We dismantle the previously held misconception that it is impossible for bulk rectification mechanisms to induce a net DC electric current when the frequency of the impinging radiation lies within the optical gap of a metal in the limit of small carrier relaxation rates. We argue that generically such in-gap rectification mechanisms are irreversible and accompanied by a continuous exchange of energy with a heat bath and must also be necessarily accompanied by a small but finite absorption of radiation in order to guarantee the positivity of the net entropy production and abide by the second law of thermodynamics. We show, however, that the intraband nonlinear Hall effect arising from the Berry curvature is a special kind of in-gap rectification mechanism that behaves as a “photovoltaic demon,” namely, it can operate as an ideal reversible and dissipationless conveyor of energy between the radiation and an external circuit. Its reversible nature allows for an interesting mode of operation as an amplifier of circularly polarized light, whose efficiency can approach 100% and which could be technologically promising, especially in the infrared frequency range.

Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. A crucial building block of these protocols is the adiabatic shuttling of MZMs through topological superconductors. Here, we consider the “piano key” approach, where MZMs are transported using local electric gates to tune sections (“keys”) of a wire between topologically trivial and nontrivial phases. We numerically simulate this transport on a single wire and calculate the diabatic error corresponding to exciting the system. We find that this error is typically reduced when transport is facilitated by using multiple keys as one may expect from modeling each piano key press as an effective Landau-Zener process. However, further increasing the number of keys increases errors; thus, there exists a nontrivial optimal number of keys that minimizes the diabatic error given a fixed total shuttle time. As we show, this optimal number of keys can be explained by modeling each key press as an effective Landau-Zener process while paying careful attention to power-law corrections that arise due to the nonanalytic behavior of the time-dependent modulation of the chemical potential at the beginning and end of each key press.

Quantum Hall edge states are the paradigmatic example of bulk-boundary correspondence. They are prone to intricate reconstructions calling for their detailed investigation at high spatial resolution. Here, we map quantum Hall edge states of monolayer graphene at a magnetic field of 7 T with scanning tunneling microscopy. Our graphene sample features a gate-tunable lateral interface between areas of different filling factor. We compare the results with detailed tight-binding calculations, quantitatively accounting for the perturbation by the tip-induced quantum dot. We find that an adequate choice of gate voltage allows for mapping the edge state pattern with little perturbation. We observe extended compressible regions, the antinodal structure of edge states, and their meandering along the lateral interface.

In recent years, interest in expanding from 2D to 3D systems has grown in the magnetism community, from exploring new geometries to broadening the knowledge on the magnetic textures present in thick samples, and with this arises the need for new characterization techniques, in particular tomographic imaging. Here, we present a new tomographic technique based on Fourier transform holography, a lensless imaging technique that uses a known reference in the sample to retrieve the object of interest from its diffraction pattern in one single step of the calculation, overcoming the phase problem inherent to reciprocal-space-based techniques. Moreover, by exploiting the phase contrast instead of the absorption contrast, thicker samples can be investigated. We obtain a 3D full-vectorial image of a 800-nm-thick extended Fe/Gd multilayer in a $5\text{−}\mu \mathrm{m}$-diameter circular field of view with a resolution of approximately 80 nm. The 3D image reveals wormlike domains with magnetization pointing mostly out of plane near the surface of the sample but that falls in-plane near the substrate. Since the FTH setup is fairly simple, it allows modifying the sample environment. Therefore this technique could enable in particular a 3D view of the magnetic configuration's response to an external magnetic field.

We study generalized multifractality that characterizes eigenstate fluctuations and correlations in disordered systems of chiral symmetry classes AIII, BDI, and CII. By using the nonlinear sigma-model field theory, we construct pure-scaling composite operators and eigenfunction observables that satisfy Abelian fusion rules. The observables are labeled by two multi-indices $\lambda , {\lambda }^{\prime }$ referring to two sublattices, at variance with other symmetry classes, where a single multi-index $\lambda$ (that can be viewed as a generalized version of a Young diagram) is needed. Further, we analyze Weyl symmetries of multifractal exponents, which are also peculiar in chiral classes, in view of a distinct root system associated with the sigma-model symmetric space. The analytical results are supported and complemented by numerical simulations that are performed for a 2D lattice Hamiltonian of class AIII, both in the metallic phase and at the Anderson transition. Both in the metallic phase and at the transition, the numerically obtained exponents satisfy Weyl symmetry relations, confirming that the sigma model is the right theory of the problem. Furthermore, in the metallic phase, we observe the generalized parabolicity (proportionality to eigenvalues of the quadratic Casimir operator), as expected in the one-loop approximation. On the other hand, the generalized parabolicity is strongly violated at the metal-insulator transition, implying violation of local conformal invariance.

The magnetism of the rocksalt fcc rare-earth monopnictide HoBi, a candidate topological material with extreme magnetoresistance, is investigated. From the ${\mathrm{Ho}}^{3+}$ non-Kramers $J=8$ spin-orbital multiplet, the cubic crystal electric field yields six nearly degenerate low-energy levels. These constitute an anisotropic magnetic moment with a Jahn-Teller-like coupling to the lattice. In the cubic phase for $T>T_N=5.72\left(1\right)\text{K}$, the paramagnetic neutron scattering is centered at $\mathbf{k}=\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ and was fit to dominant antiferromagnetic interactions between Ho spins separated by $\left\{100\right\}$ and ferromagnetic interactions between spins displaced by $\left\{\frac{1}{2}\frac{1}{2}0\right\}$. For $T<T_N$, a type-II AFM long-range order with $\mathbf{k}=\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ develops along with a tetragonal lattice distortion. While neutron diffraction from a multidomain sample cannot unambiguously determine the spin orientation within a domain, the bulk magnetization, structural distortion, and our measurements of the magnetic excitations all show the easy axis coincides with the tetragonal axis. The weakly dispersive excitons for $T<T_N$ can be accounted for by a spin Hamiltonian that includes the crystal electric field and exchange interactions within the random phase approximation.

We have performed magnetic torque and resistivity measurements on the centrosymmetric skyrmion host ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$, in which the dominant magnetic interaction leading to skyrmion formation is under debate. We observe both the de Haas–van Alphen and Shubnikov–de Haas oscillations in the forced ferromagnetic phase. The angular dependence of the quantum oscillation frequencies can be reproduced by an ab initio calculation. The de Haas–van Alphen oscillation is also observed in the double-$\mathbf{Q}$ phase with a frequency different from that in the forced ferromagnetic phase, indicating a Fermi surface reconstruction due to the coupling between localized spins and conduction electrons. Based on these experimental findings, the magnetic interactions in this system are discussed.

The ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$ alloy exhibits an anomalously low thermal expansion at ambient conditions, an effect that is known as the invar effect. Other ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ alloys do not exhibit this effect at ambient conditions but upon application of pressure even Ni-rich compositions show low thermal expansion, thus called the pressure induced invar effect. We investigate the pressure induced invar effect for ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ for $x$ = 0.64, 0.50, 0.25 by performing a large set of supercell calculations, taking into account noncollinear magnetic states. We observe anomalies in the equation of states for the three compositions. The anomalies coincide with magnetic transitions from a ferromagnetic state at high volumes to a complex magnetic state at lower volumes. Our results can be interpreted in the model of noncollinear magnetism which relates the invar effect to increasing contribution of magnetic entropy with pressure.

Strong, adjustable magnetic couplings are of great importance to all devices based on magnetic materials. Controlling the coupling between adjacent regions of a single magnetic layer, however, is challenging. In this work, we demonstrate strong exchange-based coupling between arbitrarily shaped regions of a single ferrimagnetic layer. This is achieved by spatially patterning the compensation temperature of the ferrimagnet by either oxidation or ${\mathrm{He}}^{+}$ irradiation. The coupling originates at the lateral interface between regions with different compensation temperature and scales inversely with their width. We show that this coupling generates large lateral exchange coupling fields and we demonstrate its application to control the switching of magnetically compensated dots with an electric current.

We show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of $C_{2z}T$-protected Majorana Kramers pairs appear at corners on pairing domain walls. The topology originates from the anomaly analyzed in Song et al.—the absence of a lattice support—of the single-valley band structure of twisted bilayer graphene, which is protected by $C_{2z}T$ and approximate particle-hole symmetry $\mathcal{P}$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, $C_{2z}T$, and $\mathcal{P}$ must drive the system into a higher-order topological superconductor. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and is broken to U(1) for the triplet pairing. Using a Dirac Hamiltonian, we derive the corner modes and confirm with numerics. These corner states are stable even if $\mathcal{P}$ is weakly broken, which is true in experimental setups. Finally, we suggest experimental detection via the fractional Josephson effect in a TBG-TSC Josephson junction.

We provide a theoretical interpretation of the metallic broken spin-valley (flavor) symmetry states recently discovered in hole-doped rhombohedral trilayer (ABC) graphene in large electric displacement fields. Our conclusions about the phase diagram and phase transitions combine insights from ABC graphene electronic structure models and mean-field theory, and are guided by the precise magneto-oscillation Fermi-surface-area measurements of recent experiments. We find that the principle of momentum-space condensation plays a key role in determining Fermi-surface reconstructions enabled by broken flavor symmetries when the single-particle bands imply thin annular Fermi seas. The reconstructed Fermi sea consists of one large outer Fermi-surface-enclosed majority-flavor states in reciprocal-space area $A_{\text{maj}}$ and one or more small inner holelike Fermi-surface-enclosed minority-flavor states in $A_{\text{min}}$ that are primarily responsible for nematic order. The competing ground states (valley-Ising, valley-XY, and spin-polarized state) have different $A_{\text{maj}}/A_{\text{min}}$ and exchange energy maximizes this ratio and selects valley-XY nematic metal as the lowest-energy state. We discuss how the nematic pockets explain the observed fractionalization of quantum oscillation frequencies, and propose anisotropic transport and the nonlinear Hall effect as additional observables.

Alloyed ${\mathrm{Mn}}_x{\mathrm{Zn}}_{1-x}{\mathrm{PS}}_3$ samples have been grown covering the whole compositional range and studied by means of Raman spectroscopy at temperatures from 4 to 850 K. Our results, supported by superconducting quantum interference device magnetic measurements, allowed us, on one hand, to complete the magnetic phase diagram of ${\mathrm{Mn}}_x{\mathrm{Zn}}_{1-x}{\mathrm{PS}}_3$ and establish $x\ge 0.3$ as the composition at which the alloy retains antiferromagnetism and, on the other hand, to identify the Raman signatures indicative of a magnetic transition. The origin of these Raman signatures is discussed in terms of spin-phonon coupling, resulting in the appearance of low- and high-frequency phonon modes. For the alloy, an assignation of the first- and second-order modes is provided with the aid of first-principles lattice-dynamical calculations. The compositional dependence of all phonon modes is described, and the presence of zone-folded modes is shown to take place for the alloy. Finally, a comparison of the Raman spectra of ${\mathrm{ZnPS}}_3$ to other compounds of the transition metal phosphorus trisulfide family allowed us to conclude that low-frequency phonon peaks exhibit an abnormally large broadening. This is consistent with previous claims on the occurrence of a second-order Jahn-Teller effect that takes place for ${\mathrm{ZnPS}}_3$ and Zn-rich ${\mathrm{Mn}}_x{\mathrm{Zn}}_{1-x}{\mathrm{PS}}_3$.

$\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ crystallizes in the $\mathrm{Zr}{\mathrm{Fe}}_4{\mathrm{Si}}_2$-type structure, hosting chains of Fe tetrahedra giving rise to geometric frustration and low dimensionality. The compound orders antiferromagnetically at around 36 K accompanied by a simultaneous structural transition from a tetragonal phase to an orthorhombic phase. The hydrostatic pressure dependence of the magnetic and structural transitions is investigated using electrical transport, AC magnetic susceptibility, AC calorimetry, $\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$, muon-spin relaxation ($\mu \mathrm{SR}$), and x-ray-diffraction measurements. External pressure suppresses the first-order transition to the antiferromagnetic phase (AFM1) around 1.8 GPa. The structural transition is largely unaffected by pressure and remains between 30 to 35 K for pressures up to 2 GPa. A second antiferromagnetic phase (AFM2) is observed at higher pressures. The transition from the paramagnetic to the AFM2 phase is of second-order nature and appears to be connected to the structural transition. The magnetic volume fraction obtained from $\mu \mathrm{SR}$ and $\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ measurements reveal that the entire sample undergoes magnetic ordering in both magnetic phases. In addition, similar low-temperature muon-precession frequencies in AFM1 and AFM2 phases point at similar ordered moments and magnetic structures in both phases. Our results further indicate enhanced magnetic fluctuations in the pressure-induced AFM2 phase. The experimental observations together with density functional theory calculations suggest that the magnetic- and structural-order parameters in $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ are linked by magnetic frustration, causing the simultaneous magnetostructural transition.

Moiré superlattice patterns at the interface of two-dimensional (2D) van der Waals (vdW) materials, arising from a small displacement between similar lattices, have been extensively studied over the past decade for their dramatic ability to tune material properties. However, previous work to understand the structure of these interfaces has largely focused on some special cases, particularly honeycomb lattices displaced by twist or isotropic scaling. In this work, we develop practical and analytical tools for understanding the moiré structure that can be generalized to other lattice distortions and lattice types. At large enough moiré lengths, all moiré systems relax into commensurated 2D domains separated by networks of dislocation lines. The nodes of the 2D dislocation line network can be considered as vortexlike topological defects. However, we find these topological defects to exist on a punctured torus, requiring different mathematical formalism than the topological defects in a superconductor or planar ferromagnet. In the case of twisted bilayer graphene, the defects are characterized by the free group on two generators. We find that antivortices occur in the presence of anisotropic heterostrain, such as a shear or anisotropic displacement, while arrays of vortices appear under a twist or isotropic displacement between vdW materials. Utilizing the dark field imaging capability of transmission electron microscopy (TEM), we experimentally demonstrate the existence of vortex and antivortex pair formation in a moiré system, caused by competition between different types of heterostrains in the vdW interfaces. We also present a methodology for mapping the underlying heterostrain of a moiré structure from experimental TEM data, which provides a quantitative relation between the various components of heterostrain and vortex-antivortex density in moiré systems.

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te $5p$-derived valence electrons to Hg $5d$ core states at shallow binding energy. We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg $5d$ states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.

Charge traps in the semiconductor bulk (bulk charge traps) make it difficult to predict the electric field within wide band gap semiconductors. The issue is the daunting number of bulk charge-trap candidates which means the treatment of bulk charge traps is generally qualitative or uses generalized models that do not consider the trap's particular electronic structure. The electric field within a wide band gap semiconductor is nonetheless a crucial quantity in determining the operation of semiconductor devices and the performance of solid-state single-photon emitters embedded within the semiconductor devices. In this work we accurately compute the average electric field measured at the location of $\mathrm{N}{V}^{-}$ charged defects for the substitutional N (${\mathrm{N}}_{\text{C}}$) concentration of $n_{{\text{N}}_{\text{C}}}\approx 1.41\times {10}^{18}{\mathrm{cm}}^{-3}$ for the commonly used oxygen-terminated diamond [see D. A. Broadway et al., Nature Electron. 1, 502 (2018)]. We achieve this result by evaluating the leading-order contribution to the electric field far away from the surface, which comes from the ${\mathrm{N}}_{\text{C}}$ defects that induce the ionization of the $\mathrm{N}{V}^{-}$. Our results use density-functional theory (DFT) and the principle of band bending. Our work has the potential to aid both in the prediction of the functioning of semiconductor devices and in the prediction and correction of the spectral diffusion that often plagues the optical frequencies of solid-state single-photon emitters upon repeated photoexcitation measurements. Our results for the timescales involved in thermally driven charge transfer also have the potential to aid in investigations of charge dynamics.

Although charge density wave (CDW) correlations exist in several families of cuprate superconductors, they exhibit substantial variation in CDW wave vector and correlation length, indicating a key role for CDW-lattice interactions. We investigated this interaction in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ using single-crystal x-ray diffraction to collect a large number of CDW peak intensities and determined the Cu and La/Ba atomic distortions induced by the formation of CDW order. Within the ${\mathrm{CuO}}_2$ planes, the distortions involve a periodic modulation of the Cu-Cu spacing along the direction of the ordering wave vector. The charge ordering within the copper-oxygen layer induces an out-of-plane breathing modulation of the surrounding lanthanum layers, which leads to a related distortion on the adjacent copper-oxygen layer. Our result implies that the CDW-related structural distortions do not remain confined to a single layer but rather propagate an appreciable distance through the crystal. This leads to overlapping structural modulations, in which ${\mathrm{CuO}}_2$ planes exhibit distortions arising from the orthogonal CDWs in adjacent layers as well as distortions from the CDW within the layer itself. We attribute this striking effect to the weak $c$-axis charge screening in cuprates and suggest this effect could help couple the CDWs between adjacent planes in the crystal.

We investigate the spin polarization of localized exciton-polariton condensates. We demonstrate the presence of an effective magnetic field leading to the formation of elliptically polarized condensates. We show that this synthetic field has an entirely photonic origin, which we believe is unique for the CdTe-based microcavities. Moreover, the degree of spin polarization of localized polariton condensates in samples with magnetic ions depends on the excitation power or polarization of the nonresonant excitation laser. In an external magnetic field, the semimagnetic condensate spontaneously builds up strong spin polarization. Based on the magnetic field behavior of the condensate in the presence of magnetic ions, we apply a model that allows us to estimate the polariton-polariton interaction strength in a CdTe system to $0.8\mu \text{eV}\mu {\text{m}}^2$.

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. We propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to nonperturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasiparticle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.

In this work we perform a detailed first-principles analysis of the electronic and optical properties of ${\mathrm{NiBr}}_2$ within the state-of-the-art $GW+\text{BSE}$ scheme to determine whether this system displays negative excitonic energies, which would identify it as an (half) excitonic insulator. Particular attention is paid to the convergence of the $GW$ band structure and to the consistency between approximations employed in the ground-state calculations and approximations employed in the linear response calculations. We show that these two issues play a crucial role in identifying the excitonic nature of ${\mathrm{NiBr}}_2$.