The magnetic susceptibility of an ensemble of clean metallic nanoparticles is shown to change from a paramagnetic to diamagnetic one with the onset of spin-orbit interaction. The effect is quantified on the basis of symmetry analysis with the help of the random matrix theory. In particular, the magnetic susceptibility is investigated as the function of symmetry breaking parameter representing magnetic flux in the crossover from symplectic to unitary and from orthogonal to unitary ensembles. Corresponding analytical and numerical results provide a qualitative explanation to the experimental data on diamagnetism of an ensemble of gold nanorods.

We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at $J_c$ to $J^{*}$ in the gapped phase by a value $|J^{*}-J_c|=B^2/36$, where $B^2$ is a transition width controlling the asymptotic form of the correlation length $\xi \sim exp(-B/\sqrt{|J-J_c|})$ in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. We support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at $J^{*}=0.212$ that is significantly different from $J_c=0.3048\left(3\right)$. In the spin-$3/2$ XXZ model the shift from $J_c=1$ to $J^{*}=1.0021$ is small but the narrow universal peak is much more pronounced over the nonuniversal background.

The identification and design of defects in two-dimensional (2D) materials as promising single photon emitters (SPEs) requires a deep understanding of the underlying carrier recombination mechanisms. Yet, the dominant mechanism of carrier recombination at defects in 2D materials has not been well understood, and some outstanding questions remain: How do recombination processes at defects differ between 2D and 3D systems? What factors determine defects in 2D materials as excellent SPEs at room temperature? In order to address these questions, we developed first-principles methods to accurately calculate the radiative and nonradiative recombination rates at defects in 2D materials, using $h$-BN as a prototypical example. We reveal the carrier recombination mechanism at defects in 2D materials being mostly dominated by defect-defect state recombination in contrast to defect-bulk state recombination in most 3D semiconductors. In particular, we disentangle the nonradiative recombination mechanism into key physical quantities: the zero-phonon line and Huang-Rhys factor. At the end, we identified that strain can effectively tune the electron-phonon coupling at defect centers and drastically change the nonradiative recombination rates. Our theoretical development serves as a general platform for understanding carrier recombination at defects in 2D materials, while providing pathways for engineering of quantum efficiency of SPEs.

In the absence of rotational symmetry, a fractional quantum Hall (FQH) system can exploit a geometric degree of freedom to minimize its ground-state energy. The mass anisotropy of bare particles interacting isotropically is partially inherited by the many-body FQH state, to an extent that depends on the type of interaction, filling fraction, and ground-state phase. Using numerical infinite density matrix renormalization group simulations, we investigate the transference of elliptical ($C_2$-symmetric) anisotropy from the band mass of the bare particles to the FQH states, for various power-law interactions. We map out the response of FQH states to small anisotropy as a function of power-law exponent, filling, and statistics (bosonic or fermionic) of the constituents. Interestingly, we find a nonanalyticity in the linear response of the FQH state at a special filling-dependent value of the power-law exponent, above which the interactions effectively become zero-range (pointlike). We also investigate the effect of $C_4$-symmetric band distortions, where we observe a strikingly different dependence on filling.

We study the emergence of exact Majorana zero modes (EMZMs) in a one-dimensional quantum transverse compass model with both the nearest-neighbor interactions and transverse fields varying over space. By transforming the spin system into a quadratic Majorana-fermion model, we derive an exact formula for the number of the emergent EMZMs, which is found to depend on the partition nature of the lattice sites on which the magnetic fields vanish. We also derive explicit expressions for the wave functions of these EMZMs and show that they indeed depend on fine features of the foregoing partition of site indices. Based on the above rigorous results about the EMZMs, we provide an interpretation for the interesting dependence of the eigenstate degeneracy on the transverse fields observed in prior literature. As a special case, we employ a plane-wave ansatz to exactly solve an open compass chain with alternating nearest-neighbor interactions and staggered magnetic fields. Explicit forms of the canonical Majorana modes diagonalizing the model are given even for finite chains. We show that besides the possibly existing EMZMs no almost Majorana zero modes exist unless the fields on both the two sublattices are turned off. Our results might shed light on the control of ground-state degeneracies by solely tuning the external fields in related systems.

The mixing of orbital and spin character in the wave functions of the $5d$ iridates has led to predictions of strong couplings among their lattice, electronic, and magnetic degrees of freedom. As well as realizing a novel spin-orbit assisted Mott-insulating ground state, the perovskite iridate ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ has strong similarities with the cuprate ${\mathrm{La}}_2{\mathrm{CuO}}_4$, which on doping hosts a charge-density wave that appears intimately connected to high-temperature superconductivity. These phenomena can be sensitively probed through momentum-resolved measurements of the lattice dynamics, made possible by $\mathrm{meV}$-resolution inelastic x-ray scattering. Here we report the first such measurements for both parent and electron-doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. We find that the low-energy phonon dispersions and intensities in both compounds are well described by the same nonmagnetic density functional theory calculation. In the parent compound, no changes of the phonons on magnetic ordering are discernible within the experimental resolution, and in the doped compound no anomalies are apparent due to charge-density waves. These measurements extend our knowledge of the lattice properties of (${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_2{\mathrm{IrO}}_4$ and constrain the couplings of the phonons to magnetic and charge order.

By using a combination of density functional theory, tight-binding, and effective mass calculations, we explore the electronic properties of donor and acceptor states of substitutional impurities in single-layer $h$-BN. We find that the impurity level structure inside the electronic gap is quite exotic, as it strongly depends on the sublattice position of the impurity and its behavior as a donor or an acceptor. For instance, when an acceptor atom replaces a nitrogen atom, the intervalley interaction induced by the impurity potential is found to be strong and the resulting level structure consists only of nondegenerate levels with strong valley and spin splitting. On the other hand, when an acceptor replaces a boron atom, the intervalley interaction is much weaker and near-valley-degenerate levels are found. Donor impurities behave in a similar fashion. The differences between these two types of level structures can be traced to the peculiar sublattice-resolved electronic structure of pristine $h$-BN, in which the valence and conduction wave functions at the $K$ and $K^{\prime }$ points are composed only of nitrogen and boron $p_z$ orbitals, respectively, and to the dependence of the intervalley interaction on them. We predict that this impurity level structure must also be present in other two-dimensional semiconductors and insulators with similar sublattice-resolved electronic states, such as other hexagonal III-V binary compounds and, consequently, offer the possibility of engineering the optical properties of these materials for potential applications in future devices.

We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nanowires. We modelled the non-uniform nanowires as the junction between two cylindrical nanowires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one-dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational motion of the electron about the axis of the cylindrical. Application of an external magnetic flux through the cylindrical nanowires enables us to tune the mass gap from positive to negative value across the junction. Due to this flux tunable band inversion, controlled by the external magnetic filed, Jackiw-Rebbi zero modes can be made to appear or disappear at the junction. We compute the differential conductance of our topological insulator nanowire junction and show that a quantized conductance peak appears at zero-energy (zero-bias) in the presence of the Jackiw-Rebbi mode.

We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling semiclassical limit, the displayed criticality takes the form of amplitude bistability and breaking of spatial and temporal symmetries. A period-bistable time crystal is formed, consisting of Josephson-like oscillations. Mean-field dynamics and quantum trajectories complement the spectral analysis of the Liouvillian in the approach to the semiclassical limit.

We show that interactions can drive a class of higher order topological superconductors (HOTSCs) into symmetry-enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSCs realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSCs protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry-enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSCs and the topologically ordered phase.

Ternary alloys Co-Zn-Mn with $\beta$-Mn-type structure exhibit helimagnetic order and skyrmion lattice states in a low-Mn-concentration region. Recent studies on ${\mathrm{Co}}_{10-\frac{x}{2}}{\mathrm{Zn}}_{10-\frac{x}{2}}{\mathrm{Mn}}_x$ (CZM) revealed that the magnetic modulation period and the paramagnetic-to-helimagnetic transition temperature are reduced with increasing Mn concentration $x$ [Tokunaga et al., Nat. Commun. 6, 7638 (2015)] and that the helimagnetic order is replaced with a spin-glass state in a high-$x$ region [Karube et al., Sci. Adv. 4, eaar7043 (2018)]. To understand the microscopic mechanism of the Mn substitution effect, we have performed crystal structure analyses of a series of CZM samples with $x=4,5,6,7,8,10,12,$ and 16 by neutron powder diffraction. We present a model for the site occupancies of Co, Zn, and Mn in the unit cell, which has two independent crystallographic sites, specifically $8c$ and $12d$ sites. Zn atoms are always accommodated in the $12d$ sites, and Co atoms prefer the $8c$ sites, although some of them also exist in the $12d$ sites in a low-$x$ region. Mn atoms mainly prefer the $12d$ sites but also share the $8c$ site with Co atoms in the region of $x\ge 4$. A comparison between the site occupancies and the $x-T$ magnetic phase diagram suggests that the amount of Mn in the $8c$ sites is relevant to the emergence of the spin-glass state.

Density functional theory maps an interacting Hamiltonian onto the Kohn-Sham Hamiltonian, an explicitly free model with identical local fermion densities. Using the interaction distance, the minimum distance between the ground state of the interacting system and a generic free-fermion state, we quantify the applicability and limitations of the exact Kohn-Sham model in capturing the various properties of the interacting system. As a by-product, this distance determines the optimal free state that reproduces the entanglement properties of the interacting system as faithfully as possible. The parent Hamiltonian of the optimal free state identifies a system that can determine the expectation value of any observable with controlled accuracy. This optimal entanglement model opens up the possibility of extending the systematic applicability of auxiliary free models into the nonperturbative, strongly correlated regimes.

The exact muffin tin orbital (EMTO) method features high efficiency and accuracy for first-principles simulations with density functional theory. In this paper we report our implementation of the EMTO method for electronic-structure and quantum transport simulation of device materials. We consider a device-material structure with a central device region in contact with different semi-infinite electrodes. Based on the Green's function method, the infinite device, nonperiodic in transport direction, is transformed into a calculable finite material system by treating the semi-infinite electrodes with electrode self-energies, and the Green's function of the device region is calculated with an efficient recursive technique. In the present implementation we adopt the spherical cell approximation to treat the electrostatics, and we solve the electrostatic potential of the finite device region by enforcing the boundary conditions to the known potential of electrode materials. The coherent potential approximation is incorporated for treating the atomic disorders inevitable in realistic materials, and the effects of multiple disorder scattering on electron transport are accounted for by vertex correction for simulating disordered electronic devices. To demonstrate the capability of the present implementation, we calculate the monolayer two-dimensional material ${\mathrm{MoS}}_2$ and black phosphorus, and study the spin-dependent tunneling in the Fe/MgO/Fe magnetic tunneling junction. We find the EMTO electronic structures of the calculated systems agree well with the results of the projector augmented wave method. The EMTO transport simulation produces the important spin-filtering effect of the Fe/MgO/Fe junction and the important influence of the interfacial disorders on the spin-dependent tunneling, agreeing well with previous theoretical and experimental studies. The implementation of the EMTO based device simulator provides an effective simulation tool for simulating both ordered and disordered device materials, extending the capability for theoretical design of electronic devices from first principles.

Excitons are bound electron-hole pairs that dominate the optical response of semiconductors and insulators, especially in materials where the Coulomb interaction is weakly screened. Light absorption (including excitonic effects) has been studied extensively using first-principles calculations, but methods for computing radiative recombination and light emission are still being developed. Here we show a unified ab initio approach to compute exciton radiative recombination in materials ranging from bulk crystals to nanostructures and molecules. We derive the rate of exciton radiative recombination in bulk crystals, isolated systems, and in one- and two-dimensional materials, using Fermi's golden rule within the Bethe-Salpeter equation approach. We present benchmark calculations of radiative lifetimes in a GaAs crystal and in gas-phase organic molecules. Our work provides a general method for studying exciton recombination and light emission in bulk, nanostructured, and molecular materials from first principles.

Coupling between charge and spin, and magnetoelectric effects more generally, have been an area of great interest for several years, with the sought-after ability to control magnetic degrees of freedom via charge currents serving as an impetus. The orbital Edelstein effect (OEE) is a kinetic magnetoelectric effect consisting of a bulk orbital magnetization induced by a charge current. It is the orbital analog of the spin Edelstein effect in spin-orbit coupled materials, in which a charge current drives nonzero electron spin magnetization. The OEE has recently been investigated in the context of Weyl semimetals and Weyl metals. Motivated by these developments, we study a model of electrons without spin-orbit coupling which exhibits line nodes protected by nonsymmorphic glide symmetries that get gapped out via symmetry breaking due to an interaction-induced charge density wave order. This model is shown to exhibit a temperature dependent OEE, which appears due to symmetry reduction into a nonchiral, yet gyrotropic, crystal class. We present a solenoid picture for this emergent OEE that arises from broken glide and inversion symmetries.

We show that topological phases of the Dirac system in arbitral even dimensional space are simulated by $LC$ electric circuits with operational amplifiers. The lattice Hamiltonian for the hypercubic lattice in $2n$-dimensional space is characterized by the $n\mathrm{th}$ Chern number. The boundary state is described by the Weyl theory in ($2n-1$)-dimensional space. They are well observed by measuring the admittance spectrum. The results are extended to non-Hermitian systems with complex Dirac masses. The non-Hermitian $n\mathrm{th}$ Chern number remains to be quantized for the complex Dirac mass.

Materials exhibiting multiple stable phases can be used as functional components in electronic and optical applications if the phase transition is controllable. Group-VI transition metal dichalcogenides (TMDs, ${\mathrm{MX}}_2$, where M = Mo, W and X = S, Se) are known to undergo charge induced transitions from semiconducting $H$ phases to metallic $T$ phases. This occurs, for example, when bulk TMDs are exfoliated with the aid of alkali ion intercalants. However, it is difficult to experimentally decouple the effect of composition-dependent phase transition barriers from indirect effects related to the exfoliation process. Here, using first-principles calculations, we study the energetics of transition between the different structural polytypes of four group-VI TMDs upon lithium adsorption. We find that both the activation barrier from the $H$ phase to the metallic phase in charged monolayers and the reverse barrier in neutral monolayers are required to explain experimental results. We show that the high proportion of metallic phase found in ${\mathrm{WS}}_2$ monolayers after alkali treatment can be explained by high transition barriers to revert back to the $H$ phase once in a neutral state. The calculated barriers however cannot explain the low proportion of metallic phase found in ${\mathrm{MoS}}_2$ monolayers in some experiments and so nonelectronic effects must also play a role.

We establish the presence of foliated fracton order in the Majorana checkerboard model. In particular, we describe an entanglement renormalization group transformation which utilizes toric code layers as resources of entanglement and furthermore discuss entanglement signatures and fractional excitations of the model. In fact, we give an exact local unitary equivalence between the Majorana checkerboard model and the semionic X-cube model augmented with decoupled fermionic modes. This mapping demonstrates that the model lies within the X-cube foliated fracton phase.