There exist two canonical approaches to describe open quantum systems by a time-evolution equation: the Nakajima-Zwanzig quantum master equation, featuring a time-nonlocal memory kernel $\mathcal{K}$, and the time-convolutionless equation with a time-local generator $\mathcal{G}$. These key quantities have recently been shown to be connected by an exact fixed-point relation [Phys. Rev. X 11, 021041 (2021)]. Here we show that this implies a recursive relation between their perturbative expansions, allowing a series for the kernel $\mathcal{K}$ to be translated directly into a corresponding series for the more complicated generator $\mathcal{G}$. This leads to an elegant way of computing the generator using well-developed, standard memory-kernel techniques for strongly interacting open systems. Moreover, it allows for an unbiased comparison of time-local and time-nonlocal approaches independent of the particular technique chosen to calculate expansions of $\mathcal{K}$ and $\mathcal{G}$ (Nakajima-Zwanzig projections, real-time diagrams, etc.). We illustrate this for leading and next-to-leading-order calculations of $\mathcal{K}$ and $\mathcal{G}$ for the single impurity Anderson model using both the bare expansion in the system-environment coupling and a more advanced renormalized series. We compare the different expansions obtained, quantify the legitimacy of the generated dynamics (complete positivity) and benchmark with the exact result in the noninteracting limit.

The past decades have witnessed a transformation in characterizing condensed matter systems with topology. Aided by a refined understanding of topological band structures with crystalline symmetries that has emerged recently, many electronic phases have been identified, and a plethora of materials have been predicted to host properties and functionalities. A key underlying question, also with respect to future application, is to what extent the related physical features can be manipulated, especially in the context of magnetic order. Here, we describe a paradigmatic semimetal that simultaneously incorporates multiple and sometimes conflicting topology which guarantees gaplessness and leads to an exceptionally rich family of descendent phases on lowering symmetry. We predict that this multicritical phase is realized in $\mathrm{Eu}{\mathrm{Tl}}_2$. Starting from the parent semimetallic state, which already separates two topological insulating regimes, the interplay of inherent magnetism and strain allows for an exceptionally rich phase diagram of topological descendant states.

We analyze the structure of an $s\text{−}\mathrm{wave}$ superconducting gap in systems with electron-phonon attraction and electron-electron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap, $\mathrm{\Delta }\left({\omega }_m\right)$, necessarily changes sign along the Matsubara axis. We analyze the sign-changing gap function from a topological perspective using the knowledge that a nodal point of $\mathrm{\Delta }\left({\omega }_m\right)$ is the center of dynamical vortex. We consider two models with different cutoffs for the repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane on changing the relative strength of the attractive and repulsive parts of the interaction. We discuss how the presence of dynamical vortices affects the gap structure along the real frequency axis, detectable in ARPES experiments.

The antiferromagnetic (AFM) semimetal ${\mathrm{YbMnSb}}_2$ has recently been identified as a candidate topological material, driven by time-reversal symmetry breaking. Depending on the ordered arrangement of Mn spins below the Néel temperature, $T_{\mathrm{N}}=345\mathrm{K}$, the electronic bands near the Fermi energy can either have a Dirac node, a Weyl node, or a nodal line. We have investigated the ground state magnetic structure of ${\mathrm{YbMnSb}}_2$ using unpolarized and polarized single crystal neutron diffraction. We find that the Mn moments lie along the $c$ axis of the $P4/nmm$ space group and are arranged in a $C$-type AFM structure, which implies the existence of gapped Dirac nodes near the Fermi level. The results highlight how different magnetic structures can critically affect the topological nature of fermions in semimetals.

Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require the breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl semimetals exhibit strong SHG upon application of finite current. Our experimental estimation for a Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and a magnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ suggests that the induced susceptibility ${\chi }^{\left(2\right)}$ for practical applied current densities can reach ${10}^5\mathrm{pm}{\mathrm{V}}^{-1}$ with mid-IR or far-IR light. This value is ${10}^2$–${10}^4$ times larger than those of typical nonlinear optical materials. We also discuss experimental approaches to observe the current-induced SHG and comment on current-induced SHG in other topological semimetals in connection with recent experiments.

We have measured magnetoresistance of suspended graphene in the Corbino geometry at magnetic fields up to $B=0.15\mathrm{T}$, i.e., in a regime uninfluenced by Shubnikov–de Haas oscillations. The low-temperature relative magnetoresistance $\left[R\right(B)-R(0\left)\right]/R\left(0\right)$ is strong, approaching $100\%$ at the highest magnetic field studied, with a quite weak temperature dependence below 30 K. A decrease in the relative magnetoresistance by a factor of two is found when charge carrier density is increased to $\left|n\right|\simeq 3\times {10}^{10}{\mathrm{cm}}^{-2}$. Furthermore, we find a shift in the position of the charge neutrality point with increasing magnetic field, which suggests that magnetic field changes the screening of Coulomb impurities around the Dirac point. The gate dependence of the magnetoresistance allows us to characterize the role of scattering on long-range (Coulomb impurities, ripples) and short-range disorder (adatoms, atomic defects), as well as to separate the bulk resistance from the contact one. Based on the analysis of the magnetoresistance, we propose a more reliable method to extract the bulk mobility, which does not require prior knowledge of the contact resistance. It is thus demonstrated that studying magnetoresistance in the Corbino geometry is an extremely valuable tool to characterize high-mobility graphene samples, in particular, in the vicinity of the Dirac point.

Single Fe atoms on Au(111) surfaces were hydrogenated and dehydrogenated with the Au tip of a low-temperature scanning tunneling microscope (STM). Fe and ${\mathrm{FeH}}_2$ were contacted with the tip of the microscope and show distinctly different evolutions of the conductance with the tip-substrate distance. The current shot noise of these contacts has been measured and indicates a single relevant conductance channel with the spin-polarized transmission. For ${\mathrm{FeH}}_2$, the spin polarization reaches values up to 80% for low conductances and is reduced if the tip-surface distance is decreased. These observations are partially reproduced using density functional theory (DFT)-based transport calculations. We suggest that the quantum motion of the hydrogen atoms, which is not taken into account in our DFT modeling, may have a significant effect on the results.

Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moiré potentials for electrons and holes, as well as a modulation of the hybridization across the bilayer. Here, we develop hybrid $\mathbf{k}·\mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and antiparallel (AP) orientations of the monolayer unit cells. We apply these models to describe moiré superlattice effects in twisted $\mathrm{WSe}{}_2$ bilayers, in conjunction with microscopic ab initio calculations, and considering the influence of encapsulation, pressure, and an electric displacement field. Our analysis takes into account mesoscale lattice relaxation, interlayer hybridization, piezopotentials, and a weak ferroelectric charge transfer between the layers, and it describes a multitude of possibilities offered by this system, depending on the choices of P or AP orientation, twist angle magnitude, and electron/hole valley.

We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [A. Pizzi, A. Nunnenkamp, and J. Knolle, Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these nonequilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive.

We report the crystal structure and magnetic behavior of the $4d^3$ spin-$3/2$ silicophosphate $\mathrm{Mo}{\mathrm{P}}_3\mathrm{Si}{\mathrm{O}}_{11}$ studied by high-resolution synchrotron x-ray diffraction, neutron diffraction, thermodynamic measurements, and ab initio band-structure calculations. Our data revise the crystallographic symmetry of this compound and establish its rhombohedral space group ($R\overline{3}c$) along with the geometrically perfect honeycomb lattice of the ${\mathrm{Mo}}^{3+}$ ions residing in disconnected $\mathrm{Mo}{\mathrm{O}}_6$ octahedra. Long-range antiferromagnetic order with the propagation vector $\mathbf{k}=0$ observed below $T_N=6.8$ K is a combined effect of the nearest-neighbor in-plane exchange coupling $J\simeq 2.6$ K, easy-plane single-ion anisotropy $D\simeq 2.2$ K, and a weak interlayer coupling $J_c\simeq 0.8$ K. The 12% reduction in the ordered magnetic moment of the ${\mathrm{Mo}}^{3+}$ ions and the magnon gap of $\mathrm{\Delta }\simeq 7$ K induced by the single-ion anisotropy further illustrate the impact of spin-orbit coupling on the magnetism. Our analysis puts forward single-ion anisotropy as an important ingredient of $4d^3$ honeycomb antiferromagnets despite their nominally quenched orbital moment.

We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer ${\mathrm{WTe}}_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak nonzero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of a nonexcitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the ${\mathrm{WTe}}_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link the competition between the excitonic phases to the orbital structure of electronic wave functions at the Fermi surface and hence its proximity to the underlying gapped Dirac point in ${\mathrm{WTe}}_2$. We briefly discuss collective modes of the two excitonic states, and comment on implications for experiments.

We experimentally study the tunability of the cooperativity in coupled spin-cavity systems by changing the magnetic state of the spin system via an external control parameter. As a model system, we use the skyrmion host material ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ coupled to a microwave cavity resonator. We measure a dispersive coupling between the resonator and magnon modes in different magnetic phases of the material and model our results by using the input-output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon-photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.

Amorphous dielectric materials have been known to host two-level systems (TLSs) for more than four decades. Recent developments on superconducting resonators and qubits enable detailed studies on the physics of TLSs. In particular, measuring the loss of a device over long time periods (a few days) allows us to investigate stochastic fluctuations due to the interaction between TLSs. We measure the energy relaxation time of a frequency-tunable planar superconducting qubit over time and frequency. The experiments show a variety of stochastic patterns that we are able to explain by means of extensive simulations. The model used in our simulations assumes a qubit interacting with high-frequency TLSs, which, in turn, interact with thermally activated low-frequency TLSs. Our simulations match the experiments and suggest the density of low-frequency TLSs is about three orders of magnitude larger than that of high-frequency ones.

We study how interacting localized degrees of freedom are affected by slow thermal fluctuations that change the effective local disorder. We compute the time-averaged (annealed) conductance in the insulating regime and find three distinct insulating phases, separated by two transitions. The first occurs between a nonresonating insulator and an intermittent metal. The average conductance is always dominated by rare temporal fluctuations. However, in the intermittent metal, they are so strong that the system becomes metallic for an exponentially small fraction of the time. A second transition occurs within that phase. At stronger disorder, there is a single optimal path providing the dominant contribution to the conductance at all times, but closer to delocalization, a transition to a phase with fluctuating paths occurs. This last phase displays the quantum analogon of configurational chaos in glassy systems in that thermal fluctuations induce significant changes of the dominant decay channels. While in the insulator the annealed conductance is strictly bigger than the conductance with typical, frozen disorder, we show that the threshold to delocalization is insensitive to whether or not thermal fluctuations are admitted. This rules out a potential bistability, at fixed disorder, of a localized phase with suppressed internal fluctuations and a delocalized, internally fluctuating phase.

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions $\nu =p/(p(m-1)+1)$ with $m$ odd, from integer Hall states at $\nu =p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process, as we explicitly show for the $p=2$ series of states. The construction hence provides a major step towards establishing the existence of incompressible states at these fillings.

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a topologically nontrivial way, which, roughly, means that the action for the Goldstone modes contains a quantized topological term, and could manifest in, for example, nontrivial quantum numbers of topological defects of the order parameter. We show that, in fact, such a scenario can occur only when the system is in a nontrivial symmetry-protected topological or symmetry-enriched topological phase with respect to the residual symmetry or, alternatively, if the original symmetry before spontaneous symmetry breaking acts on the system in an “anomalous” way. Our arguments are based on a general correspondence between topological defects of the order parameter and topological defects of a background gauge field for the residual symmetry.

The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet ${\mathrm{KCeO}}_2$ are investigated. Below $T_N=300$ mK, ${\mathrm{KCeO}}_2$ develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent ${\mathrm{Ce}}^{3+}$ ions in the $D_{3d}$ local environment of this compound exhibit large splittings among the lowest three $4f^1$ Kramers doublets defining for the free ion the $J=5/2$ sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions by Eldeeb et al. [Phys. Rev. Materials 4, 124001 (2020)]. An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.

In quantum dot (QD) electron transport experiments, additional features can appear in the differential conductance $dI/dV$ that do not originate from discrete states in the QD, but rather from a modulation of the density of states (DOS) in the leads. These features are particularly pronounced when the leads are strongly confined low-dimensional systems, such as in a nanowire (NW) where transport is one dimensional and quasi-zero-dimensional lead states can emerge. We study such lead states in InAs NWs. We use a QD integrated directly into the NW during the epitaxial growth as an energetically and spatially well-defined tunnel probe to perform $dI/dV$ spectroscopy of discrete bound states in the “left” and “right” NW lead segments. By tuning a sidegate in close proximity of one lead segment, we can distinguish transport features related to the modulation in the lead DOS and to excited states in the QD. We implement a noninteracting capacitance model and derive expressions for the slopes of QD and lead resonances that appear in two-dimensional plots of $dI/dV$ as a function of source-drain bias and gate voltage in terms of the different lever arms determined by the capacitive couplings. We discuss how the interplay between the lever arms affects the slopes. We verify our model by numerically calculating the $dI/dV$ using a resonant tunneling model with three noninteracting quantum dots in series. Finally, we use the model to describe the measured $dI/dV$ spectra and quantitatively extract the tunnel couplings of the lead segments. Our results constitute an important step towards a quantitative understanding of normal and superconducting subgap states in hybrid NW devices.

We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition by revealing space-time conformal covariance of entanglement entropies and mutual information for various subregions at different circuit depths. While the evolution takes place in real time, the spacetime manifold of the circuit appears to host a Euclidean field theory with imaginary time. Throughout the paper we investigate Clifford circuits with several different boundary conditions by injecting physical qubits at the spatial and/or temporal boundaries, all giving consistent characterizations of the underlying “Clifford CFT.” We emphasize (super)universal results that are consequences solely of the conformal invariance and do not depend crucially on the precise nature of the CFT. Among these are the infinite entangling speed as a consequence of measurement-induced quantum nonlocality and the critical purification dynamics of a mixed initial state.

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.