We consider the surface states of a spherical topological insulator piecewise terminated by superconductivity or ferromagnetism over various regions of the spherical surface. Such terminations gap the surface states by breaking U(1) particle-number symmetry and time-reversal symmetry, respectively. Interfaces and trijunctions between differently terminated surface regions can host propagating and bound Majorana modes, and the finite size of the spherical system makes it easily amenable to numerical analysis via exact diagonalization of the Bogoliubov–de Gennes Hamiltonian within a truncated Hilbert space. Creative termination patterning therefore allows one to prototype a variety of Majorana circuits, calculating energy spectra and plotting eigenfunctions over the spherical surface. We develop the computational framework for this approach, establishing a virtual breadboard for Majorana circuitry, and apply it to circuits of interest, including the Majorana analog of a Mach-Zehnder interferometer.

Diluted magnetic semiconductors are materials well known to exhibit strong correlations which typically manifest in carrier-mediated magnetic ordering. In this Rapid Communication, we show that the interaction between excitons and magnetic impurities in these materials is even strong enough to cause a significant deviation from the bare exciton picture in linear absorption spectra of quantum well nanostructures. It is found that exciton-impurity correlations induce a characteristic fingerprint in the form of an additional feature close to the exciton resonance in combination with a shift of the main exciton line of up to a few meV. We trace back these features to the form of the self-energy and demonstrate that reliable values of the average correlation energy per exciton can be extracted directly from the spectra. Since the only requirement for our findings is sufficiently strong correlations, the results can be generalized to other strongly correlated systems.

We present a functional renormalization-group approach to interacting topological Green's function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green's function. Our results for the phase boundary are quantitatively benchmarked against density matrix renormalization-group data.

We theoretically analyze the errors in one- and two-qubit gates in SiMOS and Si/SiGe spin qubit experiments and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise using ideal local rotations. In practice, the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: The $C$-phase infidelity comes out to be $\approx 2.5\times$ the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that $C$-phase gate infidelities can be suppressed by two orders in magnitude. Our pulse sequence is simple and we expect an experimental implementation would be relatively straightforward. We also evaluate the performance of this gate against $1/f$ noise. Assuming a soft ultraviolet cutoff, we show that the pulse sequence designed for quasistatic noise still performs well when the cutoff occurs below $\sim 1$ MHz with experimentally achievable one-qubit Rabi frequencies, suppressing the infidelity by an order of magnitude compared to the existing direct adiabatic protocol. We also analyze the effects of nonadiabaticity during finite rise periods and find that adiabaticity is not a limitation for the current values of exchange coupling.

A detailed study of the effect due to Lorentz-force gradient on the Hall voltage of a two-dimensional electron gas (2DEG) was carried out on specially prepared cylindrical nanomembranes with 2DEG. In the fabricated nanomembranes, weak and strong magnetic-field gradients and, also, sign-alternating magnetic fields acting on the electrons in the nanomembranes were obtained. It was found that an increase in the magnetic-field gradient led to an increase of the Hall constant of 2DEG in weak fields, whereas a change in the field sign caused an inversion of this constant in weak fields. An explanation based on the analysis of the dependence of electron drift velocities on the magnetic field gradient is proposed. The investigated system is of interest both for applications and fundamental research.

Variable-period x-ray standing wave (VPXSW) studies have been carried out using 3 keV x rays and photoelectron detection. Two model surfaces have been used, a native $\mathrm{Si}{\mathrm{O}}_2$ layer (20 Å thick) on bulk silicon, and a purpose-built multilayer surface comprising a chloroform/water marker layer (12 Å thick) on an ionic liquid spacer layer (211 Å thick) deposited on a $\mathrm{Si}{\mathrm{O}}_2$/Si substrate at 90 K. By using photoelectron detection, both chemical and elemental sensitivity were achieved. The surfaces were modeled using dynamic x-ray scattering for x-ray intensity, and attenuation of photoelectrons transmitted through the layers, to produce simulations which accurately reproduced the experimental VPXSW measurements. VPXSW measurements made using the substrate, spacer layer, and marker layer photoelectron signatures produced consistent structural values. This work demonstrates that VPXSW can be used to determine chemically specific layer thicknesses within thick ($\lesssim 300\AA$) surface structures composed of the light elements B, C, N, O, F, and Cl with an accuracy of 10 to 15 Å, perpendicular to the surface.

We study analytically and numerically the renormalization of the $g$-factor in semiconducting Rashba nanowires (NWs), consisting of a normal and superconducting section. If the potential barrier between the sections is high, a quantum dot (QD) is formed in the normal section. For harmonic (hard-wall) confinement, the effective $g$-factor of all QD levels is suppressed exponentially (power law) in the product of the spin-orbit interaction (SOI) wave vector and the QD length. If the barrier between the two sections is removed, the $g$-factor of the emerging Andreev bound states is suppressed less strongly. In the strong SOI regime, and if the chemical potential is tuned to the SOI energy in both sections, the $g$-factor saturates to a universal constant. Remarkably, the effective $g$-factor shows a pronounced peak at the SOI energy as function of the chemical potentials. In addition, if the SOI is uniform, the $g$-factor renormalization as a function of the chemical potential is given by a universal dependence, which is independent of the QD size. This prediction provides a powerful tool to determine experimentally whether the SOI in the whole NW is uniform and, moreover, gives direct access to the SOI strengths of the NW via $g$-factor measurements. In addition, it allows one to find the optimum position of the chemical potential for bringing the NW into the topological phase at large magnetic fields.

The negatively charged nitrogen vacancy ($\mathrm{N}{\mathrm{V}}^{-}$) defect in diamond serves as a popular platform for manipulating and exploiting long-lived coherent spin dynamics at room temperature combined with optical readout. The required spin polarization of the spin triplet ${}^{3}A_2$ electronic ground state occurs through a cycle of repetitious optical photoexcitation events to the ${}^{3}E$ electronic excited state that is accompanied by a series of electronic transitions to a ${}^{1}A_1$ and a ${}^{1}E$ electronic state, and back to the ${}^{3}A_2$ state. The timescales of these transitions are largely known, yet for the relaxation time of the ${}^{1}A_1\to {}^{1}E$ infrared transition, which predominantly occurs via nonradiative recombination, only an upper limit of 1 ns could be determined so far. Here, we employ ultrafast transient absorption spectroscopy to probe the dynamics of the nonradiative relaxation from the ${}^{1}A_1$ to the ${}^{1}E$ state after photoexcitation of the ${}^{3}E$ state and find a relaxation time of 100 ps at a temperature of 78 K.

Topological condensed-matter systems from class A and class AII of the classification table have received classical electromagnetic and mechanical analogs, and protected wave-guiding with such systems has been demonstrated experimentally. Here we introduce a map that generates classical analogs for all entries of the classification table, using only passive elements. Physical mechanical models are provided for all strong topological phases in dimension 2, as well as for three classes in dimension 3. This includes topological superconducting phases, which have never been attempted with classical systems.

Frustrated spin systems can show phases with spontaneous breaking of spin-rotational symmetry without the formation of local magnetic order. We study the dynamic response of the spin-nematic phase of one-dimensional spin-$1/2$ systems, characterized by slow large-distance decay of quadrupolar correlations, by numerically computing one-spin and two-spin dynamical structure factors at zero temperature using time-dependent density matrix renormalization group methods. We interpret the results in terms of an effective theory of gapped magnon excitations interacting with a quasicondensate of bound magnon pairs. This employs an extension of the well-known Tomonaga-Luttinger liquid theory which includes the magnon states as a mobile impurity. A good qualitative understanding of the characteristic thresholds and their intensity in the structure factors is obtained this way. Our results are useful in the interpretation of inelastic neutron scattering and resonant inelastic x-ray scattering experiments.

We study the relationship between the physics of topology and zero modes in frustrated systems and metamaterials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kinds of zero modes in the form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple question: are the robust features of frustration topologically protected and if so can we classify different types of frustration using topology? In answering these questions we invoke the tools of topological mechanics to identify the key agent at play, namely the rigidity matrix, which is a non-Hermitian matrix and decides the topology of spin-wave zero modes in a frustrated magnet or phonon modes in metamaterials. Further developments of the theory rely on combining the recent developments in our understanding of Maxwell constraint counting and generalizing the tenfold way classification of Hermitian matrices to non-Hermitian matrices. The result is a threefold way classification for each Maxwell counting index. We illustrate the classification by demonstrating the existence of a vortex-like invariant for real rigidity matrices using random matrices and through example frustrated spin models. So by classifying all the rigidity matrices, we answer the question of the origin of frustration (i.e., zero modes in the form of accidental degeneracy) in a wide class of frustrated magnets and metamaterials by linking it to topological invariants.

We investigate the spin Hall effect of W-Hf thin films, which exhibit a phase transition from a segregated phase mixture to an amorphous alloy below 70% W. The spin Hall angle was determined with a planar harmonic Hall voltage technique. Due to the accompanying jump in resistivity, the spin Hall angle shows a pronounced maximum at the composition of the phase transition. The spin Hall conductivity does, however, reduce from W to Hf with a weak discontinuity across the phase transition. The maximum spin Hall angle of ${\theta }_{\mathrm{SH}}=-0.20$ is obtained for amorphous ${\mathrm{W}}_{0.7}{\mathrm{Hf}}_{0.3}$. A detailed comparison with spin Hall conductivities calculated from first principles for hcp, fcc, and bcc solid solutions provides valuable insight into the alloying physics of this binary system.

Quantum Hall (QH) states are arguably the most ubiquitous examples of nontrivial topological order, requiring no special symmetry and elegantly characterized by the first Chern number. Their higher dimension generalizations are particularly interesting from both mathematical and phenomenological perspectives, and have attracted recent attention due to a few high profile experimental realizations. In this paper, we derive from first principles the electromagnetic response of QH systems in an arbitrary number of dimensions, and elaborate on the crucial roles played by their modified phase-space density of states under the simultaneous presence of magnetic field and Berry curvature. We provide new mathematical results relating this phase-space modification to the noncommutativity of phase space, and show how they are manifested as a Hall conductivity quantized by a higher Chern number. When a Fermi surface is present, additional response currents unrelated to these Chern numbers also appear. This unconventional response can be directly investigated through a few minimal models with specially chosen fluxes. These models, together with more generic 6D QH systems, can be realized in realistic 3D experimental setups like cold atom systems through possibly entangled synthetic dimensions.

Recent experiments on superfluid ${}^3\mathrm{He}$ in globally anisotropic aerogels have shown realization of the polar superfluid phase and of the half-quantum vortices (HQVs) in this phase upon rotation. To clarify why the HQVs, which had not been detected clearly in the $A$ phase of the bulk liquid, have been realized in the polar phase, we theoretically examine the relative stability of a HQV pair against a single phase vortex in both the bulk $A$ phase and the polar phase in an aerogel. By taking care of important roles of a higher-order gradient term, which assists the stability of HQVs but has never been incorporated so far in the Ginzburg-Landau approach, we find that several consequences, including the extension of the polar phase at lower pressures in the phase diagram, facilitate realization of the HQVs there in contrast to the case of the bulk $A$ phase in a slab geometry.

The local structures of 122-type paradium arsenides, namely ${\mathrm{BaPd}}_2{\mathrm{As}}_2$ and ${\mathrm{SrPd}}_2{\mathrm{As}}_2$, are examined by As $K$-edge extended x-ray absorption fine structure measurements to find a possible correlation between the variation of their superconducting transition temperature and the local structure. The local atomic distances are found to be consistent with average distances measured by diffraction techniques. The temperature dependence of mean square relative displacements reveal that, while ${\mathrm{BaPd}}_2{\mathrm{As}}_2$ is characterized by a local As-Pd soft mode, albeit with larger atomic disorder, ${\mathrm{SrPd}}_2{\mathrm{As}}_2$ shows anomalous As-Pd correlations with a kink at $\sim 160$ K due to hardening by raising temperature. We have discussed implications of these results and possible mechanisms of differing superconducting transition temperature in relation with the structural instability.

First-principles calculations for pristine neutral ferroelectric domain walls in ${\mathrm{BiFeO}}_3$ reveal that excess electrons are selectively trapped by the domain walls, while holes are only weakly attracted. Such trapped excess electrons may be responsible for the thermally activated electrical conductivity at domain walls observed in experiments. In the case of a periodic array of domain walls, the trapped excess electrons create a zigzag potential, whose amplitude depends on the electron concentration in the material and the domain-wall distance. The potential is asymmetric for 71° and 109° domain walls. This could modify the open-circuit voltage in a solar cell and hence influence the photoelectric effect in ${\mathrm{BiFeO}}_3$.

The lattice dynamics of potassium dihydrogen phosphate (KDP) and its deuterated analog DKDP was studied via first-principles DFT calculations. A thorough assessment of the quality of a wide range of functionals supplemented with the approximate inclusion of quantum nuclear effects indicated that the nonlocal van der Waals functional vdW-DF [M. Dion et al., Phys. Rev. Lett. 92, 246401 (2004); J. Klimeš et al., Phys. Rev. B 83, 195131 (2011)] produces the best agreement with structural data for both compounds. This enabled the calculation of full phonon dispersions in the ferroelectric phase, and hence the phonon density of states and specific heat, in very good agreement with experimental data. Phonon bands and especially modes at the $\mathrm{\Gamma }$ point of the Brillouin zone were classified according to their vibrational pattern. This allowed for the assignment of stretching and bending modes of the hydrogen bonds. Internal modes involving the phosphate units were identified at lower frequencies, while the lowest-lying modes were those involving the ${\mathrm{K}}^{+}$ ion. These assignments were used to interpret infrared and Raman spectra along the $c$ axis and in the perpendicular plane. Phonon modes calculated at the $\mathrm{\Gamma }$ point showed two types of instabilities. One was a normal mode polarized along the $c$ axis of the crystal, while the other corresponded to a twofold-degenerate mode polarized in the perpendicular plane. The former gives rise to a spontaneous polarization in the ferroelectric phase at low temperatures by coupling to an optical ${\mathrm{K}}^{+}\text{−}{\mathrm{H}}_2{\mathrm{PO}}_4^{-}$ stretching mode, consistently with a significant off-diagonal Born effective charge on the hydrogen atoms. A mode describing the opposite rotation of neighboring ${\mathrm{PO}}_4$ tetrahedra was also found to couple strongly to the ferroelectric mode, as this modulates the O-O distance, which determines the barrier for proton transfer. The present study suggests that a minimal model to describe isotope effects in KDP should involve at least three fully coupled vibrational modes.

The relaxation dynamics of photoexcited quasiparticles of three-dimensional (3D) Dirac semimetals is vital towards their application in high-performance electronic and optoelectronic devices. In this work, the relaxation dynamics of photoexcited carriers of 3D Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ is investigated by transient terahertz spectroscopy. The visible pump-THz probe spectroscopy measurement shows clear biexponential decays with two characteristic time constants. According to the pump-power and temperature dependence, these two characteristic time constants are attributed to the electron-phonon coupling (1–4 ps) and anharmonic decay of hot coupled phonons to electronic uncoupled phonons (2–9 ps), respectively. An anomalous electron-optical phonon coupling reduction and a bottleneck slowing of hot optical phonon relaxation are observed with higher excitation intensities similar to that in graphene. On the other hand, the electron-optical phonon coupling can be enhanced due to the phonon frequency broadening and softening at elevated lattice temperature. Furthermore, the transient THz spectrum response is strongly modified by the phonon assisted intraband absorption of hot carriers from a pure electronic Drude model, which is evidenced by a characteristic THz absorption dip in the transient THz absorption spectrum. This absorption dip is pinned by the mixing of discrete optical phonon energies that assist the intraband transition enabled by photoexcitation of hot carriers.

We demonstrate deterministic control of dipole-field-stabilized skyrmions by means of spin-orbit torques arising from heavy transition-metal seed layers. Experiments are performed on amorphous Fe/Gd multilayers that are patterned into wires and exhibit stripe domains and dipole skyrmions at room temperature. We show that while the domain walls and skyrmions are achiral on average due to lack of Dzyaloshinskii-Moriya interactions, the Néel-like closure domain walls at each surface are chiral and can couple to spin-orbit torques. The current-induced domain evolutions are reported for different magnetic phases, including disordered stripe domains, coexisting stripes and dipole skyrmions, and a close-packed dipole skyrmion lattice. The magnetic textures exhibit motion under current excitations with a current density $\sim {10}^8\mathrm{A}/{\mathrm{m}}^2$. By comparing the motion resulting from magnetic spin textures in Fe/Gd films with different heavy transition-metal interfaces, we confirm spin currents can be used to manipulate achiral dipole skyrmions via spin-orbit torques. We further show the current-induced response of a dipole skyrmion lattice where skyrmions move in channels between pinned regions.