We report magnetophotoluminescence spectroscopy of gated ${\mathrm{MoS}}_2$ monolayers in high magnetic fields to 28 T. At $B=0$ T and electron density $n_s\sim {10}^{12} {\mathrm{cm}}^{-2}$, we observe three trion resonances that cannot be explained within a single-particle picture. Employing ab initio calculations that take into account three-particle correlation effects as well as local and nonlocal electron-hole exchange interaction, we identify those features as quantum superpositions of inter- and intravalley spin states. We experimentally investigate the mixed character of the trion wave function via the filling factor dependent valley Zeeman shift in positive and negative magnetic fields. Our results highlight the importance of exchange interactions for exciton physics in monolayer ${\mathrm{MoS}}_2$ and provide insights into the microscopic understanding of trion physics in two-dimensional multivalley semiconductors for low excess carrier densities.

Many solid-state qubit systems are afflicted by low-frequency noise mechanisms that operate along two perpendicular axes of the Bloch sphere. Depending on the qubit control fields, either noise can be longitudinal or transverse to the quantization axis of the qubit, thus affecting its dynamics in distinct ways, generally contributing to decoherence that goes beyond pure dephasing. Here, we present a theory that provides a unified platform to study dynamics of a qubit subjected to two perpendicular low-frequency noises (assumed to be Gaussian and uncorrelated) under dynamical decoupling pulse sequences. The theory is demonstrated by the commonly encountered case of power law noise spectra, where approximate analytical results can be obtained.

We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.

Despite the high overlap with the exact Coulomb ground state, the so-called Gaffnian state fails to describe the incompressibility at the 2/5 quantum Hall filling factor and consequently it was conjectured to be a quantum critical state. To achieve a gapped state starting from the Gaffnian wave function, which we interpret as the interflavor pairing of the composite fermions, we propose a minimally “modified Gaffnian” wave function keeping the pairing intact. We find that a suitable hybridization of these two wave functions is an excellent description of the 2/5 quantum Hall state. It has a very high overlap with the exact Coulomb state and their entanglement spectra match up to reasonably higher levels. Interestingly, this hybridized wave function being a representative of a paired state suggests an exotic possibility of non-Abelian quasiparticle excitations at 2/5 filling.

Atomically thin transition metal dichalcogenides can show a rich variety of bound exciton complex states, such as trions, biexcitons, Fermi polarons, and phonon replicas, because of the reduced dielectric screening and enhanced Coulomb interaction. To date, studies have mainly focused on the complexes of intralayer excitons, while the electrically tunable interlayer exciton (IX) complexes remain elusive. Here, we report the observation of IX complexes with large out-of-plane electric dipole, strong emission intensity, and giant valley responses in bilayer ${\mathrm{MoS}}_2$, through on-resonance photoluminescence spectroscopy. In sharp contrast to the small, positive circular dichroism of intralayer excitons, the circular polarization of IX complexes in bilayer ${\mathrm{MoS}}_2$ can basically reach the theoretical limit (100%) but is negative. Such highly unusual light-valley responses of IX complexes in bilayer ${\mathrm{MoS}}_2$ demonstrate the strongly suppressed valley depolarization and spin-preserving scattering of electrons during the formation. Remarkably, by breaking the time-reversal symmetry with an out-of-plane magnetic field, a record level of spontaneous valley polarization (7.7%/Tesla) is identified for IX complexes in bilayer ${\mathrm{MoS}}_2$. The giant valley polarization of IX complexes in bilayer ${\mathrm{MoS}}_2$, together with the feasibility of electrical/optical/magnetic control, provides a firm basis for the development of next-generation electronic and optoelectronic applications with valley functionalities.

The recent discovery of long-range magnetic orders in atomically thin semiconductors ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and $\mathrm{Cr}{\mathrm{I}}_3$ as well as metal ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ has opened up exciting opportunities for fundamental physics of two-dimensional (2D) magnetism and also for technological applications based on 2D magnetic materials. To exploit these 2D metallic magnets, the mechanisms that control their physical properties should be well understood. In this paper, based on systematic first-principles density functional theory calculations, we study the magnetic anisotropy energy (MAE) and magneto-optical (MO) effects of ferromagnetic multilayers [mono-, bi-, tri-, tetra-, and pentalayer] and bulk ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ as well as their connections with the underlying electronic structures of the materials. Firstly, all the considered ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ structures are found to prefer the out-of-plane magnetization and have gigantic MAEs of $\sim 3.0$ meV/f.u. This gigantic perpendicular anisotropy results from the large magnetocrystalline anisotropy energy (MCE), which is ten times larger than the competing magnetic dipolar anisotropy energy. The giant MCEs are attributed to the large Te $p_{x,y}$ orbital density of states near the Fermi level and also to the topological nodal point just below the Fermi level at the K points in the Brillouin zone. Secondly, 2D and bulk ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ also exhibit strong MO effects with their Kerr and Faraday rotation angles being $\sim 1.0^{\circ }$ and $\sim 100 \mathrm{deg}/\mu \mathrm{m}$ in the visible-light frequency region, respectively. The strong MO Kerr and Faraday effects are found to result from the large MO conductivity (or strong magnetic circular dichroism) in these ferromagnetic materials. In particular, the calculated MO conductivity spectra are one order of magnitude larger than that of ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. The calculated MO conductivity spectra are analysed in terms of the dipole-allowed optical transitions at high symmetry $\mathrm{\Gamma }$, K, and ${\mathrm{K}}^{\prime }$ points, which further indicate that atomically thin ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ films with odd layer-number might exhibit anomalous ferrovalley Hall effect. All these interesting findings thus suggest that 2D and bulk ferromagnetic ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ are promising materials for high-density MO and spintronic nanodevices.

In $5d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double perovskites where magnetic ions form a face-centered cubic (fcc) lattice was suggested to unveil an octupolar order offering a rare example in $d$-orbital systems. The proposed order requires a ferromagnetic (FM) octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the fcc lattice. A microscopic model was recently derived for various lattices: for an edge-sharing octahedra geometry, AFM Ising octupolar and bond-dependent quadrupolar interactions were found when only dominant inter- and intraorbital hopping integrals were taken into account. Here we investigate all possible intra- and interorbital exchange processes and report that interference of two intraorbital exchanges generates a FM octupolar interaction. Applying the strong-coupling expansion results together with tight-binding parameters obtained by density functional theory, we estimate the exchange interactions for the osmium double perovskites, ${\mathrm{Ba}}_{2}B{\mathrm{OsO}}_6$ $(B=\mathrm{Mg},\mathrm{Cd},\text{and}\mathrm{Ca})$. Using classical Monte Carlo simulations, we find that these systems are close to the phase boundary between AFM type-I quadrupole and FM octupole orders. We also find that exchange processes beyond second-order perturbation theory including virtual processes via pseudospin-triplet states may stabilize an octupolar order.

We have investigated the origin of the magnetic dipole correlations $\langle {\sigma }_{\mathit{Q}}^z{\sigma }_{-\mathit{Q}}^z\rangle$ characterized by the modulation wave vector $\mathit{k}\sim (\frac{1}{2},\frac{1}{2},\frac{1}{2})$ observed in the frustrated pyrochlore magnet ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$. This magnetic short-range order cannot be accounted for by adding further-neighbor exchange interactions to the nearest-neighbor pseudospin-$\frac{1}{2}$ Hamiltonian for quantum pyrochlore magnets. Using classical Monte Carlo simulation and quantum simulation based on thermally pure quantum (TPQ) states we have shown that the spin correlations with $\mathit{k}\sim (\frac{1}{2},\frac{1}{2},\frac{1}{2})$ are induced at low temperatures by a three-spin interaction of a form ${\sigma }_{\mathit{r}}^{\pm }{\sigma }_{{\mathit{r}}^{\prime }}^z{\sigma }_{{\mathit{r}}^{\prime \prime }}^z$, which is a correction to the Hamiltonian due to the low crystal-field excitation. Simulations using TPQ states have shown that the spin correlations coexist with electric quadrupole correlations $\langle {\sigma }_{\mathit{Q}}^{\alpha }{\sigma }_{-\mathit{Q}}^{\beta }\rangle$ ($\alpha ,\beta =x,y$) with $\mathit{k}\sim \mathit{0}$. These results suggest that the putative quantum spin liquid state of ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$ is located close to phase boundaries of the spin-ice, quadrupole-ordered, and magnetic-ordered states in the classical approximation, and that the three-spin interaction brings about a quantum disordered ground state with both spin and quadrupole correlations.

Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical physics. The well-known eigenstate thermalization hypothesis (ETH) is presumed to be a key mechanism, but has defied rigorous verification for generic systems thus far. A weaker variant (weak ETH), by contrast, is provably true for a large variety of systems, including even many integrable models, but its implications with respect to the problem of thermalization are still largely unexplored. Here we analytically demonstrate that systems satisfying the weak ETH exhibit thermalization for two very natural classes of far-from-equilibrium initial conditions: the overwhelming majority of all pure states with a preset nonequilibrium expectation value of some given local observable, and the Gibbs states of a Hamiltonian which subsequently is subject to a quantum quench in the form of a sudden change of some local system properties.

Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The magnetization configuration is described in stereographic projection by the complex valued function $f$, both for the static equilibrium background and the spin-wave excitations on top of it. The topologically nontrivial ground state of SkX corresponds to simple poles of $f$ at skyrmions' positions. We use the earlier proposed ansatz for this ground-state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure in accordance with previously known results. At low energies there are two sets of bands, one set with a flat dispersion, topologically trivial, and rapidly evolving with magnetic field. Despite similarity to Landau levels scheme, the underlying equations have a different structure, making this set of bands somewhat enigmatic. Another set of bands is robust to magnetic field and is characterized by pronounced dispersion and by the Berry curvature which may be sign reversal in the Brillouin zone. We demonstrate that the dispersion is of tight-binding form and well described by nearest-neighbor hopping, which seems unexpected for smooth superlattice potential and strong nonuniform gauge field. The developed theory can be easily generalized to other types of topological spin structures and used for calculation of the dynamical susceptibility tensor and thermal transport in magnets with skyrmion lattice background.

We study the electron dynamics in magnetic conductors with frustrated interactions dominated by isotropic exchange. We present a transport theory for itinerant carriers built upon the (single-band) doped Hubbard model and the slave-boson formalism, which incorporates the spin-exchange with the magnetically frustrated background into the representation of electron operators in a clear and controllable way. We also formulate hydrodynamic equations for the itinerant charge and spin degrees of freedom, whose currents contain new contributions that depend on the spatiotemporal variations of the order parameter of the frustrated magnet, which are described by Yang-Mills fields. Furthermore, we elucidate the transfer of angular momentum from the itinerant charge fluid to the magnet (i.e., the spin-transfer torque) via reciprocity arguments. A detailed microscopic derivation of our effective theory is also provided for one of the simplest models of frustrated magnetism, namely the Heisenberg antiferromagnet on a triangular lattice. Our findings point towards the possibility of previously unanticipated Hall physics in these frustrated platforms.

Recent experiments on the dipolar-octupolar pyrochlore compound ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ indicate that it may realize a three-dimensional quantum spin liquid (QSL). In particular, the analyses of available data suggest that the system is in a region of parameter space, where the so-called $\pi$-flux $U\left(1\right)$ octupolar quantum spin ice (QSI) with an emergent photon could be realized. However, because the system is far from the perturbative classical spin ice regime, it is unclear whether the quantum ground state is primarily a coherent superposition of 2-in-2-out configurations as in the canonical QSI phases. In this work, we explore other possible competing quantum spin-liquid states beyond QSI using the Schwinger boson parton construction of the dipolar-octupolar pseudospin-1/2 model. After classifying all symmetric $U\left(1\right)$ and ${\mathbb{Z}}_2$ QSLs using the projective symmetry group (PSG), we construct a mean-field phase diagram that possesses a number of important features observed in an earlier exact diagonalization study. In the experimentally relevant frustrated region of the phase diagram, we find two closely competing gapped ${\mathbb{Z}}_2$ QSLs with a narrow spinon dispersion. The equal-time and dynamical spin structure factors of these states show key features similar to what was reported in neutron scattering experiments. Hence, these QSLs are closely competing ground states in addition to the $\pi$-flux $U\left(1\right)$ QSI, and they should be taken into account on equal footing for the interpretation of experiments on ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$.

The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy-band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight-binding formalism and find that the flat band states transform into a set of discrete bound states whose electron density is localized on a ring around the impurity mainly on two of the three sublattices. Its energy is proportional to the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb potential atomic collapse states appear that have some similarity with those found in graphene with the difference that the flat band states contribute with an additional ringlike electron density that is spatially decoupled from the atomic collapse part. At large value of the strength of the Coulomb impurity the flat band bound states anticross with the atomic collapse states.

We study the breaking of integrability by a finite density of dilute impurities, specifically the emerging diffusive transport. Provided the distance between impurities (localized perturbations) is large, one would expect the scattering rates to be additive, and therefore, the resistivity to be proportional to the number of impurities (the so-called Matthiessen's rule). We show that this is, in general, not the case. If transport is anomalous in the original integrable system without impurities, the diffusion constant in the nonintegrable system at low impurity density has a nontrivial power-law dependence on the impurity density, with the power being determined by the dynamical scaling exponent of anomalous transport. We also find a regime at high impurity density in which, counterintuitively, adding more impurities to an already diffusive system increases transport rather than decreases it.

For three-dimensional metals, Landau levels disperse as a function of the magnetic field and the momentum wave number parallel to the field. In this two-dimensional parameter space, it is shown that two conically dispersing Landau levels can touch at a diabolical point—a Landau-Dirac point. The conditions giving rise to Landau-Dirac points are shown to be magnetic breakdown (field-driven quantum tunneling) and certain crystallographic spacetime symmetry. Both conditions are realizable in topological nodal-line metals, as we exemplify with the material candidates $\mathrm{Ca}{X}_3$ $(X=\mathrm{As},\mathrm{P})$. The experimental fingerprints of a Landau-Dirac point include (a) anomalous “batman”-like peaks in the magnetoresistance, (b) circular Landau-Fermi surfaces revealed by angle-dependent ultrasonic attenuation, and (c) the tunability of the frequency onset of optical absorption to zero.

Hydrogen is involved in various important chemical processes on metal-oxide surfaces. Due to its electron-donating character, hydrogen tends to form polaronic states, where the electron is spatially separated from the proton, which exerts significant impact on the electronic properties of metal-oxide surfaces. By individually probing the proton with nuclear reaction analysis and the electron with ultraviolet photoelectron spectroscopy and in combination with density functional theory calculations, we clarify the electronic state of hydrogen on the anatase ${\mathrm{TiO}}_2\left(101\right)$ surface. Hydrogen is found to adsorb with a saturation coverage of $0.48\pm 0.12$ monolayers, donating an excess electron to the substrate without forming a midgap state, which is in contrast to the behavior of oxygen vacancies.

Demonstration of Majorana non-Abelian properties is a major challenge in the field of topological superconductivity. In this work, we propose a minimal device and protocol for testing non-Abelian properties using charge-transfer operations between a quantum dot and two Majorana bound states combined with reading the parity state using a second dot. We use an adiabatic perturbation theory to find fast adiabatic paths to perform operations and to account for nonadiabatic errors. We find the ideal parameter sweep and a region in parameter space that reduces the charge-transfer operation time 1–2 orders of magnitude with respect to constant velocity driving. Using realistic parameters, we estimate that the lower bound for the timescale can be reduced to $\sim 10\mathrm{ns}$. Deviations from the ideal parameters lead to the accumulation of an undesired dynamical phase, affecting the outcome of the proposed protocol. We furthermore suggest to reduce the influence from the dynamical phase using a flux echo. The echo protocol is based on the $4\pi$ periodicity of the topological state, absent for trivial bound states.

Translationally invariant flatband Hamiltonians with interactions lead to a many-body localization transition. Our models are obtained from single-particle lattices hosting a mix of flat and dispersive bands, and equipped with fine-tuned two–body interactions. Fine-tuning of the interaction results in an extensive set of local conserved charges and a fragmentation of the Hilbert space into irreducible sectors. In each sector, the conserved charges originate from the flatband and act as an effective disorder inducing a transition between ergodic and localized phases upon variation of the interaction strength. Such fine-tuning is possible in arbitrary lattice dimensions and for any many-body statistics. We present computational evidence for this transition with spinless fermions.

An approximate analytical solution of the boundary slip problem in magnetic field is obtained by using the general form of boundary conditions for the distribution function of fermions with the isotropic energy spectrum. Exact numerical calculations of the slip length for different models of angle-dependent specularity parameter and application of the results to the description of the Poiseuille flow demonstrate the reliability of the approximate solution for establishing a direct link between the hydrodynamic and the kinetic approaches to transport in bounded fermion systems.

Thermal conductivity is the key factor affecting thermoelectric properties of materials. Here, machine-learning techniques combined with first-principles calculations are used to identify the cubic halide perovskites ${\text{Cs}B\text{Br}}_3$ (B = Ca, Cd, and Sn) with ultralow thermal conductivity. Based on the Boltzmann transport equation within the relaxation time approximation, we demonstrate this type of perovskites have remarkably low lattice thermal conductivities ${\kappa }_L\sim 0.4-1$ W/mK at 300 K. We employ the self-consistent phonon theory incorporating both cubic and quartic anharmonicity, which is considered from the bubble and loop self-energy diagrams rather than many-body perturbation theory. We show that the approach yields a cubic-tetragonal phase transition of ${\mathrm{CsCaBr}}_3$ at temperature $T_c=226-265\mathrm{K}$, in good agreement with the experimental value of 239 K. An anomalously temperature dependence of ${\kappa }_L$ is observed in ${\mathrm{CsCdBr}}_3$, where the coherent term account for 26% of the total lattice thermal conductivity. We also demonstrate that the hardening of vibrations in low-lying phonon modes offset the phonon population effect as temperature increases by reducing the available phase space.