In a model presented in Yang et al. [Phys. Rev. B 99, 024418 (2019)] it was stated that in the linear regime spin selectivity cannot be measured when using two contacts configuration, and that the results observed when studying the chiral-induced spin-selectivity effect are not consistent with this statement. Here we claim that the results cited clearly indicate nonlinearity and therefore the spin selectivity observed is valid observation.

In this Reply, we emphasize once more the distinction between generating CISS (spin-charge current conversion) in a chiral spin-orbit system and detecting it as magnetoresistance in two-terminal electronic devices. We also highlight important differences between electrical measurement results obtained in the linear response regime and those obtained in the nonlinear regime.

In the presence of external off-resonance and circularly polarized irradiation, we have derived a many-body formalism and performed a detailed numerical analysis for both the conduction and the optical currents in $\alpha -{\mathcal{T}}_3$ lattices. The calculated complex many-body dielectric function as well as conductivities of displacement and transport currents display strong dependence on the lattice-structure parameter $\alpha$, especially approaching the graphene limit with $\alpha \to 0$. Unique features in dispersion and damping of plasmon modes are observed with different $\alpha$ values, which are further accompanied by a reduced transport conductivity under irradiation. The discovery in this paper can be used for designing novel multifunctional nanoelectronic and nanoplasmonic devices.

We present emergent ergosurfaces (ES) in a transition layer between type-I and type-II Weyl semimetals (WSMs). The Hawking temperature defined by the surface gravity at the acoustic event horizon which coincides with the ES when the tangent velocity $v_{\parallel }$ is small is in a measurable interval. On the type-II WSM side, i.e., inside the ES when $v_{\parallel }$ is large, the motion of the quasiparticles may be chaotic after a critical surface as they are governed by an effective inverted oscillator potential induced by the mismatch between the type-I and type-II Weyl nodes. In a relevant lattice model, we calculate out-of-time-ordered correlators (OTOCs). We find that the OTOCs are fast scrambling with a quantum Lyapunov exponent in high temperature and the scrambling is saturated after the Ehrenfest time. This confirms the quantum chaotic behavior.

The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g., three-dimensional (3D) strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on average at least when electron interactions on the surface are weak. However, the interplay of strong interactions and disorder with the boundary anomaly has not yet been theoretically addressed. Here we study this combination for the edge of a two-dimensional TI and the surface of a 3D weak TI, showing how it can lead to an “Anomalous Many Body Localized” (AMBL) phase that preserves the anomaly. We discuss how the anomalous Kramers parity switching with $\pi$ flux arises in the bosonized theory of the localized helical state. The anomaly can be probed in localized boundaries by electrostatically sensing nonlinear hopping transport with $e/2$ shot noise. Our AMBL construction in 3D weak TIs fails for 3D strong TIs, which suggests that their anomaly restrictions are distinguished by strong interactions.

The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the systematic error at a subpercent level. We employ the bold diagrammatic Monte Carlo method to explore the universality of QCC by considering three different two-dimensional spin-1/2 Heisenberg models. In particular, we reveal the existence of QCC in models with two parameters.

We have investigated magnetotransport properties of $\mathrm{YR}{\mathrm{h}}_6\mathrm{G}{\mathrm{e}}_4$, which was recently predicted to be a triply degenerate nodal semimetal. We find it exhibits remarkable signatures of a chiral anomaly, manifested by large negative longitudinal magnetoresistance, the quadratic field dependence of magnetoconductance and the planar Hall effect. Furthermore, we have also observed Shubnikov-de Haas (SdH) quantum oscillations in the magnetoresistivity measurements on this material. The analyses of the SdH data reveal two pointlike Fermi surfaces and these pockets are found to host nearly massless fermions. The small size of these Fermi pockets is in a good agreement with the theoretical prediction that the triply degenerate point in $\mathrm{YR}{\mathrm{h}}_6\mathrm{G}{\mathrm{e}}_4$ is much closer to the Fermi level than previously demonstrated triply degenerate nodal semimetals such as MoP and WC. These results suggest $\mathrm{YR}{\mathrm{h}}_6\mathrm{G}{\mathrm{e}}_4$ may serve as a model system to probe exotic properties of three-component fermions and understand their underlying physics.

We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photoinduced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to $M_{\mathrm{ph}}=40$ bare phonons per site by working with $O\left(10\right)$ optimal phonon modes.

Kitaev quantum spin liquids described by the Kitaev model represent an exotic state of matter with long-range entangled spins and topological order, which hold promise for quantum computation. $\alpha \text{−}{\mathrm{RuCl}}_3$, a material with van der Waals layered structure, is shown to be proximate to such a state recently. Here we report Raman spectroscopy of atomically thin $\alpha \text{−}{\mathrm{RuCl}}_3$. New phonon modes emerge at low temperature, signifying a phase transition to a crystal structure with lowered symmetry. The Fano line shape of two low-energy phonon modes and the magnetic scattering continuum in bulk $\alpha \text{−}{\mathrm{RuCl}}_3$, which evidence fractionalized Majorana fermions of the proximate quantum spin liquid, persist to the trilayer. Polarization-dependent measurements reveal increased anisotropy of the Kitaev exchange constants when approaching the two-dimensional limit. Our results demonstrate an intimate relation between the crystal structure and the symmetry of the proximate quantum spin liquid ground state.

We have developed a hierarchical nanoparticle transport simulator (hints) and adapted it to study commensuration effects in two classes of nanoparticle (NP) solids: (1) a bilayer NP solid (BNS) with an energy offset and (2) a BNS as part of a field effect transistor (FET). hints integrates the ab initio characterization of single NPs with the phonon-assisted tunneling transition model of the NP-NP transitions into a kinetic Monte Carlo based simulation of the charge transport in NP solids. First, we studied a BNS with an interlayer energy offset $\mathrm{\Delta }$, possibly caused by a fixed electric field. Our results include the following. First, in the independent energy-offset model, we observed the emergence of commensuration effects when scanning the electron filling factor (FF) across integer values. These commensuration effects were profound as they reduced the mobility by several orders of magnitude. We analyzed these commensuration effects in a five-dimensional parameter space, as a function of the on-site charging energy $E_C$, energy offset $\mathrm{\Delta }$, disorder $D$, the electron FF, and temperature $k_{B}T$. We demonstrated the complexity of our model by showing that at integer FFs commensuration effects are present in some regions of the parameter space, while they vanish in other regions, thus defining distinct dynamical phases of the model. We determined the phase boundaries between these dynamical phases. Second, using these results as a foundation, we shifted our focus to the experimentally much-studied NP-FETs. NP-FETs are also characterized by an interlayer energy offset $\mathrm{\Delta }$, which, in contrast to our first model, is set by the gate voltage $V_G$ and thereby related to the electron FF. We repeated many of our simulations and again demonstrated the emergence of commensuration effects and distinct dynamical phases in these NP-FETs. Notably, the commensuration effects in the NP-FETs showed many similarities to those in the independent energy-offset BNS.

Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity, we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality point) and modified Fermi velocity $\tilde{v}$. The $\tilde{v}$ dependence of the relevant scattering mechanisms, i.e., electron-hole Coulomb, long-range impurities, and acoustic gauge phonons, is considered in detail. We find a range of twist angles and temperatures, where the combined effect of momentum-nonconserving collisions (long-range impurities and phonons) is minimal, opening a window for the observation of strong hydrodynamic transport. Several experimental signatures are identified, such as a sharp dependence of the electric resistivity on doping density and a large enhancement of the Wiedemann-Franz ratio and the Seebeck coefficient.

The Su–Schrieffer–Heeger (SSH) model is one of the simplest topological lattice models and is a promising candidate for quantum simulations of topological systems. In this study we investigate an interacting SSH model with nearest-neighbor interactions using mean field theory and an exact diagonalization method after the Jordan-Wigner transformation. We obtain a rich phase diagram with six different phases. Majorana bound states are found and confirmed by analyzing wave functions and Majorana number. In addition, we propose to use superconducting devices to construct a one-dimensional quantum circuit, where Cooper pair boxes and Josephson junctions are alternately connected in series, to theoretically simulate the interacting SSH model. This approach also provides us a toolkit to simulate correlated topological systems.

The breaking of parity and time-reversal symmetry in two-dimensional Fermi liquids gives rise to nondissipative transport features characterized by the Hall viscosity. In magnetic fields, the Hall viscous force directly competes with the Lorentz force, since both mechanisms contribute to the Hall voltage. In this paper, we present a channel geometry that allows us to uniquely distinguish these two contributions and derive their functional dependency on all external parameters. We show that the ratio of the Hall viscous to the Lorentz force contribution is negative and that its modulus decreases with increasing width, slip length, and carrier density, while it increases with the electron-electron mean free path of our channel. In typical materials such as GaAs the Hall viscous contribution can dominate the Lorentz signal up to a few tens of millitesla until the total Hall voltage vanishes and subsequently is overcome by the Lorentz contribution. Moreover, we prove that the total Hall electric field is parabolic due to Lorentz effects, whereas the offset of this parabola is characterized by the Hall viscosity. Hence, our results pave the way to measure and identify the Hall viscosity via both global and local voltage measurements.

We study the optical transport properties of the monolayer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_2$, ${\mathrm{WS}}_2$, ${\mathrm{MoSe}}_2$, and ${\mathrm{WSe}}_2$ in the presence of a magnetic field. The TMDCs band structures are obtained and discussed by using the effective massive Dirac model, in which the spin and valley Zeeman effects as well as an external electric field are included. The magneto-optical absorption coefficient (MOAC) is derived as a function of absorbed photon energy when the carriers are scattered by random impurities combined with the intrinsic acoustic and optical phonons in TMDCs and the surface optical (SO) phonons of substrates. Our result shows that the spin-splitting feature appeared in all four TMDC materials. The combination of strong spin-orbit coupling (SOC) and Zeeman fields has doubled the Landau levels but has not changed the energy gap of the TMDCs monolayer, which can be controlled by the electric field. Because of their strong SOC effect, the absorption spectrum in monolayer TMDCs is separated into two separate peaks caused by spin up and down. At the low temperature, the MOAC intensity via impurity scattering is the biggest followed by that of the SO phonons while the intrinsic acoustic and optical phonon scatterings display the smallest. For the monolayer TMDCs on substrates, ${\mathrm{SiO}}_2$ always shows its superiority in comparison with the others. Among the four TMDC materials, ${\mathrm{MoSe}}_2$ shows the biggest MOAC intensity, while ${\mathrm{WS}}_2$ has the biggest value of the absorbed photon energy. The full-width at half-maximum (FWHM) via impurity scattering achieves its highest value in ${\mathrm{WS}}_2$, while this occurs in ${\mathrm{MoSe}}_2$ and ${\mathrm{MoS}}_2$ via intrinsic acoustic and optical phonon scatterings, respectively. Our estimation of mobility from FWHM gives good agreement with the experimental results in ${\mathrm{WS}}_2$.

In our paper, calculation of exchange interaction is carried out for two itinerant atoms ${}^{173}\mathrm{Yb}\left({}^{1}S_0\right)$ and ${}^{173}\mathrm{Yb}\left({}^{3}P_0\right)$. The fact that the exchange interaction is modified when the ${}^{173}\mathrm{Yb}({}^3{P}_0)$ atom is localized in an optical potential was overlooked. This flaw is corrected in this Erratum, and the claim that the exchange constant is antiferromagnetic (a necessary condition for achieving the Kondo effect) is established.

The ultrafast magnetic dynamics in compensated ferrimagnets not only is similar to antiferromagnetic dynamics but, more importantly, opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling the domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is also confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradients and can be slightly accelerated under large gradients due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly enhanced by the second anisotropy and interfacial Dzyaloshinskii-Moriya interaction, which is highly appreciated for further experiments, including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming and highly efficient method of controlling the domain wall in ferrimagnets, benefiting future spintronic applications.

We have examined size effect on thermal, transport, and thermodynamic properties of a ${\mathrm{CrSb}}_2$ single crystal. We demonstrate highly anisotropic quasi-one-dimensional electrical conductivity, quasiballistic phonons, and giant thermopower of $-6$ mV/K at 15 K. A thermopower peak is suppressed to $-1.6$ mV/K by changing crystal dimensions and shows linear dependence on the phonon mean-free path. Whereas electronic diffusion thermopower is significant, the bulk of the giant thermopower in ${\mathrm{CrSb}}_2$ stems from the coupling of the very long mean-free path phonons with the in-gap states.

We report an inelastic x-ray scattering investigation of phonons in FeSe superconductor. Comparing the experimental phonon dispersion with density-functional theory (DFT) calculations in the nonmagnetic state, we found a significant disagreement between them. Improved overall agreement was obtained by allowing for spin polarization in the DFT calculations, despite the absence of magnetic order in the experiment. This calculation gives a realistic approximation, at the DFT level, of the disordered paramagnetic state of FeSe, in which strong spin fluctuations are present.

Wave propagation control is of fundamental interest in many areas of physics. It can be achieved with wavelength-scaled photonic crystals, hence avoiding low-frequency applications. By contrast, metamaterials are structured on a deep-subwavelength scale, and therefore usually described through homogenization, neglecting the unit-cell structuration. Here, we show with microwaves that, by considering their inherent crystallinity, we can induce wave propagation carrying angular momenta within a subwavelength-scaled collection of wires. Then, inspired by the quantum valley Hall effect in condensed-matter physics, we exploit this bulk circular polarization to create modes propagating along particular interfaces. The latter also carry an edge angular momentum whose conservation during the propagation allows wave routing by design in specific directions. This experimental study not only evidences that crystalline metamaterials are a straightforward tabletop platform to emulate exciting solid-state physics phenomena at the macroscopic scale, but it also opens the door to crystalline polarized subwavelength waveguides.