Under optical cooling of nuclei, a strongly correlated nuclear-spin polaron state can form in semiconductor nanostructures with localized charge carriers due to the strong hyperfine interaction of the localized electron spin with the surrounding nuclear spins. Here we develop a kinetic-equation formalism describing the nuclear-spin polaron formation. We present a derivation of the kinetic equations for an electron-nuclear spin system coupled to reservoirs of different electron and nuclear spin temperatures which generate the exact thermodynamic steady state for equal temperatures independent of the system size. We illustrate our approach using the analytical solution of the central spin model in the limit of an Ising form of the hyperfine coupling. For homogeneous hyperfine coupling constants, i.e., the box model, the model is reduced to an analytically solvable form. Based on the analysis of the nuclear-spin distribution function and the electron-nuclear spin correlators, we derive a relation between the electron and nuclear spin temperatures, where the correlated nuclear-spin polaron state is formed. In the limit of large nuclear baths, this temperature line coincides with the critical temperature of the mean-field theory for polaron formation. The criteria of the polaron formation in a finite-size system are discussed. We demonstrate that the system's behavior at the transition temperature does not depend on details of the hyperfine-coupling distribution function but only on the effective number of coupled bath spins. In addition, the kinetic equations enable the analysis of the temporal formation of the nuclear-polaron state, where we find the build-up process predominated by the nuclear spin-flip dynamics.

Twisted bilayer graphene at the magic twist angle features flat energy bands, which lead to superconductivity and strong correlation physics. These unique properties are typically limited to a narrow range of twist angles around the magic angle with a small allowed tolerance. Here, we report on a mechanism that enables flattening of the band structure using coherent optical illumination, leading to emergence of flat isolated Floquet-Bloch bands. We show that the effect can be realized with relatively weak optical beams at the visible-infrared range (below the material bandwidth) and persist for a wide range of small twist angles, increasing the allowed twist tolerance by an order of magnitude. We discuss the conditions under which these bands exhibit a nonzero Chern number. These optically induced flat bands could potentially host strongly correlated nonequilibrium electronic states of matter.

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the nonlinear Schrödinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.

We present a novel approach to understanding the extraordinary diversity of magnetic skyrmion solutions. Our approach combines an original classification scheme with efficient analytical and numerical methods. We introduce the concept of chiral kinks to account for regions of disfavored chirality in spin textures, and classify two-dimensional magnetic skyrmions in terms of closed domain walls carrying such chiral kinks. In particular, we show that the topological charge of magnetic skyrmions can be expressed in terms of the constituent closed domain walls and chiral kinks. Guided by our classification scheme, we propose a method for creating hitherto unknown magnetic skyrmions which involves initial spin configurations formulated in terms of holomorphic functions and subsequent numerical energy minimization. We numerically study the stability of the resulting magnetic skyrmions for a range of external fields and anisotropy parameters, and provide quantitative estimates of the stability range for the whole variety of skyrmions with kinks. We show that the parameters limiting this range can be well described in terms of the relative energies of particular skyrmion solutions and isolated stripes with and without chiral kinks.

In this paper, we present a detailed comparative study of various analytical and numerical methods intended for the evaluation of the escape rate over high-energy barriers (transition rate or, equivalently, switching times) in magnetic systems, using the archetypal application-relevant model of a biaxial macrospin. First, we derive a closed-form analytical expression of the transition rate for such a particle, using the general formalism of Dejardin et al. [Phys. Rev. E 63, 021102 (2001)], and define a parameter which determines whether the system is in the low, intermediate, or high damping regimes. Then we carry out a comprehensive analysis of three numerical algorithms: time-temperature extrapolation method, “energy bounce” methods [S. Wang and P. Visscher, J. Appl. Phys. 99, 08G106 (2006)], and the forward-flux sampling [R. J. Allen et al., Phys. Rev. Lett. 94, 018104 (2005)], which appear to be the most promising candidates for evaluating the transition rate using computer simulations. Based on underlying physical principles and peculiarities of magnetic moment systems, we suggest several optimization possibilities, which strongly improve the performance of these methods for our applications. For energy barriers $\mathrm{\Delta }E$ in the range $10k_{\mathrm{B}}T\le \mathrm{\Delta }E\le 60k_{\mathrm{B}}T$ we compare the switching times, which correspondingly span more than 20 orders of magnitude, obtained with all the above-mentioned analytical and numerical techniques. We show that although for relatively small barriers all methods agree well with each other (and with straightforward Langevin dynamics simulations), for larger barriers the differences become significant, so that only the forward-flux method provides physically reasonable results, giving switching times which exceed the prediction of analytical approaches (interestingly, the ratio ${\tau }_{\mathrm{sw}}^{\mathrm{FFS}}/{\tau }_{\mathrm{sw}}^{\mathrm{an}}$ is nearly constant for a very broad interval of switching times). The reasons for the corresponding behavior of numerical methods are explained. Finally, we discuss the perspectives of the application of the analyzed numerical techniques to full-scale micromagnetic simulations, where the presence of several contributions to the total system energy makes the situation qualitatively different from that for the macrospin approach.

We present a general unified approach for the study of quantum thermal machines, including both heat engines and refrigerators, operating under periodic adiabatic driving and in contact with thermal reservoirs kept at different temperatures. We show that many observables characterizing this operating mode and the performance of the machine are of geometric nature. Heat-work conversion mechanisms and dissipation of energy can be described, respectively, by the antisymmetric and symmetric components of a thermal geometric tensor defined in the space of time-dependent parameters generalized to include the temperature bias. The antisymmetric component can be identified as a Berry curvature, while the symmetric component defines the metric of the manifold. We show that the operation of adiabatic thermal machines, and consequently also their efficiency, are intimately related to these geometric aspects. We illustrate these ideas by discussing two specific cases: a slowly driven qubit asymmetrically coupled to two bosonic reservoirs kept at different temperatures, and a quantum dot driven by a rotating magnetic field and strongly coupled to electron reservoirs with different polarizations. Both examples are already amenable for experimental verification.

We investigated the static and dynamic magnetic properties of the polar ferrimagnet ${\mathrm{Mn}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ in three magnetically ordered phases via magnetization, magnetic torque, and THz absorption spectroscopy measurements. The observed magnetic field dependence of the spin-wave resonances, including Brillouin zone-center and zone-boundary excitations, magnetization, and torque, are well described by an extended two-sublattice antiferromagnetic classical mean-field model. In this orbitally quenched system, the competing weak easy-plane and easy-axis single-ion anisotropies of the two crystallographic sites are determined from the model and assigned to the tetrahedral and octahedral sites, respectively, by ab initio calculations.

We report a muon spin rotation (${\mu }^{+}\mathrm{SR}$) study of the magnetic properties of the double perovskite compound ${\mathrm{LaSrNiReO}}_6$. Using the unique length and time scales of the ${\mu }^{+}\mathrm{SR}$ technique, we successfully clarify the magnetic ground state of ${\mathrm{LaSrNiReO}}_6$, which was previously deemed as a spin glass state. Instead, our ${\mu }^{+}\mathrm{SR}$ results point toward a long-range dynamically ordered ground state below $T_{\mathrm{C}}=23$ K, for which a static limit is foreseen at $T=0$. Furthermore, between $23\text{K}<T\le 300\text{K}$, three different magnetic phases are identified: a dense ($23\text{K}<T<75\text{K}$), a dilute ($75\text{K}\le T\le 250\text{K}$), and a paramagnetic ($T>250$ K) state. Our results reveal how two separate yet intertwined magnetic lattices interact within the unique double perovskite structure and the importance of using complementary experimental techniques to obtain a complete understanding of the microscopic magnetic properties of complex materials.

We study Shubnikov–de Haas oscillations in a $p$-type $\mathrm{W}{\mathrm{Se}}_2$ monolayer under very high magnetic field. The oscillation pattern is complex due to a large spin and valley splitting, in the non-fully-resolved Landau level regime. Our experimental data can be reproduced with a model in which the main parameter is the ratio between the Zeeman energy and the cyclotron energy. The model takes into account the Landau levels from both valleys with the same Gaussian broadening, which allows to predict the relative amplitude of the resistance oscillation originating from each valley. The Zeeman energy is found to be several times larger than the cyclotron energy. It translates into a large and increasing effective Landé factor as the hole density decreases, in the continuity of the values reported in the literature at lower carrier density.

We investigate a multiterminal mesoscopic conductor in the quantum Hall regime, subject to temperature and voltage biases. The device can be considered as a nonequilibrium resource acting on a working substance. We previously showed that cooling and power production can occur in the absence of energy and particle currents from a nonequilibrium resource (calling this an N-demon). Here we allow energy or particle currents from the nonequilibrium resource and find that the device seemingly operates at a better efficiency than a Carnot engine. To overcome this problem, we define free-energy efficiencies which incorporate the fact that a nonequilibrium resource is consumed in addition to heat or power. These efficiencies are well behaved for equilibrium and nonequilibrium resources and have an upper bound imposed by the laws of thermodynamics. We optimize power production and cooling in experimentally relevant parameter regimes.

Symmetry principles play a critical role in formulating the fundamental laws of nature, with a large number of symmetry-protected topological states identified in recent studies of quantum materials. As compelling examples, massless Dirac fermions are jointly protected by the space inversion symmetry $P$ and time-reversal symmetry $T$ supplemented by additional crystalline symmetry, while evolving into Weyl fermions when either $P$ or $T$ is broken. Here, based on first-principles calculations, we reveal that massless Dirac fermions are present in a layered FeSn crystal containing antiferromagnetically coupled ferromagnetic Fe kagome layers, where each of the $P$ and $T$ symmetries is individually broken but the combined $PT$ symmetry is preserved. These stable Dirac fermions, protected by the combined $PT$ symmetry with additional nonsymmorphic $S_{2z}$ symmetry, can be transformed to either massless/massive Weyl or massive Dirac fermions by breaking the $PT$ or $S_{2z}$ symmetry. Our angle-resolved photoemission spectroscopy experiments indeed observed the Dirac states in the bulk and two-dimensional Weyl-like states at the surface. The present paper substantially enriches our fundamental understanding of the intricate connections between symmetries and topologies of matter, especially with the spin degree of freedom playing a vital role.

We propose driven dissipative Majorana platforms for the stabilization and manipulation of robust quantum states. For Majorana box setups, in the presence of environmental electromagnetic noise and with tunnel couplings to quantum dots, we show that the time evolution of the Majorana sector is governed by a Lindblad master equation over a wide parameter regime. For the single-box case, arbitrary pure states (“dark states”) can be stabilized by adjusting suitable gate voltages. For devices with two tunnel-coupled boxes, we outline how to engineer dark spaces, i.e., manifolds of degenerate dark states, and how to stabilize fault-tolerant Bell states. The proposed Majorana-based dark space platforms rely on the constructive interplay of topological protection mechanisms and the autonomous quantum error correction capabilities of engineered driven dissipative systems. Once a working Majorana platform becomes available, only standard hardware requirements are needed to implement our ideas.

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. This capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

Paramagnetic ions in solid state crystals form the basis for many advanced technologies such as lasers, masers, frequency standards, and quantum-enhanced sensors. One of the most-studied examples is the ${\mathrm{Cr}}^{3+}$ ion in sapphire (${\mathrm{Al}}_2{\mathrm{O}}_3$), also known as ruby, which has been intensely studied in the 1950s and 1960s. However, despite decades of research on ruby, some of its fundamental optical and spin properties have not yet been characterized at ultralow temperatures. In this paper, we present optical measurements on a ruby crystal in a dilution refrigerator at ultralow temperatures down to 20 mK. Analyzing the relative populations of its ${}^{4}A{}_2$ ground-state spin levels, we extract a lattice temperature of $143\pm 7\mathrm{mK}$ under continuous laser excitation. We perform spin-lattice relaxation $T_1$ measurements in excellent agreement with the direct, one-phonon model. Furthermore, we perform optically detected magnetic resonance measurements showing magnetically driven transitions between the ground-state spin levels for various magnetic fields. Our measurements characterize some of ruby's low-temperature spin properties, and lay the foundations for more advanced spin control experiments.

Discrete quantum trajectories of systems under random unitary gates and projective measurements have been shown to feature transitions in the entanglement scaling that are not encoded in the density matrix. In this paper, we study the projective transverse field Ising model, a stochastic model with two noncommuting projective measurements and no unitary dynamics. We numerically demonstrate that their competition drives an entanglement transition between two distinct steady states that both exhibit area law entanglement, and introduce a classical but nonlocal model that captures the entanglement dynamics completely. Exploiting a map to bond percolation, we argue that the critical system in one dimension is described by a conformal field theory, and derive the universal scaling of the entanglement entropy and the critical exponent for the scaling of the mutual information of two spins exactly. We conclude with an interpretation of the entanglement transition in the context of quantum error correction.

The low-dimensional magnetic systems tend to reveal exotic spin-liquid ground states or form peculiar types of long-range order. Among systems of vivid interest are those characterized by the triangular motif in two dimensions. The realization of either ordered or disordered ground state in triangular, honeycomb, or kagome lattices is dictated by the competition of exchange interactions, also being sensitive to anisotropy and the spin value of magnetic ions. While the low-spin Heisenberg systems may arrive to a spin-liquid long-range entangled quantum state with emergent gauge structures, the high-spin Ising systems may establish the rigid noncollinear structures. Here, we present the case of chiral noncoplanar inverted umbrella-type ferrimagnet formed in cobalt nitrate $\mathrm{Co}{\left({\mathrm{NO}}_3\right)}_2$ below $T_{\mathrm{C}}=3\mathrm{K}$ with the comparable spin and orbital contributions to the total magnetic moment.

The electronic and magnetic properties of transition metal dichalcogenides are known to be extremely sensitive to their structure. In this paper we study the effect of structure on the electronic and magnetic properties of mono- and bilayer $\mathrm{V}{\mathrm{Se}}_2$ films grown using molecular beam epitaxy. $\mathrm{V}{\mathrm{Se}}_2$ has recently attracted much attention due to reports of emergent ferromagnetism in the two-dimensional (2D) limit. To understand this compound, high-quality $1T$ and distorted $1T$ films were grown at temperatures of 200 °C and 450 °C, respectively, and studied using 4 K scanning tunneling microscopy and spectroscopy. The measured density of states and the charge density wave (CDW) patterns were compared to band structure and phonon dispersion calculations. Films in the $1T$ phase reveal different CDW patterns in the first layer compared to the second. Interestingly, we find the second layer of the $1T$ film shows a CDW pattern with $4a\times 4a$ periodicity which is the 2D version of the bulk CDW observed in this compound. Our phonon dispersion calculations confirm the presence of a soft phonon at the correct wave vector that leads to this CDW. In contrast, the first layer of distorted $1T$ phase films shows a strong stripe feature with varying periodicities, while the second layer displays no observable CDW pattern. Finally, we find that the monolayer $1T \mathrm{VS}{\mathrm{e}}_2$ film is weakly ferromagnetic, with ∼3.5 ${\mu }_B$ per unit similar to previous reports.

Improper ferroelectrics are described by two order parameters: a primary one, driving a transition to long-range distortive, magnetic, or otherwise nonelectric order, and the electric polarization, which is induced by the primary order parameter as a secondary, complementary effect. Using low-temperature scanning probe microscopy, we show that improper ferroelectric domains in ${\mathrm{YMnO}}_3$ can be locally switched by electric field poling. However, subsequent temperature changes restore the as-grown domain structure as determined by the primary lattice distortion. The backswitching is explained by uncompensated bound charges occurring at the newly written domain walls due to the lack of mobile screening charges at low temperature. Thus, the polarization of improper ferroelectrics is in many ways subject to the same electrostatics as in their proper counterparts, yet complemented by additional functionalities arising from the primary order parameter. Tailoring the complex interplay between primary order parameter, polarization, and electrostatics is therefore likely to result in novel functionalities specific to improper ferroelectrics.

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough qualitative level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus, we show that this MBL transition is in a universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\nu \to \infty$, but the divergence is weaker than for the KT transition.

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three-dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent ($2+1$)-dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such “floating topological phases,” as well as their diagnosis by means of a nonlocal order parameter. Such a phase can produce a divergent ratio ${\rho }_{\perp }/{\rho }_{\parallel }$ of the interlayer to intralayer resistivity as $T\to 0$, even in an insulator where both ${\rho }_{\perp }$ and ${\rho }_{\parallel }$ individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g., spin-liquid) phase.