Melting in the deep rocky portions of planets is important for understanding the thermal evolution of these bodies and the possible generation of magnetic fields in their underlying metallic cores. But the melting temperature of silicates is poorly constrained at the pressures expected in super-Earth exoplanets, the most abundant type of planets in the galaxy. Here, we propose an iterative learning scheme that combines enhanced sampling, feature selection, and deep learning, and develop a unified machine learning potential of ab initio quality valid over a wide pressure-temperature range to determine the melting temperature of $\mathrm{MgSi}{\mathrm{O}}_3$. The melting temperature of the high-pressure, post-perovskite phase, important for super-Earths, increases more rapidly with increasing pressure than that of the lower pressure perovskite phase, stable at the base of Earth's mantle. The volume of the liquid closely approaches that of the solid phases at the highest pressure of our study. Our computed triple point constrains the Clapeyron slope of the perovskite to post-perovskite transition, which we compare with observations of seismic reflectivity at the base of Earth's mantle to calibrate Earth's core heat flux.

The size of the orbital moment in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ has been the subject of a long-standing and contentious debate. In this paper, we make use of ferromagnetic resonance (FMR) spectroscopy and x-ray magnetic circular dichroism (XMCD) to provide complementary determinations of the size of the orbital moment in “bulklike” epitaxial ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films grown on yttria-stabilized zirconia (111) substrates. Annealing the 100 nm as-grown films to $1100{}^{\circ }\mathrm{C}$ in a reducing atmosphere improves the stoichiometry and microstructure of the films, allowing for bulklike properties to be recovered as evidenced by x-ray diffraction and vibrating sample magnetometry. In addition, in-plane angular FMR spectra exhibit a crossover from a fourfold symmetry to the expected sixfold symmetry of the (111) surface, together with an anomalous peak in the FMR linewidth at $\sim 10$ GHz; this is indicative of low Gilbert damping in combination with two-magnon scattering. For the bulklike annealed sample, a spectroscopic splitting factor $g\approx 2.18$ is obtained using both FMR and XMCD techniques, providing evidence for the presence of a finite orbital moment in ${\mathrm{Fe}}_3{\mathrm{O}}_4$.

Grain boundaries often exhibit ordered atomic structures. Increasing amounts of evidence have been provided by transmission electron microscopy and atomistic computer simulations that different stable and metastable grain boundary structures can occur. Meanwhile, theories to treat them thermodynamically as grain boundary phases have been developed. Whereas atomic structures were identified at particular grain boundaries for particular materials, it remains an open question if these structures and their thermodynamic excess properties are material specific or generalizable to, e.g., all fcc metals. In order to elucidate that question, we use atomistic simulations with classical interatomic potentials to investigate a range of high-angle $\left[11\overline{1}\right]$ symmetric tilt grain boundaries in Ni, Cu, Pd, Ag, Au, Al, and Pb. We could indeed find two families of grain boundary phases in all of the investigated grain boundaries, which cover most of the standard fcc materials. Where possible, we compared the atomic structures to atomic-resolution electron microscopy images and found that the structures match. This poses the question if the grain boundary phases are simply the result of sphere-packing geometry or if material-specific bonding physics play a role. We tested this using simple model pair potentials and found that medium-ranged interactions are required to reproduce the atomic structures, while the more realistic material models mostly affect the grain boundary (free) energy. In addition to the structural investigation, we also report the thermodynamic excess properties of the grain boundaries, explore how they influence the thermodynamic stability of the grain boundary phases, and detail the commonalities and differences between the materials.

Cluster states were introduced in the context of measurement-based quantum computing. In one dimension, the cluster Hamiltonian possesses topologically protected states. We investigate the Floquet dynamics of the cluster spin chain in an external field, interacting with a particle. We explore the entanglement properties of the topological and magnetic phases, first in the integrable spin lattice case and then in the interacting quantum walk case. We find, in addition to thermalization, dynamical phase transitions separating low- and high-entanglement nonthermal states, reminiscent of the ones present in the integrable case, but differing in their magnetic properties. The nonergodic phases are characterized by the emergence of magnetic order, persistent at long times.

We introduce spiral boundary conditions (SBCs) as a useful tool for handling the shape of finite-size periodic clusters. Using SBCs, a lattice model for more than two dimensions can be exactly projected onto a one-dimensional (1D) periodic chain with translational invariance. Hence, the existing 1D techniques such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., can be effectively applied to the projected 1D model. First, we describe the 1D projection scheme for the two-dimensional (2D) square- and honeycomb-lattice tight-binding models in real and momentum space. Next, we discuss how the density of states and the ground-state energy approach their thermodynamic limits. Finally, to demonstrate the utility of SBCs in DMRG simulations, we estimate the magnitude of staggered magnetization of the 2D XXZ Heisenberg model as a function of XXZ anisotropy.

High-harmonic generation (HHG) is a versatile technique for probing ultrafast electron dynamics. While HHG is sensitive to the electronic properties of the target, HHG also depends on the waveform of the laser pulse. As is well known, (peak) positions, $\omega$, in the high-harmonic spectrum can shift when the carrier envelope phase (CEP), $\phi$, is varied. We derive formulæ describing the corresponding parametric dependencies of CEP shifts; in particular, we have a transparent result for the (peak) shift, $d\omega /d\phi =-2{\overline{\mathfrak{f}}}^{\prime }\omega /{\omega }_0$, where ${\omega }_0$ describes the fundamental frequency and ${\overline{\mathfrak{f}}}^{\prime }$ characterizes the chirp of the driving laser pulse. We compare the analytical formula to full-fledged numerical simulations finding only 17% average relative absolute deviation in $d\omega /d\phi$. Our analytical result is fully consistent with experimental observations.

We report on an experimental investigation of the combined effect of nonequilibrium quasiparticle injection and supercurrent in superconducting aluminum wires. At low temperature, we observe the supercurrent-induced coupling of energy and charge imbalance with spectral resolution. At high magnetic fields, in the presence of a Zeeman splitting of the density of states, we find evidence for an additional spin-dependent coupling which has been recently predicted theoretically.

We have measured the electronic energy-loss straggling of protons, helium, boron, and silicon ions in silicon using a transmission time-of-flight approach. Ions with velocities between 0.25 and 1.6 times the Bohr velocity were transmitted through single-crystalline Si(100) nanomembranes in either channeling or random geometry to study the impact parameter dependence of energy-loss straggling. Nuclear and path length contributions to the straggling were determined with the help of Monte Carlo simulations. Our results exhibit an increase in straggling with increasing ion velocity for channeled trajectories for all projectiles as well as for protons and helium in random geometry. In contrast for heavier ions, electronic straggling at low velocities does not decrease further but plateaus and even seems to increase again. We compare our experimental results with transport cross section calculations. The satisfying agreement for helium shows that electronic stopping for light ions is dominated by electron-hole pair excitations, and that the previously observed trajectory dependence can indeed be attributed to a higher mean charge state for random trajectories. No agreement is found for boron and silicon indicating the breakdown of models based solely on electron-hole pair excitations, and that local electron-promotion and charge-exchange events significantly contribute to energy loss at low velocities.

We study the nonlinear magnon spin current induced by an ac electric field under light irradiation in collinear antiferromagnets with broken inversion symmetry. For linearly polarized light, we find that a dc spin current appears through “the magnon spin shift current” mechanism, which is driven by a spin polarization generation in the two magnon creation process and has a close relationship to the geometry of magnon bands through Berry connection. For circularly polarized light, a dc spin current appears through “the spin injection current” mechanism, which is proportional to the relaxation time of magnons and can be large when the magnon lifetime is long. We demonstrate the generation of the magnon spin shift and injection currents, based on a few toy models and a realistic model for a multiferroic material $\mathit{M}{}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$.

Pathways and energy barriers for the migration of Ga vacancies ($V_{\mathrm{Ga}}$) and Ga interstitials (${\mathrm{Ga}}_{\mathrm{i}}$) in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are explored using hybrid functional calculations and the nudged elastic band method. Considering $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ as primarily being an $n$-type semiconductor, we focus on defect charge states relevant under such conditions: $V_{\mathrm{Ga}}^{3-}, {\mathrm{Ga}}_{\mathrm{i}}^{3+}$, and ${\mathrm{Ga}}_{\mathrm{i}}^{+}$. Notably, we describe a mechanism by which $V_{\mathrm{Ga}}$ can transform between its different split configurations. In all cases, the intermediate state consists of a vacancy split between three Ga sites—a three-split vacancy—which enables passage over a significantly lower energy barrier. This is because it avoids the unfavorable simple vacancy at the tetrahedral Ga site. The proposed mechanism lowers the overall barrier for $V_{\mathrm{Ga}}^{3-}$ diffusion along the [001] crystal direction from 1.73 to 0.97 eV, whereas the 2.08 eV barrier for the [100] and [010] directions is unaffected. For ${\mathrm{Ga}}_{\mathrm{i}}^{3+}$, we obtain similar overall migration barriers of 0.72, 0.80, and 1.02 eV for the [010], [001], and [100] directions, respectively. ${\mathrm{Ga}}_{\mathrm{i}}^{+}$ exhibits a strong preference for diffusion within the large eight-sided channel; the overall migration barrier is 0.92 eV for the [010] direction, and 2.16 eV for the [001] and [100] directions. The limiting step for the two latter directions involves ionization of ${\mathrm{Ga}}_{\mathrm{i}}^{+}$ followed by a jump to an adjacent large eight-sided channel as ${\mathrm{Ga}}_{\mathrm{i}}^{3+}$. Our results are discussed in light of experimental observations of thermally activated recovery processes in irradiated material.

We present a systematic high-pressure study of layered van der Waals semiconductor GaTe through electrical transport, photoluminescence, and Raman spectroscopy measurements. We report observation of pressure-induced metallization and superconductivity (SC) in GaTe simultaneously occurring at ∼3 GPa, with an onset superconducting critical temperature of $T_{\mathrm{C}}^{\mathrm{onset}}\sim 5.0\mathrm{K}$. Analysis shows that a quasi–two-dimensional to three-dimensional structural crossover plays a crucial role in driving the observed metallization and SC. Upon further compression, $T_{\mathrm{C}}^{\mathrm{onset}}$ first decreases gradually and then begins to increase above ∼10 GPa, displaying a V-shaped feature (SC-I→SC-II) due to a structural transition ($C2/m\to Fm\text{−}3m$). After reaching a local maximum of 4.5 K at ∼18 GPa, $T_{\mathrm{C}}^{\mathrm{onset}}$ remains almost unchanged up to a highest pressure of 48.1 GPa. A comparison of the upper critical fields at different pressures spanning the SC-I and SC-II phases reveals that their pairing mechanisms may be different from each other. These results demonstrate that the band gap of layered semiconductor GaTe is highly tunable, which may stimulate further investigations by strain engineering, intercalation, and electrostatic doping.

We report measurements of the compressibility of ramp compressed tantalum to a final stress of 2.3 TPa corresponding to threefold volumetric compression. Using these data, we extended the experimental constraint on the Ta cold compression curve by an order of magnitude in pressure. By combining the resulting data with previous measurements of shock compression and ambient pressure heating, we construct an experimentally bounded and thermodynamically consistent equation of state model for Ta which has 2% uncertainty in pressure at 1 TPa. We therefore propose Ta as an in situ pressure scale for laser-heated static compression experiments which were recently able to reach terapascal pressures and thousands of degrees Kelvin. Our new equation of state of Ta is experimentally constrained at extreme pressures and temperatures relevant to a wide range of planetary interiors and will allow for more accurate comparison between experimental measurements and theory at extreme conditions.

Lanthanide atoms on surfaces are an exceptional platform for atomic-scale magnetic information storage. However, their potential as qubits remains unexplored due to the limited number of experimental setups that can coherently drive the spins of single adatoms. Here we propose a combined experimental and theoretical method to estimate the performance of surface-adsorbed lanthanide atoms for quantum coherent operations. We investigate Er and Tm on MgO(100)/Ag(100) with x-ray absorption spectroscopy to address their magnetic and electronic properties and with scanning tunneling microscopy (STM) to identify their adsorption sites. With atomic multiplet calculations and density functional theory, we infer for both atoms a magnetic ground state that is suitable for quantum coherent operations. We investigate whether these systems lend themselves to electron spin resonance scanning tunneling microscopy (ESR-STM). By adapting the piezoelectric model of ESR-STM to the case of lanthanide atoms, we show that these systems should exhibit a detectable signal and that they have a higher Rabi rate compared to the systems studied up to date. In addition to their suitable electron spin properties, these elements possess a nontrivial nuclear spin that could be exploited to perform two-qubit operations on a single atom or to store quantum states in the nuclear spin.

We have investigated the local electronic structure of $\mathrm{PbCr}{\mathrm{O}}_3$ by conducting x-ray absorption spectroscopy at the lead $L_3$ and chromium $L_{2,3}$ edges. We found that lead is divalent and chromium is charge-disproportionated into trivalent and hexavalent states at ambient pressures, explaining their insulating behavior. The high-resolution partial fluorescence yield of lead $L_3$ spectra as a function of pressure revealed that the divalent state of lead ions remains unchanged at high pressures, when $\mathrm{PbCr}{\mathrm{O}}_3$ changes into metal and its volume collapses by more than 10%. We infer that the insulator-to-metal transition does not involve a Pb-Cr charge transfer, but is associated with the conversion of ${\mathrm{Cr}}^{3+}/{\mathrm{Cr}}^{6+}$ charge-disproportionated states into a ${\mathrm{Cr}}^{4+}$ valence state.

The velocities of the quasiparticles that form Cooper pairs in a superconductor are revealed by the upper critical magnetic field. Here we use this property to assess superconductivity in magic-angle twisted bilayer graphene (MATBG), which has been observed over a range of moiré band-filling, twist angle, and screening environment conditions. An average Fermi velocity can be defined as $v_F^{*}\equiv k_B{T}_c{\ell }_c/\hslash$, where $T_c$ and ${\ell }_c$ are the critical temperature and magnetic length, respectively. An advantage of this definition is that $v_F^{*}$ can be directly extracted from the existing experimental data. Mean-field theory calculations of upper critical fields in model superconductors are consistent with the expectation that Fermi velocities defined in this way are nearly independent of the strength of pairing interaction. Moreover, for fixed strength pairing interaction, minima in $v_F^{*}$ as a function of band filling are coincident with maxima in $T_c$, as expected from the McMillan formula. Since no association between $T_c$ maxima and $v_F^{*}$ minima is present in MATBG experimental data, we argue that the pairing interaction in MATBG is strongly filling-factor dependent. Any theory of MATBG superconductivity must explain this dependence, which is apparently primarily responsible for the observed superconducting domes.

A recent proof of concept showed that cavity photons can mediate superconducting (SC) signatures to a ferromagnetic insulator (FI) over a macroscopic distance [A. T. G. Janssønn et al., Phys. Rev. B 102, 180506(R) (2020)]. In contrast with conventional proximity systems, this facilitates long-distance FI–SC coupling, local subjection to different drives and temperatures, and studies of their mutual interactions without proximal disruption of their orders. Here we derive a microscopic theory for these interactions, with an emphasis on the leading effect on the FI, namely, an induced anisotropy field. In an arbitrary practical example, we find an anisotropy field of $14–16\mu \mathrm{T}$, which is expected to yield an experimentally appreciable tilt of the FI spins for low-coercivity FIs such as Bi-YIG. We discuss the implications and potential applications of such a system in the context of superconducting spintronics.

Using Landau-level spectroscopy, we determine the temperature dependence of the energy band gap in zirconium pentatelluride (${\mathrm{ZrTe}}_5$). We find that the band gap reaches $E_g=(5\pm 1)\mathrm{meV}$ at low temperatures and increases monotonically when the temperature is raised. This implies that ${\mathrm{ZrTe}}_5$ is a weak topological insulator, with noninverted ordering of electronic bands in the center of the Brillouin zone. Our magnetotransport experiments performed in parallel show that the resistivity anomaly in ${\mathrm{ZrTe}}_5$ is not connected with the temperature dependence of the band gap.

We consider a spin circuit-QED device where a superconducting microwave resonator is capacitively coupled to a single hole confined in a semiconductor quantum dot. Thanks to the strong spin-orbit coupling intrinsic to valence-band states, the gyromagnetic $\mathtt{g}$ matrix of the hole can be modulated electrically. This modulation couples the photons in the resonator to the hole spin. We show that the applied gate voltages and the magnetic-field orientation enable a versatile control of the spin-photon interaction, whose character can be switched from fully transverse to fully longitudinal. The longitudinal coupling is actually maximal when the transverse one vanishes and vice versa. This “reciprocal sweetness” results from geometrical properties of the $\mathtt{g}$ matrix and protects the spin against dephasing or relaxation. We estimate coupling rates reaching $\sim 10\mathrm{MHz}$ in realistic settings and discuss potential circuit-QED applications harnessing either the transverse or the longitudinal spin-photon interaction. Furthermore, we demonstrate that the $\mathtt{g}$-matrix curvature can be used to achieve parametric longitudinal coupling with enhanced coherence.

The Su, Schrieffer, and Heeger (SSH) model, describing the soliton excitations in polyacetylene due to the formation of antiphase domain walls (DW) from the alternating bond pattern, has served as a paradigmatic example of one-dimensional (1D) chiral topological insulators. While the SSH model has been realized in photonic and plasmonic systems, there have been limited analogs in three-dimensional (3D) electronic systems, especially regarding the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in which the dimerization of (111) atomic layers renders alternating covalent and van der Waals bonding within and between successive (111) bilayers, respectively, serves as a 3D analog of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$ by considering the parity eigenvalues and Wannier charge centers, while the previously reported bulk topological phases of Bi remain invariant under the dimerization reversal. Next, we demonstrate the existence of topologically nontrivial (111) and trivial $\left(11\overline{2}\right)$ DWs in which the number of in-gap DW states (ignoring spin) is odd and even respectively, and show how this controls the interlinking of the Zak phases of the two adjacent domains. Finally, we derive general criteria specifying when a DW of arbitrary orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization reversal in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.

We show that Ge concentration oscillations within the quantum well region of a Si/SiGe heterostructure can significantly enhance the spin-orbit coupling of the low-energy conduction-band valleys. Specifically, we find that for Ge oscillation wavelengths near $\lambda =1.57\text{nm}$ with an average Ge concentration of ${\overline{n}}_{\text{Ge}}=5\%$ in the quantum well region, a Dresselhaus spin-orbit coupling is induced, at all physically relevant electric field strengths, which is over an order of magnitude larger than what is found in conventional Si/SiGe heterostructures without Ge concentration oscillations. This enhancement is caused by the Ge concentration oscillations producing wave-function satellite peaks a distance $2\pi /\lambda$ away in momentum space from each valley, which then couple to the opposite valley through Dresselhaus spin-orbit coupling. Our results indicate that the enhanced spin-orbit coupling can enable fast spin manipulation within Si quantum dots using electric dipole spin resonance in the absence of micromagnets. Indeed, our calculations yield a Rabi frequency ${\mathrm{\Omega }}_{\text{Rabi}}/B>500\text{MHz/T}$ near the optimal Ge oscillation wavelength $\lambda =1.57\text{nm}$.