We classify the band degeneracies in three-dimensional crystals with screw symmetry $n_m$ and broken $\mathcal{P}*\mathcal{T}$ symmetry, where $\mathcal{P}$ stands for spatial inversion and $\mathcal{T}$ for time reversal. The generic degeneracies along symmetry lines are Weyl nodes: chiral contact points between pairs of bands. They can be single nodes with a chiral charge of magnitude $\left|\chi \right|=1$ or composite nodes with $\left|\chi \right|=2$ or 3, and the possible $\chi$ values only depend on the order $n$ of the axis, not on the pitch $m/n$ of the screw. Double Weyl nodes require $n=4$ or 6, and triple nodes require $n=6$. In all cases, the bands split linearly along the axis, and for composite nodes the splitting is quadratic on the orthogonal plane. This is true for triple as well as double nodes, due to the presence in the effective two-band Hamiltonian of a nonchiral quadratic term that masks the chiral cubic dispersion. If $\mathcal{T}$ symmetry is present and $\mathcal{P}$ is broken, there may exist on some symmetry lines Weyl nodes pinned to $\mathcal{T}$-invariant momenta, which in some cases are unavoidable. In the absence of other symmetries, their classification depends on $n,m$, and the type of $\mathcal{T}$ symmetry. With spinless $\mathcal{T}$ such $\mathcal{T}$-invariant Weyl nodes are always double nodes, while with spinful $\mathcal{T}$ they can be single or triple nodes. $\mathcal{T}$-invariant triples nodes can occur not only on sixfold axes but also on threefold ones, and their in-plane band splitting is cubic, not quadratic as in the case of generic triple nodes. These rules are illustrated by means of first-principles calculations for hcp cobalt, a $\mathcal{T}$-broken, $\mathcal{P}$-invariant crystal with $6_3$ symmetry, and for trigonal tellurium and hexagonal ${\mathrm{NbSi}}_2$, which are $\mathcal{T}$-invariant, $\mathcal{P}$-broken crystals with threefold and sixfold screw symmetry, respectively.

We combine extensive precision measurements of the optically detected spin dynamics and magneto-transport measurements in a contiguous set of n-doped bulk GaAs structures, in order to unambiguously unravel the intriguing but complex contributions to the spin relaxation at the metal-to-insulator transition (MIT). Just below the MIT, the interplay between hopping induced loss of spin coherence and hyperfine interaction yields a maximum spin lifetime exceeding 800 ns. At slightly higher doping concentrations, however, the spin relaxation deviates from the expected Dyakonov-Perel mechanism which is consistently explained by a reduction of the effective motional narrowing close to the MIT. The reduction is attributed to the change of the dominant momentum scattering mechanism in the metallic impurity band, where scattering by local conductivity domain boundaries due to the intrinsic random distribution of donors becomes significant. Here, we fully identify and model all intricate contributions of the relevant microscopic scattering mechanisms, which allows the complete quantitative modeling of the electron spin relaxation in the entire regime from weakly interacting up to fully delocalized electrons.

We define single electron spin qubits in a silicon metal-oxide-semiconductor double quantum dot system. By mapping the qubit resonance frequency as a function of a gate-induced electric field, the spectrum reveals an anticrossing that is consistent with an intervalley spin-orbit coupling. We fit the data from which we extract an intervalley coupling strength of 43 MHz. In addition, we observe a narrow resonance near the primary qubit resonance when we operate the device in the $(1,1)$ charge configuration. The experimental data are consistent with a simulation involving two weakly exchanged-coupled spins with a Zeeman energy difference of 1 MHz, of the same order as the Rabi frequency. We conclude that the narrow resonance is the result of driven transitions between the $T_{-}$ and $T_{+}$ triplet states, using an electron spin resonance signal of frequency located halfway between the resonance frequencies of the two individual spins. The findings presented here offer an alternative method of implementing two-qubit gates, of relevance to the operation of larger-scale spin qubit systems.

The electrical resistivity $\rho$ and Hall coefficient $R_{\mathrm{H}}$ of the tetragonal single-layer cuprate ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ were measured in magnetic fields up to $H=37.5$ T, large enough to access the normal state at $T\to 0$, for closely spaced dopings $p$ across the pseudogap critical point at $p^{☆}=0.23$. Below $p^{☆}$, both coefficients exhibit an upturn at low temperature, which gets more pronounced with decreasing $p$. Taken together, these upturns show that the normal-state carrier density $n$ at $T=0$ drops upon entering the pseudogap phase. Quantitatively, it goes from $n=1+p$ at $p=0.24$ to $n=p$ at $p=0.20$. By contrast, the mobility does not change appreciably, as revealed by the magnetoresistance. Our data are in excellent agreement with recent high-field data on ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ and ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. The quantitative consistency across three different cuprates shows that a drop in carrier density from $1+p$ to $p$ is a universal signature of the pseudogap transition at $T=0$. We discuss the implication of these findings for the nature of the pseudogap phase.

In this paper, we present a comprehensive study of the low-energy optical magnetic response of the skyrmionic Mott insulator ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ via high resolution time-domain THz spectroscopy. In zero field, a new magnetic excitation ($f_0=2.03\mathrm{THz}$) which has not been predicted by spin-wave theory is observed and shown, with accompanying time-of-flight neutron scattering experiments, to be a zone folded magnon from the $\mathrm{R}$ to $\mathrm{\Gamma }$ points of the Brillouin zone. Highly sensitive polarimetry experiments performed in weak magnetic fields, ${\mu }_0\mathrm{H}<200\mathrm{mT}$, observe Faraday and Kerr rotations which are proportional to the sample magnetization, allowing for optical detection of the skyrmion phase and construction of a magnetic phase diagram. From these measurements, we extract a critical exponent of $\beta =0.35\pm 0.04$, in good agreement with the expected value for the 3D Heisenberg universality class of $\beta =0.367$. In large magnetic fields, ${\mu }_0\mathrm{H}>5\mathrm{T}$, we observe the magnetically active uniform mode of the ferrimagnetic field polarized phase whose dynamics as a function of field and temperature are studied. In addition to extracting a $g_{\text{eff}}=2.08\pm 0.03$, we observe the uniform mode to decay through a non-Gilbert damping mechanism and to possess a finite spontaneous decay rate, ${\mathrm{\Gamma }}_0\approx 25\mathrm{GHz}$, in the zero temperature limit. Our observations are attributed to Dzyaloshinkii-Moriya interactions, which have been proposed to be exceptionally strong in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ and are expected to impact the low-energy magnetic response of such chiral magnets.

We have compared the magnetic, transport, galvanomagnetic, and specific-heat properties of ${\mathrm{CeNiC}}_2$, ${\mathrm{PrNiC}}_2$, and ${\mathrm{NdNiC}}_2$ to study the interplay between charge density waves (CDW) and magnetism in these compounds. The negative magnetoresistance in ${\mathrm{NdNiC}}_2$ is discussed in terms of the partial destruction of charge density waves and an irreversible phase transition stabilized by the field-induced ferromagnetic transformation is reported. For ${\mathrm{PrNiC}}_2$ we demonstrate that the magnetic field initially weakens the CDW state, due to the Zeeman splitting of conduction bands. However, the Fermi surface nesting is enhanced at a temperature related to the magnetic anomaly.

In magnetic nanowires with perpendicular magnetic anisotropy (PMA) magnetic domain walls (DWs) are narrow and can move rapidly driven by current induced torques. This enables important applications like high-density memories for which the precise detection of the position and motion of a propagating DW is of utmost interest. Today's DW detection tools are often limited in resolution, require complex instrumentation, or can only be applied on specific materials. Here we show that the anomalous Nernst effect provides a simple and powerful tool to precisely track the position and motion of a single DW propagating in a PMA nanowire. We detect field and current driven DW propagation in both metallic heterostructures and dilute magnetic semiconductors over a broad temperature range. The demonstrated spatial accuracy below 20 nm is comparable to the DW width in typical metallic PMA systems.

The effective Mott gap measured by scanning tunneling microscopy (STM) in the lightly doped Mott insulator ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ differs greatly from values reported by photoemission and optical experiments. Here we show that this is a consequence of the poor electronic screening of the tip-induced electric field in this material. Such effects are well known from STM experiments on semiconductors and go under the name of tip-induced band bending (TIBB). We show that this phenomenon also exists in the lightly doped Mott insulator ${\left({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x\right)}_2{\mathrm{IrO}}_4$ and that, at doping concentrations of $x\le 4\%$, it causes the measured energy gap in the sample density of states to be bigger than the one measured with other techniques. We develop a model able to retrieve the intrinsic energy gap leading to a value which is in rough agreement with other experiments, bridging the apparent contradiction. At doping $x\approx 5\%$ we further observe circular features in the conductance layers that point to the emergence of a significant density of free carriers in this doping range and to the presence of a small concentration of donor atoms. We illustrate the importance of considering the presence of TIBB when doing STM experiments on correlated-electron systems and discuss the similarities and differences between STM measurements on semiconductors and lightly doped Mott insulators.

In 2+1-dimensional space-time, gapped quantum states are always gapped quantum liquids (GQL) which include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQLs for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by nondegenerate unitary braided fusion categories over a symmetric fusion category (SFC) $\mathcal{E}$, abbreviated as ${\mathrm{UMTC}}_{/\mathcal{E}}$, together with their modular extensions and total chiral central charges. In our classification, SFC $\mathcal{E}$ describes the symmetry, which is $\text{Rep}\left(G\right)$ for bosonic symmetry $G$, or $\text{sRep}\left(G^f\right)$ for fermionic symmetry $G^f$. As a special case of the above result, we find that the modular extensions of $\text{Rep}\left(G\right)$ classify the 2+1D bosonic SPT states of symmetry $G$, while the $c=0$ modular extensions of $\text{sRep}\left(G^f\right)$ classify the 2+1D fermionic SPT states of symmetry $G^f$. Many fermionic SPT states are studied based on the constructions from free-fermion models. But free-fermion constructions cannot produce all fermionic SPT states. Our classification does not have such a drawback. We show that, for interacting 2+1D fermionic systems, there are exactly 16 superconducting phases with no symmetry and no fractional excitations (up to $E_8$ bosonic quantum Hall states). Also, there are exactly 8 $Z_2\times Z_2^f$-SPT phases, 2 $Z_8^f$-SPT phases, and so on. Besides, we show that two topological orders with identical bulk excitations and central charge always differ by the stacking of the SPT states of the same symmetry.

We have investigated the longitudinal thermal conductivity of $\alpha \text{−}{\mathrm{RuCl}}_3$, the magnetic state of which is considered to be proximate to a Kitaev honeycomb model, along with the spin susceptibility and magnetic specific heat. We found that the temperature dependence of the thermal conductivity exhibits an additional peak around 100 K, which is well above the phonon peak temperature ($\sim 50$ K). The higher-temperature peak position is comparable to the temperature scale of the Kitaev couplings rather than the Néel temperatures below 15 K. Additional heat conduction was observed for all five samples used in this study, and was found to be rather immune to a structural phase transition of $\alpha \text{−}{\mathrm{RuCl}}_3$, which suggests its different origin from phonons. Combined with experimental results of the magnetic specific heat, our transport measurement suggests strongly that the higher-temperature peak in the thermal conductivity is attributed to itinerant spin excitations associated with the Kitaev couplings of $\alpha \text{−}{\mathrm{RuCl}}_3$. A kinetic approximation of the magnetic thermal conductivity yields a mean free path of $\sim 20$ nm at 100 K, which is much longer than the nearest Ru-Ru distance ($\sim 3$ Å), suggesting the long-distance coherent propagation of magnetic excitations driven by the Kitaev couplings.

We demonstrate submicrotesla sensitivity of organic magnetoresistance in thin-film diodes made of the conducting polymer poly(styrene sulfonate)-doped poly(3,4-ethylenedioxythiophene) (PEDOT:PSS). The magnetoresistance sensitivity is shown to be better than 20 parts per billion (ppb). As for other conjugated polymers, magnetoresistance can be separated into two regimes of field strength: the nonmonotonic ultrasmall magnetic field effect on magnetic field scales below 2 mT, and the monotonic intermediate magnetic field effect on scales over several tens of mT. The former gives the PEDOT:PSS magnetoresistance curve a characteristic W-shaped functionality, with inverted turning points compared to those found in conventional organic light-emitting diode (OLED) devices. We succeed in resolving the ultrasmall magnetic field effect of the PEDOT:PSS layer incorporated within an OLED structure, which is responsible for an additional magnetoresistive feature on the ppm scale. Such a device shows unprecedented complexity in magnetoresistance with a total of four extrema within a field range of ±1 mT. We propose that these unique characteristics arise from spin-spin interactions in the weakly bound carrier pairs responsible for the spin-dependent recombination probed in magnetoresistance.

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

Dynamical antiferromagnets can pump spins into adjacent conductors. The high antiferromagnetic resonance frequencies represent a challenge for experimental detection, but magnetic fields can reduce these resonance frequencies. We compute the ac and dc inverse spin Hall voltages resulting from dynamical spin excitations as a function of a magnetic field along the easy axis and the polarization of the driving ac magnetic field perpendicular to the easy axis. We consider the insulating antiferromagnets ${\mathrm{MnF}}_2,{\mathrm{FeF}}_2$, and NiO. Near the spin-flop transition, there is a significant enhancement of the dc spin pumping and inverse spin Hall voltage for the uniaxial antiferromagnets ${\mathrm{MnF}}_2$ and ${\mathrm{FeF}}_2$. In the uniaxial antiferromagnets it is also found that the ac spin pumping is independent of the external magnetic field when the driving field has the optimal circular polarization. In the biaxial NiO, the voltages are much weaker, and there is no spin-flop enhancement of the dc component.

We formulate topological crystalline materials on the basis of the twisted equivariant $K$ theory. Basic ideas of the twisted equivariant $K$ theory are explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an application of our formulation, we present a complete classification of topological crystalline surface states, in the absence of time-reversal invariance. The classification works for gapless surface states of three-dimensional insulators, as well as full gapped two-dimensional insulators. Such surface states and two-dimensional insulators are classified in a unified way by 17 wallpaper groups, together with the presence or the absence of (sublattice) chiral symmetry. We identify the topological numbers and their representations under the wallpaper group operation. We also exemplify the usefulness of our formulation in the classification of bulk gapless phases. We present a class of Weyl semimetals and Weyl superconductors that are topologically protected by inversion symmetry.

We explore the ${\mathbb{Z}}_N$ parafermionic clock-model generalizations of the $p$-wave Majorana wire model. In particular, we examine whether zero-mode operators analogous to Majorana zero modes can be found in these models when one introduces chiral parameters to break time reversal symmetry. The existence of such zero modes implies $N$-fold degeneracies throughout the energy spectrum. We address the question directly through these degeneracies by characterizing the entire energy spectrum using perturbation theory and exact diagonalization. We find that when $N$ is prime, and the length $L$ of the wire is finite, the spectrum exhibits degeneracies up to a splitting that decays exponentially with system size, for generic values of the chiral parameters. However, at particular parameter values (resonance points), band crossings appear in the unperturbed spectrum that typically result in a splitting of the degeneracy at finite order. We find strong evidence that these preclude the existence of strong zero modes for generic values of the chiral parameters. In particular we show that in the thermodynamic limit, the resonance points become dense in the chiral parameter space. When $N$ is not prime, the situation is qualitatively different, and degeneracies in the energy spectrum are split at finite order in perturbation theory for generic parameter values, even when the length of the wire $L$ is finite. Exceptions to these general findings can occur at special “antiresonant” points. Here the evidence points to the existence of strong zero modes and, in the case of the achiral point of the $N=4$ model, we are able to construct these modes exactly.

We study coherent transport of levitons through a single-level quantum dot system driven by Lorentzian-shaped voltage pulses. We demonstrate the repeated emergence of the Kondo resonance in the dynamical regimes where the Fermi sea is driven by optimal pulses free of particle-hole excitations. The formation of the Kondo resonance significantly enhances the dc transport of levitons.

We analyze, through resonant photoluminescence, the spin dynamics of an individual magnetic atom (Mn) coupled to a hole in a semiconductor quantum dot. The hybrid Mn hole spin and the positively charged exciton in a CdTe/ZnTe quantum dot form an ensemble of $\mathrm{\Lambda }$ systems which can be addressed optically. Autocorrelation of the resonant photoluminescence and resonant optical pumping experiments are used to study the spin relaxation channels in this multilevel spin system. We identified for the hybrid Mn hole spin an efficient relaxation channel driven by the interplay of the Mn hole exchange interaction and the coupling to acoustic phonons. We also show that the optical $\mathrm{\Lambda }$ systems are connected through inefficient spin flips than can be enhanced under weak transverse magnetic field. The dynamics of the resonant photoluminescence in a $p$-doped magnetic quantum dot is well described by a complete rate equation model. Our results suggest that long-lived hybrid Mn hole spin could be obtained in quantum dot systems with large heavy-hole/light-hole splitting.

Anyon condensation forms a mechanism that allows us to relate different topological phases. We study anyon condensation in the framework of projected entangled pair states (PEPS) where topological order is characterized through local symmetries of the entanglement. We show that anyon condensation is in one-to-one correspondence to the behavior of the virtual entanglement state at the boundary (i.e., the entanglement spectrum) under those symmetries, which encompasses both symmetry breaking and symmetry protected (SPT) order, and we use this to characterize all anyon condensations for Abelian double models through the structure of their entanglement spectrum. We illustrate our findings with the ${\mathbb{Z}}_4$ double model, which can give rise to both toric code and doubled semion order through condensation, distinguished by the SPT structure of their entanglement. Using the ability of our framework to directly measure order parameters for condensation and deconfinement, we numerically study the phase diagram of the model, including direct phase transitions between the doubled semion and the toric code phase, which are not described by anyon condensation.

We study the interaction of the charge states of a superconducting double dot, comprising two superconducting islands coupled by a Josephson junction, with microwaves between 2 and 55 GHz. We observe resonant transitions between even-parity charge states at relatively low frequencies and breaking of Cooper pairs under higher-frequency irradiation, allowing our device to act as a click detector for microwave photons. By applying a magnetic field and tuning the pair-breaking energy, we perform spectroscopy on the environment in our cryostat and determine the temperature of a nonequilibrium photon bath. Finally, we exploit the band structure of our device to break Cooper pairs dependent on the symmetry of the initial Cooper pair state.

We report on large thermoelectric effects in superconductor-ferromagnet tunnel junctions in proximity contact with the ferromagnetic insulator europium sulfide. The combination of a spin-splitting field and spin-polarized tunnel conductance in these systems breaks the electron-hole symmetry and leads to spin-dependent thermoelectric currents. We show that the exchange splitting induced by europium sulfide boosts the thermoelectric effect in small applied fields and can therefore eliminate the need to apply large magnetic fields, which might otherwise impede applications in thermometry or cooling.