Collective-mode fluctuations play an essential role in ensuring the electromagnetic response of superfluids is gauge invariant. The contribution of these fluctuations, however, is known to drop out from the Meissner response of uniform superfluids. The same phenomenon is not so established in the context of nonuniform superfluids. To clarify this issue, we revisit how collective modes appear in the Meissner effect. We find that their contribution vanishes both in uniform and nonuniform systems, unless an external length scale is present—as in Fulde-Ferrell or finite-sized superfluids. As examples, we consider $s$-wave and chiral $p+ip$ superconductors. To facilitate this analysis, we formulate a path-integral matrix methodology for computing the response of fermionic fluids in the presence of multiple collective modes. Closed-form expressions are provided, incorporating effects from phase and amplitude of the superconducting order parameter and electronic density fluctuations. All microscopic symmetries and invariances are manifestly satisfied in this approach, and it can be straightforwardly extended to other scenarios.

Spin-bath noise characterization, which is typically performed by multipulse control sequences, is essential for understanding most spin dynamics in the solid state. Here, we theoretically propose a method for extracting the characteristic parameters of a noise source with a known spectrum, using modified Hahn-echo pulses. By varying the application time of the pulse, measuring the coherence curves of an addressable spin, and fitting these curves to a theoretical function derived by us, we extract parameters characterizing the physical nature of the noise. Assuming a Lorentzian noise spectrum, we illustrate this method for extracting the correlation time of a bath of nitrogen paramagnetic impurities in diamond, and its coupling strength to the addressable spin of a nitrogen-vacancy center. First, we demonstrate that fitting conventional Hahn-echo measurements to the explicit coherence function is essential for extracting the correct parameters in the general physical regime, for which common methods relying on the assumption of a slow bath are inaccurate. Second, considering a realistic experimental scenario with a $5\%$ noise floor, we simulate the extraction of these parameters utilizing the asymmetric Hahn-echo scheme. The scheme is effective for samples having a natural homogeneous coherence time $\left(T_2\right)$ up to two orders of magnitude greater than the inhomogeneous coherence time $\left(T_2^{*}\right)$. In the presence of realistic technical drifts for which averaging capabilities are limited, we simulate more than a factor of 3 improvement of the extracted parameter uncertainties over conventional Hahn-echo measurements. Beyond its potential for reducing experiment times by an order of magnitude, such single-pulse noise characterization could minimize the effects of long timescale drifts and accumulating pulse imperfections and numerical errors.

We quantitatively study the out-of-equilibrium edge-Majorana correlation in a linearly ramped one-dimensional Kitaev chain of finite length in a dissipative environment. The chemical potential is dynamically ramped to drive the chain from its topologically trivial to nontrivial phase in the presence of couplings to nonthermal Markovian baths. We consider two distinctive situations: In the first situation, the bath is quasilocal in the site basis (local in quasiparticle basis) while in the other it is local. Following a Lindbladian approach, we compute the early time dynamics as well as the asymptotic behavior of the edge-Majorana correlation to probe the interplay between two competing timescales—one due to the coherent ramping while the other to the dissipative coupling. For the quasilocal bath, we establish that there is a steady generation of Majorana correlations in asymptotic time and the presence of an optimal ramping time which facilitates a quicker approach to the topological steady state. In the second scenario, we analyze the action of a local particle-loss type of bath in which we have established the existence of an optimal ramping time which results from the competing dynamics between the unitary ramp and the dissipative coupling. While the defect generated by the former decays exponentially with increasing ramp duration, the later scales linearly with the same. This linear scaling is further established through a perturbation theory formulated using the nondimensionalized coupling to the bath as a small parameter.

We study an asymmetric $J_1-J_2$ zigzag ladder consisting of two different spin-$\frac{1}{2}$ antiferromagnetic (AFM; $J_2, \gamma J_2>0$) Heisenberg legs coupled by zigzag-shaped ferromagnetic (FM; $J_1<0$) interleg interaction. On the basis of density-matrix renormalization group based calculations, the ground-state phase diagram is obtained as functions of $\gamma$ and $J_2/\left|J_1\right|$. It contains four kinds of frustration-induced ordered phases except a trivial FM phase. Two of the ordered phases are valence bond solid (VBS) with spin-singlet dimerization, which is a rather conventional order by disorder. Still, it is interesting to note that the VBS states possesses an Affleck-Kennedy-Lieb-Tasaki–type topological hidden order. The remaining two phases are ferrimagnetic orders, each of which is distinguished by commensurate or incommensurate spin-spin correlation. It is striking that the ferrimagnetic orders are not associated with geometrical symmetry breaking; instead, the global spin-rotation symmetry is broken. In other words, the system lowers its energy via the FM interleg interaction by polarizing both of the AFM Heisenberg legs. This is a rare type of order by disorder. Besides, the incommensurate ferrimagnetic state appears as a consequence of the competition between a polarization and a critical Tomonaga-Luttinger–liquid behavior in the AFM Heisenberg legs.

Using density functional theory (DFT), we investigate the interplay among the sequence of bilayers composed of an Fe and a Rh layer on Re(0001), their stacking order, and their magnetic properties. We find that bilayers in which both layers are in fcc stacking are energetically very unfavorable, while all other combinations of hcp and fcc stacking are energetically relatively close. The magnetic interactions are evaluated by mapping the DFT energies onto an atomistic spin model, which contains the Heisenberg exchange, the Dzyaloshinskii-Moriya interaction (DMI), the magnetocrystalline anisotropy energy, and the higher-order exchange interactions. We find that the stacking sequence of the bilayer significantly modifies the magnetic interactions. For bilayers in which Fe is the topmost layer, the nearest-neighbor exchange interaction is ferromagnetic, but varies in strength by a factor of up to 3 for different stacking sequences. The DMI even changes up to a factor of 4. As a result, we find a DMI driven cycloidal spin spiral ground state with a period of 11 nm for hcp-Fe/hcp-Rh/Re(0001). For fcc-Fe/hcp-Rh/Re(0001) and hcp-Fe/fcc-Rh/Re(0001), we obtain a ferromagnetic ground state. The spin spiral energy dispersion of hcp-Fe/hcp-Rh/Re(0001) including spin-orbit coupling suggests that isolated skyrmions can be stabilized in the field-polarized ferromagnetic background at external magnetic fields. If the Fe layer is sandwiched between the Rh overlayer and the Re(0001) substrate, there is a competition between the ferromagnetic coupling preferred by the Rh-Fe hybridization and the antiferromagnetic coupling induced by the Fe-Re hybridization. Due to the Fe/Re interface, the DMI can become very large. For fcc-Rh/hcp-Fe/Re(0001), we obtain a cycloidal spin spiral with a period of 1.7 nm, which is induced by frustration of exchange interactions and further stabilized by the DMI. For hcp-Rh/hcp-Fe/Re(0001), we find a DMI driven cycloidal spin spiral with a period of 4 nm and locally nearly antiparallel magnetic moments due to antiferromagnetic nearest-neighbor exchange. The higher-order exchange constants can be significant in the considered films; however, they do not lead to $\mathrm{multi}-Q$ states as the ground state.

Magnetite nanoparticles (particle diameter $d_{\text{NP}}=20\mathrm{nm}$) were arranged into chains of cylinderlike entities of fixed radius $R$ with constant spacings $D$ between neighboring entities. For this purpose, chains of circular openings were defined in a 250-nm-thick electron-sensitive resist on a Si substrate by electron beam lithography. These patterns were subsequently filled with the magnetite nanoparticles using a variant of the meniscus force deposition method. To study the dipolar magnetic interaction between the spherical magnetite particles within the cylinders as well as that between cylinders, three series of chain arrangements were prepared, each with another constant average cylinder radius ($R$ = 360, 240, and 160 nm). The three samples of each series differ in terms of their $D$ values, which vary between 700 nm (no intercylinder coupling) and 50 nm (magnetic coupling between cylinders). Angle-dependent ferromagnetic resonance (FMR) measurements revealed that for large $R$ and $D$ only one broad resonance appears, while for $R$ = 240 and 160 nm two resonances are present. At short $D$, an angular dependence of the resonances induced by the coupling between the cylinders is clearly visible. Furthermore, the amplitude of the main resonance decreases, and side bands occur when the cylinders of the chain are hollow, i.e., when some nanoparticles are removed from the center of each cylinderlike entity. The dynamics of the coupled magnetic dipoles of the magnetite particles and its impact on the FMR spectra of the samples, i.e., associating the different resonances to characteristic collective oscillations of the magnetic moments within the ordered arrangement of magnetite nanoparticles, can be understood using micromagnetic simulations based on a numerical solution of the Landau-Lifschitz-Gilbert equation.

We studied electron spin resonance in a quantum magnet ${\mathrm{NiCl}}_2\text{−}4\mathrm{SC}{\left({\mathrm{NH}}_2\right)}_2$, demonstrating a field-induced quantum phase transition from a quantum-disordered phase to an antiferromagnet. We observe two branches of the antiferromagnetic resonance of the ordered phase, one of them has a gap, and the other is a Goldstone mode with zero frequency at a magnetic field along the fourfold axis. This zero-frequency mode acquires a gap at a small tilting of the magnetic field with respect to this direction. The upper gap was found to be reduced in the Br-substituted compound $\mathrm{Ni}{\left({\mathrm{Cl}}_{1-x}{\mathrm{Br}}_x\right)}_2\text{−}4\mathrm{SC}{\left({\mathrm{NH}}_2\right)}_2$ with $x=0.21$. This reduction is unexpected because of the previously reported rise in the main exchange constant in a substituted compound. Furthermore, a nonresonant diamagnetic susceptibility ${\chi }^{\prime }$ was found for the ordered phase in a wide frequency range above the quasi-Goldstone mode. This dynamic diamagnetism is as large as the dynamic susceptibility of the paramagnetic resonance. We speculate that it originates from a two-magnon absorption band of the low-frequency dispersive magnon branch.

We present accurate optical spectra of semiconductors and insulators within a pure Kohn-Sham time-dependent density functional approach. In particular, we show that the onset of the absorption is well reproduced when comparing to experiment. No empirical information nor a theory beyond Kohn-Sham density functional theory, such as $GW$, is invoked to correct the Kohn-Sham gap. Our approach relies on the link between the exchange-correlation kernel of time-dependent density functional theory and the derivative discontinuity of ground-state density functional theory. We show explicitly how to relate these two quantities. We illustrate the accuracy and simplicity of our approach by applying it to various semiconductors (Si, GaP, GaAs) and wide-gap insulators (C, LiF, Ar).

Hourglasslike band structures protected by nonsymmorphic space group symmetries can appear along the high-symmetry lines or on the high-symmetry surfaces of the Brillouin zone. In this work, from symmetry analysis, we demonstrate that $n$-hourglasslike band structures, a generalization of hourglasslike band structures, are enforced along screw-invariant lines in nonmagnetic materials with an $N$-fold screw axis when spin-orbit coupling is finite, where $n$, a nonunity factor of $N$, denotes the degree of the screw-invariant line. The $n$-hourglass has a minimum of $n-1$ crossings, which are Weyl points with monopole charge $\pm 1$. Using compatibility relations, we identify all the space groups that host $n$-hourglasslike band structures induced by screw symmetries, with $n=2,3,4$. For $N=3$ we find Weyl points that are indirectly enforced by symmetries. We construct an effective model, from which we see how the $n$-hourglasses appear when spin-orbit coupling is turned on. As examples, BiPd, the cinnabar phase of HgTe, and the high-temperature phase of ${\mathrm{Tl}}_3{\mathrm{PbBr}}_5$ are shown from first-principles calculations to exhibit $n$-hourglasslike band structures, with $N=2,3,4$, respectively, which confirms our symmetry analysis. For $N=3$ and 4, there are minimally two particle and two hole Fermi pockets enclosing Weyl points at proper fillings, where submanifold nesting may lead to topological density waves.

We propose a general way to construct an effective Hamiltonian in the self-learning Monte Carlo method (SLMC), which speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. Its applications are, however, limited. This is because it is not obvious to find the explicit form of the effective Hamiltonians. Particularly, it is difficult to make trainable effective Hamiltonians including many-body interactions. In order to overcome this critical difficulty, we introduce the Behler-Parrinello neural networks (BPNNs) as effective Hamiltonian without any prior knowledge, which is used to construct the potential-energy surfaces in interacting many particle systems for molecular dynamics. We combine SLMC with BPNN by focusing on a divisibility of Hamiltonian and propose how to construct the elementwise configurations. We apply it to quantum impurity models. We observed significant improvement of the acceptance ratio from 0.01 (the effective Hamiltonian with the explicit form) to 0.76 (BPNN). This drastic improvement implies that the BPNN effective Hamiltonian includes many-body interaction, which is omitted in the effective Hamiltonian with the explicit forms. The BPNNs make SLMC more promising.

We report on an apparent low-energy nanoscale electronic inhomogeneity in ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ due to the distribution of selenium and tellurium atoms revealed through unsupervised machine learning. Through an unsupervised clustering algorithm, characteristic spectra of selenium- and tellurium-rich regions are identified. The inhomogeneity linked to these spectra can clearly be traced in the differential conductance and is detected both at energy scales of a few electron volts as well as within a few millielectronvolts of the Fermi energy. By comparison with angle-resolved photoemission spectroscopy, this inhomogeneity can be linked to an electronlike band just above the Fermi energy. It is directly correlated with the local distribution of selenium and tellurium. There is no clear correlation with the magnitude of the superconducting gap, however, the height of the coherence peaks shows a significant correlation with the intensity with which this band is detected, and hence with the local chemical composition.

We construct a short-range resonating-valence-bond (RVB) state on the ruby lattice, using projected entangled-pair states with bond dimension $D=3$. By introducing nonlocal moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining a nonzero topological contribution, $\gamma =-\ln 2$, consistent with that of a ${\mathbb{Z}}_2$ topological quantum spin liquid. We also calculate the ground-state energy of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

Robust fractional charge localized at disclination defects has recently been found as a topological response in $C_6$-symmetric 2D topological crystalline insulators (TCIs). In this article, we thoroughly investigate the fractional charge on disclinations in $C_n$-symmetric TCIs, with or without time-reversal symmetry, and including spinless and spin-$\frac{1}{2}$ cases. We compute the fractional disclination charges from the Wannier representations in real space and use band representation theory to construct topological indices of the fractional disclination charge for all 2D TCIs that admit a (generalized) Wannier representation. We find the disclination charge is fractionalized in units of $\frac{e}{n}$ for $C_n$-symmetric TCIs, and for spin-$\frac{1}{2}$ TCIs, with additional time-reversal symmetry, the disclination charge is fractionalized in units of $\frac{2e}{n}$. We furthermore prove that with electron-electron interactions that preserve the $C_n$ symmetry and many-body bulk gap, though we can deform a TCI into another which is topologically distinct in the free fermion case, the fractional disclination charge determined by our topological indices will not change in this process. Moreover, we use an algebraic technique to generalize the indices for TCIs with nonzero Chern numbers, where a Wannier representation is not applicable. With the inclusion of the Chern number, our generalized fractional disclination indices apply for all $C_n$-symmetric TCIs. Finally, we briefly discuss the connection between the Chern number dependence of our generalized indices and the Wen-Zee term.

We study the spin textures of a confined two-dimensional electron in inhomogeneous magnetic fields. These fields can either be external or effective fields due to a background magnetic texture in the plane in which the electron resides. By analytical considerations, WKB-type approximations, and by performing numerical diagonalizations, we show that the in-plane spin field components of a single electron can form vortices while the total spin field can become a skyrmion. Most interestingly, we find that topological trivial magnetic fields can induce topological spin field configurations in the eigenstates of the electron due to quantum effects.

We investigate spin transport in a set of $\text{Ge}/{\text{Si}}_{0.15}{\text{Ge}}_{0.85}$ multiple quantum wells (MQWs) as a function of the well thickness. We exploit optical orientation to photogenerate spin-polarized electrons in the discrete energy levels of the well conduction band at the $\mathrm{\Gamma }$ point of the Brillouin zone. After diffusion, we detect the optically oriented spins by means of the inverse spin-Hall effect (ISHE) taking place in a thin Pt layer grown on top of the heterostructure. The employed spin injection/detection scheme is sensitive to in-plane spin-polarized electrons, therefore, by detecting the ISHE signal as a function of the photon energy, we evaluate the spin polarization generated by optical transitions driven by the component of the light wave vector in the plane of the wells. In this way, we also gain insight into the electron spin-diffusion length in the MQWs. The sensitivity of the technique to in-plane spin-related properties is a powerful tool for the investigation of the in-plane component of the spin polarization in MQWs, which is otherwise commonly inaccessible.

We calculate the linear conductance of a two-dimensional electron-gas-based junction between a normal semiconductor section and a hybrid semiconductor-superconductor section, under perpendicular magnetic field. We consider two important terms often neglected in the literature, the magneto-orbital and transverse Rashba spin-orbit. The strong orbital effect due to the magnetic field yields topological phase transitions to nontrivial phases hosting Majorana modes in the hybrid section. The presence of a potential barrier at the junction interface reveals the Majorana phases as quantized plateaus of high conductance, for low values of the chemical potential. In wide junctions (or large chemical potentials) the phase transitions occur at low magnetic fields but the magneto-conductance becomes anomalous and lacks clearly quantized plateaus.

Metal-to-insulator phase transitions in complex oxide thin films are exciting phenomena which may be useful for device applications, but in many cases the physical mechanism responsible for the transition is not fully understood. Here we demonstrate that epitaxial strain generates local disproportionation of the $\mathrm{Ni}{\mathrm{O}}_6$ octahedra, driven through changes in the oxygen stoichiometry, and that this directly modifies the metal-to-insulator phase transition in epitaxial (001) $\mathrm{NdNi}{\mathrm{O}}_3$ thin films. Theoretically, we predict that the Ni-O-Ni bond angle decreases, while octahedral tilt and local disproportionation of the $\mathrm{Ni}{\mathrm{O}}_6$ octahedra increases resulting in a small band gap in an otherwise metallic system. This is driven by an increase in oxygen vacancy concentration in the rare-earth nickelates with increasing in-plane biaxial tensile strain. Experimentally, we find an increase in pseudocubic unit-cell volume and resistivity with increasing biaxial tensile strain, corroborating our theoretical predictions. With electron-energy-loss spectroscopy and x-ray absorption, we find a reduction of the Ni valence with increasing tensile strain. These results indicate that epitaxial strain modifies the oxygen stoichiometry of rare-earth perovskite thin films and through this mechanism affects the metal-to-insulator phase transition in these compounds.

The Zeeman interaction is a quantum mechanical effect that underpins spin-based quantum devices such as spin qubits. Typically, identification of the Zeeman interaction needs a large out-of-plane magnetic field coupled with ultralow temperatures, which limits the practicality of spin-based devices. However, in two-dimensional (2D) semiconductor holes, the strong spin-orbit interaction causes the Zeeman interaction to couple the spin, the magnetic field, and the momentum, and has terms with different winding numbers. In this work, we demonstrate a physical mechanism by which the Zeeman terms can be detected in classical transport. The effect we predict is very strong, and tunable by means of both the density and the in-plane magnetic field. It is a direct signature of the topological properties of the 2D hole system, and a manifestation in classical transport of an effect stemming from relativistic quantum mechanics. We discuss experimental observation and implications for quantum technologies.

The structural parameters and electronic structure of rare-earth pnictides are calculated using density functional theory (DFT) with the Heyd, Scuseria, and Ernzerhof (HSE06) screened hybrid functional. We focus on RE-V compounds, with RE=La, Gd, Er, and Lu, and V=As, Sb, and Bi, and analyze the effects of spin-orbit coupling and treating the RE $4f$ electrons as valence electrons in the projector augmented wave approach. The results of HSE06 calculations are compared with DFT within the generalized gradient approximation (DFT-GGA) and other previous calculations. We find that all these RE-V compounds are semimetals with electron pockets at the $X$ point and hole pockets at $\mathrm{\Gamma }$. Whereas in DFT-GGA the carrier density is significantly overestimated, the computed carrier densities using HSE06 is in good agreement with the available experimental data.