4{\mathrm{Cl}}_2$ is one of the best vdW multiferroics studied so far in terms of the multiferroic performance. The measured linear ME coefficient exhibits the emergent oscillation dependence of the angle between magnetic field and electric field, and the maximal value is as big as 45 ps/m. It is suggested that ${\mathrm{Co}}_5{\left(\mathrm{Te}{\mathrm{O}}_3\right)}_4{\mathrm{Cl}}_2$ is an appreciated platform for exploring the emergent multiferroicity in vdW layered compounds.

We study the imaginary-time relaxation critical dynamics of the Néel paramagnetic quantum phase transition in the two-dimensional dimerized $S=\frac{1}{2}$ Heisenberg model. We focus on the scaling correction in the short-time region. A unified scaling form including both short-time and finite-size corrections is proposed. According to this full scaling form, improved short-imaginary-time scaling relations are obtained. We numerically verify the scaling form and the improved short-time scaling relations for different initial states using projector quantum Monte Carlo algorithm.