Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called $l$ bits. These spin algebras define quasilocal $l$-bit measurement (${\tau }_i^z$) and $l$-bit flip (${\tau }_i^x$) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate $l$-bit flip operators by first calculating them exactly on small windows of systems using an algorithm called operator localization optimization. We then extend the $l$-bit operators onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates of the Hamiltonian. Finally, we describe a method to calculate products of local observables on these eigenstates for systems of size $L$ in $O\left(L^2\right)$ time. This method is used to calculate the variance of the energy of the approximate eigenstates, yielding an estimate of the error of the approximation.

Engineering the magnetic properties (Gilbert damping, saturation magnetization, exchange stiffness, and magnetic anisotropy) of multicomponent magnetic compounds plays a key role in fundamental magnetism and its applications. Here, we perform a systematic study of ${\left({\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}\right)}_{100-x}{\mathrm{Gd}}_x$ films with $x=0\%$, 5%, 9%, and $13\%$ using ferromagnetic resonance (FMR), element-specific time-resolved x-ray magnetic resonance, and femtosecond time-resolved magneto-optical pump-probe techniques. The comparative analysis of field and time domain FMR methods, with complimentary information extracted from the dynamics of high-frequency exchange magnons in ferromagnetic thin films, is used to investigate the dependence of Gilbert damping on the Gd concentration.

We observe domain-wall (DW) motion in ferrimagnetic TbFe wires with perpendicular anisotropy under combined field and current in the creep regime. The current action on the DW is double: Joule heating and spin-transfer torque. We propose a genuinely robust analysis of velocity, separating thermal effects and spin-transfer torque, quantifying the latter as an equivalent field in the so-called one-dimensional (1D) model. Its efficiency is much larger than in transition-metal ferromagnets above room temperature. The equivalent field reveals the large polarization-to-magnetization ratio in ferrimagnets despite a vanishing $M_s$. The usual 1D DW model is extended to mimic creep and predicts that, in low net magnetization systems, the internal DW structure precesses with currents above a field-independent threshold, leading to two propagation regimes with different mobilities. This is another example of how the internal DW magnetization is relevant in creep. We could not detect experimentally these two regimes, possibly because of the dispersion of the data.

The normal state of cuprate superconductors exhibits many exotic behaviors qualitatively different from the Fermi liquid, the foundation of condensed-matter physics. Here we demonstrate that non-Fermi-liquid behaviors emerge naturally from scattering against an emergent Bose liquid. Particularly, we find a finite zero-energy scattering rate at the low-temperature limit that grows linearly with respect to temperature, against clean fermions' generic nondissipative characteristics. Surprisingly, three other seemingly unrelated experimental observations are also produced, including the well-studied “kink” in the quasiparticle dispersion, as well as the puzzling correspondences between the normal and superconducting states. Our findings provide a general route for fermionic systems to generate non-Fermi-liquid behavior and suggest that by room temperature large number of the doped holes in the cuprates have already formed an emergent Bose liquid of tightly bound pairs, whose low-temperature condensation gives unconventional superconductivity.

In this paper, we investigate the mechanical properties, electronic band structure, lattice dynamics, and electron-phonon interaction in $\delta \text{−}\mathrm{NbN}$, $\varepsilon \text{−}\mathrm{NbN}$, WC-NbN, and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ by performing systematic ab initio calculations based on density functional theory with the generalized gradient approximation. We find that all the four structures are mechanically stable with $\varepsilon \text{−}\mathrm{NbN}$ being the ground-state structure. The calculated elastic constants, which agree well with available experimental data, demonstrate that all four NbN polytypes are hard materials with bulk moduli being close to that of boron nitride. The calculated electronic band structures show that all four polytypes are metallic with the Nb $d$-orbital dominated energy bands near the Fermi level ($E_F$). The calculated phonon dispersion relations of $\delta \text{−}\mathrm{NbN}$ are in good agreement with neutron scattering experiments. The electron-phonon coupling ($\lambda$) in $\delta \text{−}\mathrm{NbN}$ ($\lambda =0.98$) is much stronger than in $\varepsilon \text{−}\mathrm{NbN}$ ($\lambda =0.16$), WC-NbN ($\lambda =0.11$), and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ ($\lambda =0.17$). This results in a much higher superconducting transition temperature ($T_c=18.2\mathrm{K}$) than in $\varepsilon \text{−}\mathrm{NbN}$, WC-NbN, and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ ($T_c\le 1.0\mathrm{K}$). The stronger $\lambda$ and higher $T_c$ in $\delta \text{−}\mathrm{NbN}$ are attributed to its large density of states at $E_F$ and small Debye temperature. The calculated $T_c$ of $\delta \text{−}\mathrm{NbN}$ is in good agreement with the experimental values. However, the predicted $T_c$ of $\varepsilon \text{−}\mathrm{NbN}$ is much smaller than the recent experiment (11.6 K) but agrees well with the earlier experiment, suggesting further experiments on single-phase samples. Finally, the calculated relativistic band structures reveal that all four NbN polytypes are topological metals. Specifically, $\varepsilon \text{−}\mathrm{NbN}$ and ${\delta }^{\prime }\text{−}\mathrm{NbN}$ are type-I Dirac metals whereas $\delta \text{−}\mathrm{NbN}$ is type-II Dirac metal, while WC-NbN is an emergent topological metal that has rare triply degenerate nodes. All these results indicate that all the four NbN polytypes should be hard superconductors with nontrivial band topology that would provide valuable opportunities for studying fascinating phenomena arising from the interplay of band topology and superconductivity.

We study the effect of uncorrelated random disorder on the temperature dependence of the superfluid stiffness in the two-dimensional classical XY model. By means of a perturbative expansion in the disorder potential, equivalent to the $T$-matrix approximation, we provide an extension of the effective-medium-theory result able to describe the low-temperature stiffness and its separate diamagnetic and paramagnetic contributions. These analytical results provide an excellent description of the Monte Carlo simulations for two prototype examples of uncorrelated disorder. Our findings offer an interesting perspective on the effects of quenched disorder on longitudinal phase fluctuations in two-dimensional superfluid systems.

The paper we comment on reports measurements of the transverse spin-Seebeck effect in metals using a novel technique. We provide an estimation of the size of the effect reported by McLaughlin et al. [Phys. Rev. B 95, 180401 (2017)], which turns out to be exceptionally large: comparison of the estimated amount of spin accumulation with the spin-dependent Seebeck effect would require a temperature difference of the order of 1000 K. Considering the null results reported in previous papers, we suggest that the signal measured by McLaughlin et al. is not or not only caused by the transverse spin-Seebeck effect.

In the Comment on our original paper [R. McLaughlin et al., Phys. Rev. B 95, 180401(R) (2017)], Kimling et al. claimed that our optically detected change of Kerr rotation angle in a ferromagnetic slab subjected to a lateral temperature gradient measured by magneto-optical Kerr effect (MOKE) is not, or not only, caused by the transverse spin-Seebeck effect. In this Reply, we experimentally confirm the conclusion in the original paper by measuring MOKE in a striped patterned NiFe slab, thereby refuting the criticism in the Comment.

It was proposed recently by some of the authors that the quantum phase transition of a topological insulator like the Su-Schrieffer-Heeger (SSH) model may be detected by the eigenvalues and eigenvectors of the reduced density matrix. Here we further extend the scheme of identifying the order parameters by considering the SSH model with the addition of triplet superconductivity. This model has a rich phase diagram due to the competition of the SSH “order” and the Kitaev “order,” which requires the introduction of four order parameters to describe the various topological phases. We show how these order parameters can be expressed simply as averages of projection operators on the ground state at certain points deep in each phase and how one can simply obtain the phase boundaries. A scaling analysis in the vicinity of the transition lines is consistent with the quantum Ising universality class.

The ability to pump quantized amounts of charge is one of the hallmarks of topological materials. An archetypical example is Laughlin's gauge argument for transporting an integer number of electrons between the edges of a quantum Hall cylinder upon insertion of a magnetic flux quantum. This is mathematically equivalent to the equally famous suggestion of Thouless that an integer number of electrons is pumped between two ends of a one-dimensional quantum wire upon sliding a charge-density wave over a single wavelength. We use the correspondence between these descriptions to visualize the detailed dynamics of the electron flow during a single pumping cycle, which is difficult to do directly in the quantum Hall setup because of the gauge freedom inherent in its description. We find a close correspondence between topological edge states and the mobility edges in charge-density wave, quantum Hall, and other topological systems. We illustrate this connection by describing an alternative, nonadiabatic mode of topological transport that displaces precisely the opposite amount of charge compared to the adiabatic pump. We discuss possible experimental realizations in the context of ultracold atoms and photonic waveguide experiments.

We consider time-dependent processes in the optically excited hybrid system formed by a quantum well (QW) coupled to a remote spin-split correlated bound state. The spin-dependent tunneling from the QW to the bound state results in the nonequilibrium electron spin polarization in the QW. The Coulomb correlations at the bound state enhance the spin polarization in the QW. We propose a mechanism for ultrafast switching of the spin polarization in the QW by tuning the laser pulse frequency between the bound state spin sublevels. Mn-doped core/multishell nanoplatelets and hybrid bound state-semiconductor heterostructures are suggested as promising candidates to prove the predicted effect experimentally. The obtained results open a possibility for spin polarization control in nanoscale systems.

The single-wall carbon nanotube (SWNT) can be a one-dimensional topological insulator, which is characterized by a $\mathbb{Z}$-topological invariant, winding number. Using the analytical expression for the winding number, we classify the topology for all possible chiralities of SWNTs in the absence and presence of a magnetic field, which belongs to the topological categories of BDI and AIII, respectively. We find that the majority of SWNTs are nontrivial topological insulators in the absence of a magnetic field. In addition, the topological phase transition takes place when the band gap is closed by applying a magnetic field along the tube axis, in all the SWNTs except armchair nanotubes. The winding number determines the number of edge states localized at the tube ends by the bulk-edge correspondence, the proof of which is given for SWNTs in general. This enables the identification of the topology in experiments.

The Kane-Mele model of time-reversal symmetry, which simultaneously contains spin and valley degrees of freedom, is simulated in a topological circuit network. By varying capacitances and inductances, we are able to demonstrate the quantum valley Hall states, in addition to the quantum spin Hall states, as well as the topological phase transition between them. We also study the rich topological interface states between nontrivial phases with different spin and valley Chern numbers via tuning capacitances and inductances so as to tune the couplings and gauge fields. Finally, we demonstrate the spin-valley locking in the Kane-Mele circuit network. The topological circuit network provides us with a platform to simultaneously control spin and valley degrees of freedom so that a spin splitter and a valley splitter can be realized.

We developed the theory which describes the Floquet engineering of surface electronic modes in bulk mercury telluride (HgTe) by a circularly polarized electromagnetic field. The analysis shows that the field results in the appearance of the surface states which arise from the mixing of conduction and valence bands of HgTe. Their branches lie near the center of the Brillouin zone and have the Dirac dispersion characteristic for topological states. Besides them, the irradiation induces the gap between the conduction and valence bands of HgTe. Thus, the irradiation can turn mercury telluride into a topological insulator from a gapless semiconductor. It is demonstrated that the optically induced states differ substantially from the nontopological surface states existing in HgTe without irradiation. The structure of the found states is studied both analytically and numerically in the broad range of their parameters.

Using Landau-Ginsburg-Devonshire theory, we derive and analyze analytical expressions for the frequency dispersion of soft phonon modes in nanosized ferroics and perform numerical calculations for a thin $\mathrm{SrTi}{\mathrm{O}}_3$ film. We revealed the pronounced “true” size effect in the dependence of soft phonon spatial dispersion on the film thickness and predict that it can lead to the “apparent” or “false” size effect of dynamic flexoelectric coupling constants. Also, we derived analytical expressions describing the influence of finite size effect on the appearance and properties of the incommensurate spatial modulation induced by the static flexoelectric effect in ferroic thin films. To verify the theoretical predictions experimental measurements of the soft phonon dispersion in nanosized ferroics seem urgent.

We consider the nonlinear terahertz response of n-doped monolayer graphene at room temperature using a microscopic theory of carrier dynamics. Our tight-binding model treats the carrier-field interaction in the length gauge, includes phonon as well as short-range neutral-impurity scattering, and fully accounts for the intrinsic nonlinear response of graphene near the Dirac point. Treating each interaction microscopically allows us to separate contributions from current clipping, phonon creation, and elastic impurity scattering. Although neutral impurity scattering and phonon scattering are both highly energy dependent, we find that they impact conduction-band electron dynamics very differently, and that together they can help explain experimental results concerning field-dependent terahertz transmission through graphene.