Spin relaxation is conventionally discussed using two different approaches for materials with and without inversion symmetry. The former is known as the Elliott-Yafet (EY) theory and for the latter the D'yakonov-Perel' (DP) theory applies. We discuss herein a simple and intuitive approach to demonstrate that the two seemingly disparate mechanisms are closely related. A compelling analogy between the respective Hamiltonians is presented, and that the usual derivation of spin-relaxation times, in the respective frameworks of the two theories, can be performed. The result also allows us to obtain less canonical spin-relaxation regimes, i.e. the generalization of the EY when the material has a large quasiparticle broadening, and the DP mechanism in ultrapure semiconductors. The method also allows a practical and intuitive numerical implementation of the spin-relaxation calculation, which is demonstrated for ${\mathrm{MgB}}_2$, which has anomalous spin-relaxation properties.

It has been proposed that the pseudogap state of underdoped cuprate superconductors may be due to a transition to a phase which has circulating currents within each unit cell. Here, we use polarized neutron diffraction to search for the corresponding orbital moments in two samples of underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ with doping levels $p=0.104$ and 0.123. In contrast to some other reports using polarized neutrons, but in agreement with nuclear magnetic resonance and muon spin rotation measurements, we find no evidence for the appearance of magnetic order below 300 K. Thus, our experiment suggests that such order is not an intrinsic property of high-quality cuprate superconductor single crystals. Our results provide an upper bound for a possible orbital loop moment which depends on the pattern of currents within the unit cell. For example, for the CC-${\theta }_{II}$ pattern proposed by Varma, we find that the ordered moment per current loop is less than 0.013 ${\mu }_B$ for $p=0.104$.

We theoretically discover a family of nonequilibrium fractional topological phases in which time-periodic driving of a 2D system produces excitations with fractional statistics, and produces chiral quantum channels that propagate a quantized fractional number of qubits along the sample edge during each driving period. These phases share some common features with fractional quantum Hall states, but are sharply distinct dynamical phenomena. Unlike the integer-valued invariant characterizing the equilibrium quantum Hall conductance, these phases are characterized by a dynamical topological invariant that is a square root of a rational number, inspiring the label: radical chiral Floquet phases. We construct solvable models of driven and interacting spin systems with these properties, and identify an unusual bulk-boundary correspondence between the chiral edge dynamics and bulk “anyon time-crystal” order characterized by dynamical transmutation of electric-charge into magnetic-flux excitations in the bulk.

We extend the theory of dipole moments in crystalline insulators to higher multipole moments. As first formulated in Benalcazar et al. [Science 357, 61 (2017)], we show that bulk quadrupole and octupole moments can be realized in crystalline insulators. In this paper, we expand in great detail the theory presented previously [Benalcazar et al., Science 357, 61 (2017)] and extend it to cover associated topological pumping phenomena, and a class of three-dimensional (3D) insulator with chiral hinge states. We start by deriving the boundary properties of continuous classical dielectrics hosting only bulk dipole, quadrupole, or octupole moments. In quantum mechanical crystalline insulators, these higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments are quantized, and their boundary signatures are fractionalized. These multipole moments then correspond to new symmetry-protected topological phases. The topological structure of these phases is described by “nested” Wilson loops, which we define. These Wilson loops reflect the bulk-boundary correspondence in a way that makes evident a hierarchical classification of the multipole moments. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For nontrivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the quantized multipole moments, the nontrivial pumping processes, and the hinge Chern insulator, and describe the topological invariants that protect them.

Recent theoretical work has established the presence of hidden spin and orbital textures in nonmagnetic materials with inversion symmetry. Here, we propose that these textures can be detected by nuclear magnetic resonance (NMR) measurements carried out in the presence of an electric field. In crystals with hidden polarizations, a uniform electric field produces a staggered magnetic field that points to opposite directions at atomic sites related by spatial inversion. As a result, the NMR resonance peak corresponding to inversion partner nuclei is split into two peaks. The magnitude of the splitting is proportional to the electric field and depends on the orientation of the electric field with respect to the crystallographic axes and the external magnetic field. As a case study, we present a theory of electric-field-induced splitting of NMR peaks for ${}^{77}\mathrm{Se},{}^{125}\mathrm{Te}$, and ${}^{209}\mathrm{Bi}$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$  and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. In conducting samples with current densities of $\simeq {10}^6{\mathrm{A}/\mathrm{cm}}^2$, the splitting for Bi can reach $100\mathrm{kHz}$, which is comparable to or larger than the intrinsic width of the NMR lines. In order to observe the effect experimentally, the peak splitting must also exceed the linewidth produced by the Oersted field. In ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, this requires narrow wires of radius $\lesssim 1\mu \mathrm{m}$. We also discuss other potentially more promising candidate materials, such as ${\mathrm{SrRuO}}_3$ and ${\mathrm{BaIr}}_2{\mathrm{Ge}}_2$, whose crystal symmetry enables strategies to suppress the linewidth produced by the Oersted field.

The evolution of the electron spin dynamics as consequence of carrier delocalization in $n$-type GaAs is investigated by the recently developed extended pump-probe Kerr/Faraday rotation spectroscopy. We find that isolated electrons localized on donors demonstrate a prominent difference between the longitudinal and transverse spin relaxation rates in a magnetic field, which is almost absent in the metallic phase. The inhomogeneous transverse dephasing time $T_2^{*}$ of the spin ensemble strongly increases upon electron delocalization as a result of motional narrowing that can be induced by increasing either the donor concentration or the temperature. An unexpected relation between $T_2^{*}$ and the longitudinal spin relaxation time $T_1$ is found, namely, that their product is about constant, as explained by the magnetic field effect on the spin diffusion. We observe a two-stage longitudinal spin relaxation, which suggests the establishment of spin temperature in the system of exchange-coupled donor-bound electrons.

We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-André model to higher dimensions. In three dimensions (3D) we find that the Anderson localization transitions appear to be in the same universality class as for random potentials. In scaling or renormalization group terms, this means that randomness of the potential is irrelevant at the Anderson localization transitions in 3D. In two dimensions (2D) we also explore the Ando model, which is in the symplectic symmetry class and shows an Anderson localization transition for random potentials. Here, unlike in 3D, we find that the universality class changes when we instead use a quasiperiodic potential.

Recent experiments have shown that the high-temperature incommensurate (I) charge density wave (CDW) phase of 1T-${\mathrm{TaS}}_2$ can be photoinduced from the lower-temperature, nearly commensurate CDW state. Here we report a time-resolved x-ray diffraction study of the growth process of the photoinduced I-CDW domains. The layered nature of the material results in a marked anisotropy in the size of the photoinduced domains of the I-phase. These are found to grow self-similarly, their shape remaining unchanged throughout the growth process. The photoinduced dynamics of the newly formed I-CDW phase was probed at various stages of the growth process using a double pump scheme, where a first pump creates I-CDW domains and a second pump excites the newly formed I-CDW state. We observe larger magnitudes of the coherently excited I-CDW amplitude mode in smaller domains, which suggests that the incommensurate lattice distortion is less stable for smaller domain sizes.

The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries of the underlying lattice systems. Artificially engineered lattices, such as heterostructures and other superlattices, provide promising avenues to realize desired crystal symmetries that protect lower-dimensional Fermi surfaces, such as nodal lines. In this work, we investigate a Weyl semimetal subjected to spatially periodic onsite potential, giving rise to several phases, including a nodal-line semimetal phase. In contrast to proposals that purely focus on lattice symmetries, the emergence of the nodal line in this setup does not require small spin-orbit coupling, but rather relies on its presence. We show that the stability of the nodal line is understood from reflection symmetry and a combination of a fractional lattice translation and charge-conjugation symmetry. Depending on the choice of parameters, this model exhibits drumhead surface states that are exponentially localized at the surface, or weakly localized surface states that decay into the bulk at all energies.

In the recently discovered Weyl semimetals, the Fermi surface may feature disjoint, open segments—the so-called Fermi arcs—associated with topological states bound to exposed crystal surfaces. Here we show that the collective dynamics of electrons near such surfaces sharply departs from that of a conventional three-dimensional metal. In magnetic systems with broken time reversal symmetry, the resulting Fermi arc plasmons (FAPs) are chiral, with dispersion relations featuring open, hyperbolic constant frequency contours. As a result, a large range of surface plasmon wave vectors can be supported at a given frequency, with corresponding group velocity vectors directed along a few specific collimated directions. Fermi arc plasmons can be probed using near-field photonics techniques, which may be used to launch highly directional, focused surface plasmon beams. The unusual characteristics of FAPs arise from the interplay of bulk and surface Fermi arc carrier dynamics and give a window into the unusual fermiology of Weyl semimetals.

We have studied the longitudinal spin Seebeck effect in a polar antiferromagnet $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ in contact with a Pt film. Below the antiferromagnetic transition temperature of $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$, spin Seebeck voltages whose magnetic-field dependence is similar to that reported in antiferromagnetic ${\mathrm{MnF}}_2|\mathrm{Pt}$ bilayers are observed. Though a small weak-ferromagnetic moment appears owing to the Dzyaloshinskii-Moriya interaction in $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$, the magnetic-field dependence of spin Seebeck voltages is found to be irrelevant to the weak-ferromagnetic moments. The dependences of the spin Seebeck voltages on magnetic fields and temperature are analyzed by a magnon spin-current theory. The numerical calculation of spin Seebeck voltages using magnetic parameters of $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ determined by previous neutron-scattering studies reveals that the magnetic-field and temperature dependences of the spin Seebeck voltages for $\alpha \text{−}{\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7|\mathrm{Pt}$ are governed by the changes in magnon lifetimes with magnetic fields and temperature.

The phase diagram associated with high-$T_c$ superconductors is complicated by an array of different ground states. The parent material represents an antiferromagnetic insulator but with doping superconductivity becomes possible with transition temperatures previously thought unattainable. The underdoped region of the phase diagram is dominated by the so-called pseudogap phenomena, whereby in the normal state the system mimics superconductivity in its spectral response but does not show the complete loss of resistivity associated with the superconducting state. An understanding of this regime presents one of the great challenges for the field. In the present study we revisit the structure of the phase diagram as determined in photoemission studies. By careful analysis of the role of nanoscale inhomogeneities in the overdoped region, we are able to more carefully separate out the gaps due to the pseudogap phenomena from the gaps due to the superconducting transition. Within a mean-field description, we are thus able to link the magnitude of the doping-dependent pseudogap directly to the Heisenberg exchange interaction term, $J\sum s_i{s}_j$, contained in the $t-J$ model. This approach provides a clear indication that the pseudogap is associated with spin singlet formation.

Connecting the complex electronic excitations of hybrid perovskites to their intricate organic-inorganic lattice structure has critical implications for energy conversion and optoelectronic technologies. Here we detail the multiband, multivalley electronic structure of a halide hybrid perovskite by measuring the absorption transients of a millimeter-scale-grain thin film as it undergoes a thermally controlled reversible tetragonal-to-orthogonal phase transition. Probing nearly single grains of this hybrid perovskite, we observe an unreported energy splitting (degeneracy lifting) of the high-energy 2.6 eV band in the tetragonal phase that further splits as the rotational degrees of freedom of the disordered $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{{\mathrm{H}}_3}^{+}$ molecules are reduced when the sample is cooled. This energy splitting drastically increases during an extended phase-transition coexistence region that persists from 160 to 120 K, becoming more pronounced in the orthorhombic phase. By tracking the temperature-dependent optical transition energies and using symmetry analysis that describes the evolution of electronic states from the tetragonal phase to the orthorhombic phase, we assign this energy splitting to the nearly degenerate transitions in the tetragonal phase from both the $R$- and $M$-point-derived states. Importantly, these assignments explain how momentum conservation effects lead to long hot-carrier lifetimes in the room-temperature tetragonal phase, with faster hot-carrier relaxation when the hybrid perovskite structurally transitions to the orthorhombic phase due to enhanced scattering at the Γ point.

The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in $n$-doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed buildup of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warmup in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time $T_2$ determined from nuclear magnetic resonance.

We report single-crystal ${}^{51}\mathrm{V}$ NMR studies on volborthite ${\mathrm{Cu}}_3{\mathrm{V}}_2{\mathrm{O}}_7{\left(\mathrm{OH}\right)}_2·2{\mathrm{H}}_2\mathrm{O}$, which is regarded as a quasi-two-dimensional frustrated magnet with competing ferromagnetic and antiferromagnetic interactions. In the 1/3 magnetization plateau above 28 T, the nuclear spin-lattice relaxation rate $1/T_1$ indicates an excitation gap with a large effective $g$ factor in the range of 4.6–5.9, pointing to magnon bound states. Below 26 T where the gap has closed, the NMR spectra indicate small internal fields with a Gaussian-like distribution, whereas $1/T_1$ shows a power-law-like temperature dependence in the paramagnetic state, which resembles a slowing down of spin fluctuations associated with magnetic order. We discuss the possibility of an exotic spin state caused by the condensation of magnon bound states below the magnetization plateau.

We investigate the existence of quantum-disentangled liquid (QDL) states in the half-filled Hubbard model on bipartite lattices. In the one-dimensional case we employ a combination of integrability and strong-coupling expansion methods to argue that there are indeed finite energy-density eigenstates that exhibit QDL behavior in the sense of Grover and Fisher [J. Stat. Mech. (2014) P10010]. The states exhibiting the QDL property are atypical in the sense that while their entropy density is nonzero, it is smaller than that of thermal states at the same energy density. We argue that for $U\gg t$ these latter thermal states exhibit a weaker form of the QDL property, which carries over to the higher dimensional case.

Monolayers of transition metal dichalcogenides (TMDCs) possess unique optoelectronic properties, including strongly bound excitons and trions. To date, most studies have focused on optically active excitations, but recent experiments have highlighted the existence of dark states, which are equally important in many respects. Here, we use ab initio many-body calculations to unravel the nature of the dark excitations in monolayer ${\mathrm{MoSe}}_2$, ${\mathrm{MoS}}_2$, ${\mathrm{WSe}}_2$, and ${\mathrm{WS}}_2$. Our results show that all these monolayer TMDCs host dark states as their lowest neutral and charged excitations. We further show that dark excitons possess larger binding energies than their bright counterparts while the opposite holds for trions.

The Drude-Smith model has been used extensively in fitting the THz conductivities of nanomaterials with carrier confinement on the mesoscopic scale. Here, we show that the conventional “backscattering” explanation for the suppression of low-frequency conductivities in the Drude-Smith model is not consistent with a confined Drude gas of classical noninteracting electrons and we derive a modified Drude-Smith conductivity formula based on a diffusive restoring current. We perform Monte Carlo simulations of a model system and show that the modified Drude-Smith model reproduces the extracted conductivities without free parameters. This alternate route to the Drude-Smith model provides the popular formula with a more solid physical foundation and well-defined fit parameters.

A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (arising from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires to understand possible intrinsic deviations from the predicted conductance quantization. We find that the full temperature and the tunneling transmission dependence of the tunnel conductance does not obey any simple scaling relation, and estimating the zero-temperature conductance from finite-temperature and finite-tunnel-broadening tunneling data is difficult in general. A scaling relation, however, does hold at the extreme weak-tunneling low-temperature limit where the conductance depends only on the dimensionless ratio of the temperature and tunnel broadening. We also consider the tunneling contributions from nontopological Andreev bound states which may produce almost-zero-bias conductance peaks, which are not easy to distinguish from the Majorana-induced zero-bias peaks, finding that the nontopological almost-zero modes associated with Andreev bound states manifest similar temperature and transmission dependence as the topological Majorana modes. We comment on the Zeeman splitting dependence of the zero-bias conductance peak for finite temperature and tunnel coupling.

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.