In a quantum Hall interferometer, the dependence of the signal on source-drain voltage is controlled by details of the edge physics, such as the velocities of edge modes and the interaction between them and with screening layers. Such dependence of the signal has been seen in recent experiments at various integer and fractional filling factors, including $\nu =2$ and $2/5$, where two edge modes are present. Here we study theoretically the current-voltage curves for various values of the relative edge velocities, interaction strength, and the temperature, in a model containing two edge modes. We consider separate cases in which the inner mode or the outer mode is weakly backscattered at the tunneling contacts. When the inner mode is completely reflected and the outer mode is partially transmitted, we find striking features at very low temperatures related to resonance of excitations of the closed inner channel. Fluctuations in the charge of the closed inner mode, caused by sparse tunneling events, lead to an exponential suppression of the interference visibility at high voltages, in agreement with experiments.

Ultrafast optical switching of materials properties promises future technological applications, enabled by fundamental insights about microscopic couplings and nonequilibrium phenomena. Transition-metal dichalcogenides (TMDCs) combine photosensitivity with strong correlations, furthering rich phase diagrams and enhanced tunability. The compound $1T^{\prime }\text{−}{\mathrm{TaTe}}_2$ exhibits an electronically and structurally unique set of charge density waves (CDWs), featuring an unusual increase in conductivity and amplitude modes of low prominence. Compared to other charge-ordered TMDCs, only very few studies addressed the ultrafast response of this material to optical excitation. In particular, the question whether such unconventional properties translate to unusual quench dynamics remains largely unresolved. Here, we investigate the structural dynamics in $1T^{\prime }\text{−}{\mathrm{TaTe}}_2$ by means of ultrafast nanobeam electron diffraction at an unprecedented repetition rate of $2\mathrm{MHz}$. We reveal a strongly directional cooperative atomic motion during the one-dimensional quench of the low-temperature trimer lattice. These dynamics are completed within less than $500\mathrm{fs}$, substantially faster than reported previously. In striking contrast, the periodic lattice distortion of the room-temperature phase is unusually robust against high-density electronic excitation. In conjunction with the known sensitivity of $1T^{\prime }\text{−}{\mathrm{TaTe}}_2$ to chemical doping, we thus expect the material to serve as a versatile platform for tunable structural control by optical stimuli.

We study a phase-tunable four-terminal Josephson junction formed in an InSbAs two-dimensional electron gas proximitized by aluminum. By embedding the two pairs of junction terminals in asymmetric DC superconducting quantum-interference devices (SQUIDs) we can control the superconducting phase difference across each pair, thereby gaining information about their current-phase relation. Using a current-bias line to locally control the magnetic flux through one SQUID, we measure a nonlocal Josephson effect, whereby the current-phase relation across two terminals in the junction is strongly dependent on the superconducting phase difference across two completely different terminals. In particular, each pair behaves as a ${\varphi }_0$ junction with a phase offset tuned by the phase difference across the other junction terminals. Lastly, we demonstrate that the behavior of an array of two-terminal junctions replicates most features of the current-phase relation of different multiterminal junctions. This highlights that these signatures alone are not sufficient evidence of true multiterminal Josephson effects arising from hybridization of Andreev bound states in the junction.

$\mathrm{P}{\mathrm{d}}_3\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_2$ is a rare realization of a superconducting metal with a nonzero $Z_2$ topological invariant. Here, we report the growth of high-quality single crystals of layered $\mathrm{P}{\mathrm{d}}_3\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_2$ with a superconducting transition at $T_{\mathrm{c}} \approx$ 0.80 K and upper critical fields of ∼10 and ∼5 mT for the in-plane and out-of-plane directions, respectively. Our density-functional theory (DFT) calculations reveal three pairs of doubly degenerate bands crossing the Fermi level, all displaying clear three-dimensional dispersion consistent with the overall low electronic anisotropy (<2). The multiband electronic nature of $\mathrm{P}{\mathrm{d}}_3\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_2$ is evident in magnetotransport measurements, yielding a sign-changing Hall resistivity at low temperatures. The magnetoresistance is nonsaturating and follows Kohler's scaling rule. We interpret the magnetotransport data in terms of open orbits that are revealed in the DFT-calculated Fermi surface. de Haas–van Alphen (dHvA) oscillation measurements using torque magnetometry on single crystals yield four frequencies for out-of-plane fields: $F_{\alpha }=150\pm 26\mathrm{T}, F_{\beta }=293\pm 10\mathrm{T}, F_{\gamma }=375\pm 20\mathrm{T}$, and $F_{\eta }=1017\pm 12\mathrm{T}$, with the low frequency dominating the spectrum. Through the measurement of angular-dependent dHvA oscillations and DFT calculations we identify the $F_{\alpha }$ frequency with an approximately ellipsoidal electron pocket centered on the $L_2$ point of the Brillouin zone. Lifshitz-Kosevich analysis of the dHvA oscillations reveals a small cyclotron effective mass $m^{*}=(0.11\pm 0.02)m_0$ and a nontrivial Berry phase for the dominant orbit. The presence of nontrivial topology in a bulk superconductor positions $\mathrm{P}{\mathrm{d}}_3\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_2$ as a potential candidate for exploring topological superconductivity.

The theory of the shift current is thus far geometrical without being topological. This means that the real-space displacement of a photoexcited quasiparticle depends on the geometric Berry phase, but the Berry phase is not quantized to a rational multiple of $2\pi$ in any known material. I rectify this status quo by introducing a new class of topological insulators whose band topology is only compatible with a noncentrosymmetric space group. For such insulators, it is impossible to continuously tune the $\mathit{k}$-dependent shift vector to zero throughout the Brillouin zone. Suitably averaged, the shift vector is quantized to a rational multiple of a Bravais lattice vector. Even with wide band gaps, the frequency-integrated shift conductivity greatly exceeds $e^3/h^2$, and is at least three orders of magnitude larger than the conductivity of the prototypical ferroelectric ${\mathrm{BaTiO}}_3$. The large conductivity is attributed to an interplay between quantized intra- and interband Berry phases. In particular, topological defects of the interband Berry phase can enhance the shift current, even for unpolarized insulators with negligible intraband Berry phase.

Controlled processing of transparent materials with ultrashort laser pulses requires a detailed and precise knowledge of the various laser-matter interaction mechanisms from laser energy deposition and conversion in internal energy of the material to hydrodynamic relaxation and mechanical response. To address this issue, we first develop a multi-timescale experimental approach based on a femtosecond pump-and-probe microscope-polariscope. The pump is a 360-fs, 1-µJ infrared (1030-nm) laser pulse which is split to provide a 515-nm femtosecond probe with delay adjustable from femtoseconds to nanoseconds. The obtained time-resolved shadowgraphy images allow measurement of the transient probe transmission. Then, the carrier density is determined by use of the Beer-Lambert law and Drude model approach, demonstrating the ultrafast formation of a slightly overcritical plasma inside the bulk of fused silica. In parallel, quantitative birefringence images provide a measurement of stress by use of the photoelastic law revealing the partial dissipation of the absorbed laser energy through emission of a gigapascal stress wave, a few hundreds of picoseconds after the laser pulse. A multiscale-multiphysics model is then used to interpret the experimental observations, accounting for the electron dynamics, laser propagation, and hydrodynamic response. Following experimental validation, simulations allow determining the temporal evolution of local fundamental material properties (stress, density, and temperature). This combination of experimental and simulation results enables us to quantitatively discuss the importance of the different laser energy relaxation channels in the material, uncovering the full scenario of the interaction. Our model predicts a 20-GPa maximum initial stress loading with maximum lattice temperatures reaching. $3.5\times {10}^4\mathrm{K}$. We also show that a fraction of $\sim 2\%$ of the total absorbed laser energy is dissipated through emission of a weak shockwave. Our approach could be used in the future to account for mechanically driven transparent material structuring induced by ultrashort laser pulses.

We present electrical and thermal transport measurements in single crystals of the metallic oxide ${\mathrm{RuO}}_2$. The resistivity and Seebeck coefficient measured up to 970 K confirm the metallic nature of transport. Magnetoresistance and Hall effect measurements as a function of orientation can be most easily described by a multiband transport model. We find that the ordinary Hall effect dominates any anomalous Hall signal in single crystals.

There is considerable evidence that the superconductivity of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ has two components. Among this evidence is a jump in the shear elastic modulus $c_{66}$ at the critical temperature $T_c$, observed in ultrasound measurements. Such a jump is forbidden for homogeneous single-component order parameters, and it implies that $T_c$ should develop as a cusp under the application of shear strain with $\langle 110\rangle$ principal axes. This shear strain should split the onset temperatures of the two components, if they coexist, or select one component if they do not. Here, we report measurements of $T_c$ and the elastocaloric effect of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ under uniaxial stress applied along the [110] lattice direction. Within experimental resolution, we resolve neither a cusp in the stress dependence of $T_c$, nor any second transition in the elastocaloric effect data. We show that reconciling these null results with the observed jumps in $c_{66}$ requires extraordinarily fine tuning to a triple point of the Ginzburg-Landau parameter space. In addition, our results are inconsistent with homogeneous time-reversal symmetry breaking at a temperature $T_2\le T_c$ as identified in muon spin relaxation experiments.

The unambiguous identification of Majorana zero modes (MZMs) is one of the most outstanding problems of condensed matter physics. Thermal transport provides a detection tool that is sensitive to these chargeless quasiparticles. We study thermoelectric transport between metallic leads transverse to a Josephson junction. The central double quantum dot hosts conventional or topological Andreev states that depend on the phase difference $\varphi$. We show that the presence of MZMs can be identified by a significant amplification of both the electrical and thermal conductance at $\varphi \approx \pi$ as well as the Seebeck coefficient at $\varphi \approx 0$. In addition, we show that the Wiedemann-Franz law is strongly violated in the presence of MZMs around $\varphi \approx \pi$ when compared to the conventional case. We further investigate the robustness of our results against Cooper pair splitting processes.

A key to understanding unconventional superconductivity lies in unraveling the pairing mechanism of mobile charge carriers in doped antiferromagnets, yielding an effective attraction between charges even in the presence of strong repulsive Coulomb interactions. Here, we study pairing in a mixed-dimensional (mixD) $t\text{−}J$ model, featuring robust binding energies—despite dominant repulsive interactions—that are strongly enhanced in the finite doping regime. The single and coupled mixD ladders we study, corresponding to bilayers of width $w\le 2$, feature a crossover from tightly bound pairs of holes (closed channel) at small repulsion to more spatially extended, correlated pairs of individual holes (open channel) at large repulsion. We derive an effective model for the latter, in which the attraction is mediated by the closed channel, in analogy to atomic Feshbach resonances. Using density matrix renormalization group simulations we reveal a dome of large binding energies at around $30\%$ doping, accompanied by a change of the Fermi surface volume and a crossover from extended to tightly bound hole pairs. Our work provides a microscopic theory of pairing in the doped mixD system with dominant repulsion, closely related to bilayer, Ni-based superconductors, and our predictions can be tested in state-of-the-art quantum simulators.

We have investigated the magnetic microstructure of two-phase Fe-Nb-B based Nanoperm alloys using unpolarized small-angle neutron scattering (SANS) and small-angle x-ray scattering (SAXS). Our SANS analysis reveals a significantly large magnetic scattering contribution due to spin misalignment, primarily originating from the substantial jump in the longitudinal magnetization at the interfaces between the particles and the matrix. The magnetic scattering exhibits an angular anisotropy that resembles a clover-leaf-type pattern, consistent with the predictions of micromagnetic SANS theory. Analysis of the one-dimensional SANS data yields values for the exchange-stiffness constant and the average anisotropy and magnetostatic fields. The micromagnetic correlation lengths for all three samples exhibit a similar field variation with sizes ranging between about $10–35\mathrm{nm}$. We also find that the nuclear and magnetic residual scattering component of the SANS cross section exhibits a similar $q$ dependency as the SAXS data. These findings further validate the applicability of the micromagnetic SANS theory, and the mesoscopic information obtained is important for the advancement of the soft magnetic properties of this class of material.

We construct a subsystem code in three dimensions that exhibits single-shot error correction in a user-friendly and transparent way. As this code is a subsystem version of coupled toric codes, we call it the intertwined toric code (ITC). Although previous codes share the property of single-shot error correction, the ITC is distinguished by its physically motivated origin, geometrically straightforward logical operators and errors, and a simple phase diagram. The code arises from three-dimensional (3D) stabilizer toric codes in a way that emphasizes the physical origin of the single-shot property. In particular, starting with two copies of the 3D toric code, we add check operators that provide for the confinement of pointlike excitations without condensing the loop excitations. Geometrically, the bare and dressed logical operators in the ITC derive from logical operators in the underlying toric codes, creating a clear relationship between errors and measurement outcomes. The syndromes of the ITC resemble the syndromes of the single-shot code by Kubica and Vasmer, allowing us to use their decoding schemes. We also extract the phase diagram corresponding to ITC and show that it contains the phases found in the Kubica-Vasmer code. Finally, we suggest various connections to Walker-Wang models and measurement-based quantum computation.

The interaction between electrons and phonons leads to a renormalization of the electronic band structure and the associated band gap. In solids this renormalization can be calculated from first principles using the supercell-based frozen phonon method or the perturbation-based Allen-Heine-Cardona theory. Each approach relies on certain assumptions and can become computationally expensive. In this work we present an ab initio implementation that aims to increase the accuracy and the efficiency of such calculations by combining the nonadiabatic Allen-Heine-Cardona theory and supercell calculations. Additionally, the benefits of a localized basis set of Gaussian orbitals are exploited. Due to its computational complexity the Debye-Waller component of Allen-Heine-Cardona theory is usually treated on a rigid-ion approximation level using a version of the acoustic sum rule. In our implementation the evaluation of the Debye-Waller component is straightforward and contributions beyond the rigid-ion approximation from several shells of nearest neighbors can easily be included. We use bulk silicon and diamond as test systems and find a good agreement with the literature on the level of the rigid-ion approximation. Beyond that we calculate the contributions up to third-nearest neighbors and find that these contributions are small with up to about 5% of the rigid-ion contribution but not necessarily negligible. For silicon the calculated zero-point renormalization of the direct (indirect) band gap is $-43.5\mathrm{meV}$ ($-54.9\mathrm{meV}$). At high temperature, the band gaps shrink at a rate of $-0.17$ and $-0.27\mathrm{meV}/\mathrm{K}$, respectively. For diamond we find a zero-point renormalization of $-405.2\mathrm{meV}$ ($-313.7\mathrm{meV}$) for the direct (indirect) band gap. The reduction at high temperature is $-0.46$ and $-0.37\mathrm{meV}/\mathrm{K}$, respectively.

The surprising discovery of ultrafast demagnetization—where the electric field of a femtosecond laser pulse interacts with electrons of a ferromagnetic (FM) layer to cause its magnetization vector to shrink while not rotating, $M_z\left(t\right)/M_z(t=0)<1$—is also assumed to be accompanied by generation of spin current in the direction orthogonal to electric field. However, understanding the microscopic origin of such a spin current, its frequency spectrum, and how efficiently it can be converted into charge current as the putative source of THz radiation, is lacking despite nearly three decades of intense studies. Conversely, quantum transport theory rigorously explains how microwave-driven precession of a magnetization vector of fixed length $\mathbf{M}\left(t\right)$ leads to pumping of spin current into adjacent normal metal (NM) layers, sandwiching the FM layer to form two-terminal geometry without any applied bias voltage. Here we connect these two apparently disparate phenomena by replacing periodic time dependence of magnetization precession with nonperiodic time dependence of demagnetization, as obtained from experiments on an ultrafast-light-driven Ni layer, within the same two-terminal setup of standard spin pumping theory. Applying time-dependent nonequilibrium Green's functions, able to evolve such setup with arbitrary time dependence, predicts phenomenon of charge pumping by demagnetization dynamics, as well as spin, with such currents flowing in directions both parallel and orthogonal to the electric field of laser pulse. The pumping of charge current directly by ultrafast demagnetization dynamics occurs even in the absence of spin-orbit coupling (SOC) and, presumed to be necessary, spin-to-charge conversion via SOC. Although pumped currents follow $d{M}_z/dt$ in some setups, this becomes obscured when NM layers are disconnected and pumped currents start to reflect from FM boundaries (as in realistic experimental setups). Finally, we use the Jefimenko equations to compute electromagnetic radiation by charge current pumped in a disconnected setup during demagnetization, or later during its slow recovery, unraveling that radiated electric field only in the former time interval exhibits features in 0.1–30 THz frequency range probed experimentally or explored for applications of spintronic THz emitters.

We present a framework for investigating wave function spreading in $\mathcal{PT}$-symmetric quantum systems using spread complexity and spread entropy. We consider a tight-binding chain with complex on-site potentials at the boundary sites. In the $\mathcal{PT}$-unbroken phase, the wave function is delocalized. We find that in the $\mathcal{PT}$-broken phase, it becomes localized on one edge of the tight-binding lattice. This localization is a realization of the non-Hermitian skin effect. Localization in the $\mathcal{PT}$-broken phase is observed both in the lattice chain basis and the Krylov basis. Spread entropy, entropic complexity, and a further measure that we term the Krylov inverse participation ratio probe the dynamics of wave function spreading and quantify the strength of localization probed in the Krylov basis. The number of Krylov basis vectors required to store the information of the state reduces with the strength of localization. Our results demonstrate how measures in Krylov space can be used to characterize the non-Hermitian skin effect and its localization phase transition.

The exchange-bias (EB) effect between a ferromagnet and antiferromagnet is crucial for many existing, as well as proposed, spintronic devices. For understanding, utilizing, and engineering EB, it is critical to understand how EB affects microscopic reversal processes, such as nucleation and propagation of domains, and how these in turn can govern macroscopic characteristics, including hysteresis loop shape. In this work, we disentangle the EB for nucleation and propagation by combining typical magneto-optical Kerr effect (MOKE) measurements with a method based on domain-wall (DW) motion. We show that MOKE is well suited for locating the nucleation sites and measuring the EB at these sites, while by measuring DW propagation, the effective field that the DW is subjected to can be quantified and the EB field inferred. Our experiments reveal that nucleation sites can experience wide-ranging EB fields, in contrast to propagation EB, and that there can be a significant difference in the EB that these two processes experience. Furthermore, we explore the consequences of unequal nucleation and propagation EB and discover that in addition to the EB of the nucleation site affecting measurements in the surrounding area, it can also give rise to asymmetry in hysteresis loop shape, something that has been observed widely but is not fully understood. This work describes surprising phenomena in systems that have been studied for decades, and we believe that the insights into how the interplay between different components of magnetization reversal can give rise to unexpected outcomes can be broadly useful for anyone working with coupled magnetic systems.

A comprehensive set of muon spin spectroscopy and neutron scattering measurements supported by ab initio and model Hamiltonian simulations have been used to investigate the magnetic ground state of ${\mathrm{Na}}_2{\mathrm{PrO}}_3$. $\mu \mathrm{SR}$ reveals a Néel antiferromagnetic order below $T_N\sim 4.9\mathrm{K}$, with a small static magnetic moment $m_{\mathrm{static}}\le 0.22{\mu }_{\mathrm{B}}/\mathrm{Pr}$ collinearly aligned along the $c$ axis. Inelastic neutron measurements reveal the full spectrum of crystal field excitations and confirm that the ${\mathrm{Pr}}^{4+}$ ground-state wave function deviates significantly from the ${\mathrm{\Gamma }}_7$ limit that is relevant to the Kitaev model. Single- and two-magnon excitations are observed in the ordered state below $T_N=4.6\mathrm{K}$ and are well described by nonlinear spin wave theory from the Néel state using a magnetic Hamiltonian with Heisenberg exchange $J=1\mathrm{meV}$ and symmetric anisotropic exchange $\mathrm{\Gamma }/J=0.1$, corresponding to an $XY$ model. Intense two magnon excitations are accounted for by $g$-factor anisotropy $g_{\mathrm{z}}/g_{\pm }=1.29$. A fluctuating moment $\delta m^2=0.57\left(22\right){\mu }_{\mathrm{B}}^2/\mathrm{Pr}$ extracted from the energy and momentum integrated inelastic neutron signal is reduced from expectations for a local $J=1/2$ moment with average $g$ factor $g_{\mathrm{avg}}\approx 1.1$. Together, the results demonstrate that the small moment in ${\mathrm{Na}}_2{\mathrm{PrO}}_3$ arises from crystal field and covalency effects and the material does not exhibit significant quantum fluctuations.

Recently, Nathan and Rudner derived a Gorini-Kossakowski-Sudarshan-Lindblad master equation from the Redfield equation. The claim is that the level of approximation is equal to that of the Redfield equation. Here we benchmark the Nathan-Rudner equation (NRE) against the exact solution of a damped harmonic oscillator, and we compare its performance to that of the time-dependent Redfield equation (RE). We find that which of the equations performs better depends on the regime considered. It turns out that the short-time dynamics is generally much better captured by the RE, whereas the NRE delivers results comparable to those of the rotating-wave approximation. For the steady state, in the high-temperature limit the RE again performs better and its solution approaches the exact result for ultrahigh temperatures. Nevertheless, here also the NRE constitutes a good approximation. In the low-temperature limit, in turn, the NRE provides a better approximation than the RE. For too strong coupling, here the RE might even fail completely by predicting unphysical behavior.

A lateral Josephson junction in which the surface of a three-dimensional (3D) topological insulator (TI) serves as the weak link should support topologically protected excitations related to Majorana fermions. The resulting $4\pi$-periodic current-phase relationship could be detected under high-frequency excitation by the suppression of odd Shapiro steps. Here, we demonstrate such devices through the self-formation of a Pd-Te superconducting layer from a telluride TI and observe suppressed first and third Shapiro steps. Other devices, including those where the Pd-Te layer is bolstered by an additional Al layer, show no suppression of Shapiro steps, a difference supported by simulations. Though we rule out the known trivial causes of suppressed Shapiro steps in our devices, we nevertheless argue that corroborating measurements and disorder-aware theoretical descriptions of these systems are needed before confidently claiming the observation of Majorana states.

$\alpha -\mathrm{RuC}{\mathrm{l}}_3$ is a Kitaev material suggested to be a proximate quantum spin liquid in a certain temperature and magnetic field range. Nonequilibrium measurements of transient dynamics have been proposed to detect fractionalized particles that emerge in the spin liquid and to possibly drive the system into novel photoinduced magnetic states that cannot be accessed by conventional equilibrium probes. Here we study ultrafast spin dynamics of photoinduced excitations in $\alpha -\mathrm{RuC}{\mathrm{l}}_3$ using pump-probe transient grating spectroscopy. In the real part of the complex transient reflection coefficient $\mathrm{\Delta }r/r$, we observe evidence of long-range antiferromagnetic correlations near the Néel temperature. Most intriguingly, above the Néel temperature in the Kitaev paramagnetic phase, we reveal a photoexcitation component sensitive to the in-plane magnetic field in the imaginary part of $\mathrm{\Delta }r/r$. This component exhibits two distinct lifetimes of about tens of picoseconds. This photoexcitation component may be connected to novel photoexcited states in the Kitaev quantum spin liquid, and its lifetimes likely reflect the dynamics of unconventional spin excitations in the Kitaev model.