We evaluate the spin-density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: A half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot so that the presence or absence of the fractional charge can be deduced from the in-plane spin density. We show that, when the dot is coupled with a magnetized tip, the spatial shift induced in the chemical potential allows for probing these peculiar features.

We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic field traps a Majorana zero mode, so that it can be observed in the gate-voltage-averaged differential conductance $\langle dI/dV\rangle$ as a $4e^2/h$ zero-bias peak above a $(\frac{2}{3}{\pi }^2-4)e^2/h$ background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.

We report a high-field magneto-optical study on first and second subband transitions of single-chirality single-walled carbon nanotubes. The ordering and relative energy splitting between bright and dark excitonic states were found to be inverse between the first and second subbands. We verified that the zero-momentum dark singlet exciton lies below the bright exciton for the first subband transitions, while for the second subband transitions, it was found to have higher energy than the bright excitonic state. The effect of this peculiar excitonic structure was found to manifest itself in distinctive Aharonov-Bohm splitting in ultrahigh magnetic fields up to 190 T.

In transition-metal-doped ZnO the energy position of the dopant 3$d$ states relative to the host conduction and valence bands determines the possibility of long-range ferromagnetism. Density functional theory (DFT) can estimate the energy position of the Co-3$d$ states in ZnO:Co but this depends substantially upon the choice of exchange-correlation functional. In this paper we investigate many-body $GW$ corrections built on top of DFT$+U$ and hybrid-DFT ground states to provide a theoretical benchmark for the quasiparticle energies in wurtzite ZnO:Co. Both single shot $G_0{W}_0$ as well as partially self-consistent $G{W}_0$, wherein the wave functions are held fixed at the DFT level but the eigenvalues in $G$ are iterated, are considered. The predicted energy position of the minority spin Co-$t_2$ states is 3.0–3.6 eV above the ZnO conduction band minimum, which is closer to hybrid-DFT-based estimates. Such an electronic structure does not support carrier-mediated long-range ferromagnetism at achievable $n$-doping conditions.

We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors $\nu =1/q$) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the $Z_2$ properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflect gapless edge states as was discussed by Li and Haldane.

Electrons subjected to a strong spin-orbit coupling in two spatial dimensions could form fractional incompressible quantum liquids without violating the time-reversal symmetry. Here, we construct a Lagrangian description of such fractional topological insulators by combining the available experimental information on potential host materials and the fundamental principles of quantum field theory. This Lagrangian is a Landau-Ginzburg theory of spinor fields, enhanced by a topological term that implements a state-dependent fractional statistics of excitations whenever both particles and vortices are incompressible. The spin-orbit coupling is captured by an external static SU(2) gauge field. The presence of spin conservation or emergent U(1) symmetries would reduce the topological term to the Chern-Simons effective theory tailored to the ensuing quantum Hall state. However, the Rashba spin-orbit coupling in solid-state materials does not conserve spin. We predict that it can nevertheless produce incompressible quantum liquids with topological order but without a quantized Hall conductivity. We discuss two examples of such liquids whose description requires a generalization of the Chern-Simons theory. One is an Abelian Laughlin-type state, while the other has a new kind of non-Abelian many-body entanglement. Their quasiparticles exhibit fractional spin-dependent exchange statistics, and have fractional quantum numbers derived from the electron's charge and spin according to their transformations under time reversal. In addition to conventional phases of matter, the proposed topological Lagrangian can capture a broad class of hierarchical Abelian and non-Abelian topological states, involving particles with arbitrary spin or general emergent SU(N) charges.

To acquire knowledge on the lattice and grain boundary diffusion processes in alumina, we have determined the activation energies of elementary O and Al diffusive jumps in the bulk crystal, Σ3(0001) grain boundaries, and Σ3($10\overline{1}0$) grain boundaries of α-Al${}_2$O${}_3$ using the first-principles density functional theory method. Specifically, we calculated the activation energies for four elementary jumps of both O and Al lattice diffusion in alumina. It was predicted that the activation energy of O lattice diffusion varied from 3.58 to 5.03 eV, while the activation energy of Al lattice diffusion ranged from 1.80 to 3.17 eV. As compared with experimental measurements, the theoretical predictions of the activation energy for lattice diffusion were lower and thus implied that there might be other high-energy diffusive jumps in the experimental alumina samples. Moreover, our results suggested that the Al lattice diffusion was faster than the O lattice diffusion in alumina, in agreement with experiment observations. Furthermore, it was found from our calculations for α-Al${}_2$O${}_3$ that the activation energies of O and Al grain boundary diffusion in the high-energy Σ3(0001) grain boundaries were significantly lower than those of the lattice diffusion. In contrast, the activation energies of O and Al grain boundary diffusion in the low-energy Σ3($10\overline{1}0$) grain boundaries could be even higher than those of the lattice diffusion.

Nonlocal entanglement between two quantum dots (QDs) can be generated through Majorana fermions. The two Majorana fermions at the ends of a one-dimensional topological superconductor form a nonlocal electronic level, which couples the occupation states of the two QDs located close to the two ends and brings the whole system into an entangled state, even at low temperatures and zero bias voltage. Upon introducing a charging energy by a capacitor, entanglement of the whole system can manifest itself through the nonlocal entanglement between the two QDs. Explicitly, the conditional probabilities of electron occupation on one QD with and without electron occupation on the other QD deviate from each other, with the difference proportional to the concurrence of quantum entanglement between the two QDs. Therefore detecting the difference in conditional probabilities, which is achievable experimentally by established techniques, provides evidence of the nonlocal nature of the fermion level constructed by the two end Majorana fermions.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking “clustering” phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the “mixed” role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

We have carried out muon spin relaxation (μSR), neutron diffraction, and inelastic neutron scattering (INS) investigations on polycrystalline samples of Ce(Ru${}_{1-x}$Fe${}_x$)${}_2$Al${}_{10}$ ($x=0$, 0.3, 0.5, 0.8, and 1) to investigate the nature of the ground state (magnetic ordered versus paramagnetic) and the origin of the spin-gap formation as evident from the bulk measurements in the end members. Our zero-field μSR spectra clearly reveal coherent two-frequency oscillations at low temperature in $x=0$, 0.3, and 0.5 samples, which confirm the long-range magnetic ordering of the Ce moment with Nèel temperature T${}_{\mathrm{N}}=27$, 26, and 21 K, respectively. On the other hand, the μSR spectra of $x=0.8$ and $x=1$ down to 1.4 K and 0.045 K, respectively, exhibit a temperature-independent Kubo-Toyabe term, confirming a paramagnetic ground state. The long-range magnetic ordering in $x=0.5$ below 21 K has been confirmed through the neutron diffraction study. INS measurements of $x=0$ clearly reveal the presence of a sharp inelastic excitation near 8 meV between 5 K and 26 K, due to an opening of a gap in the spin excitation spectrum, which transforms into a broad response at and above 30 K. Interestingly, at 4.5 K, the spin-gap excitation broadens in $x=0.3$ and exhibits two clear peaks at 8.4(3) and 12.0(5) meV in $x=0.5$. In the $x=0.8$ sample, which remains paramagnetic down to 1.2 K, there is a clear signature of a spin gap of 10–12 meV at 7 K, with a strong wave-vector–dependent intensity. Evidence of a spin gap of 12.5(5) meV has also been found in $x=1$. The observation of a spin gap in the paramagnetic samples ($x=0.8$ and 1) is an interesting finding in this study, and it challenges our understanding of the origin of the semiconducting gap in Ce$T_2$Al${}_{10}$ ($T$ = Ru and Os) compounds in terms of a hybridization gap opening only a small part of the Fermi surface, gapped spin waves, or a spin-dimer gap.

We theoretically study the acoustic phonon limited mobility in $n$-doped two-dimensional MoS${}_2$ for temperatures $T<100$ K and high carrier densities using the Boltzmann equation and first-principles calculations of the acoustic electron-phonon (el-ph) interaction. In combination with a continuum elastic model, analytic expressions and the coupling strengths for the deformation potential and piezoelectric interactions are established. We furthermore show that the deformation potential interaction has contributions from both normal and umklapp processes and that the latter contribution is only weakly affected by carrier screening. Consequently, the calculated mobilities show a transition from a high-temperature $\mu \sim T^{-1}$ behavior to a stronger $\mu \sim T^{-4}$ behavior in the low-temperature Bloch-Grüneisen regime characteristic of unscreened deformation potential scattering. Intrinsic mobilities in excess of ${10}^5$ cm${}^2$ V${}^{-1}$ s${}^{-1}$ are predicted at $T<10$ K and high carrier densities ($n\gtrsim {10}^{11}$ cm${}^{-2}$). At 100 K, the mobility does not exceed $\sim 7\times {10}^3$ cm${}^2$ V${}^{-1}$ s${}^{-1}$. Our findings provide new and important understanding of the acoustic el-ph interaction and its screening by free carriers, and is of high relevance for the understanding of acoustic phonon-limited mobilities in general.

Motivated by the recent advances in studying Majorana states in nanowires under conditions of the superconducting proximity effect, we address the correspondence between the common topological transition in an infinite system and a topological transition of another type that manifests itself in the positions of the poles of the scattering matrices. We establish a universal dependence of the pole positions in the vicinity of the common transition on the parameter controlling the transition, and discuss the manifestations of the pole transitions in the differential conductance.

The close-packed (111) surface of gold is well known to show a $22\times \sqrt{3}$ reconstruction on single nm lengths with a long-range herringbone pattern on scales of a few hundred nm. Here we investigate the local reconstruction using density functional theory and compare the results to scanning tunneling microscopy experiments. Moreover, we use hydrogen and fluorine as probe atoms to investigate changes in the ability of the Au(111) surface to catalyze the reactions involved in the formation of molecular nanostructures. We find a small variation of the reactivity across different surface sites and link those results to the local coordination environment of the face-centered-cubic (fcc), hexagonal-close-packed (hcp), and ridge regions. Finally, we scrutinize a commonly used approximation in density functional studies, namely that Au(111) is atomically flat and a perfect termination of the fcc lattice.

We provide ab initio characterization of the negatively charged substitutional nickel (Ni${}_s^{-}$) impurity in diamond using a hybrid density functional calculation. Ni${}_s^{-}$ is shown to carry a spin $S=3/2$. The calculated hyperfine couplings on this defect support the identification of the W8 electron paramagnetic resonance center with Ni${}_s^{-}$ defect. We unambiguously determine the position of the Ni${}_s^{-}$ acceptor level in the gap. This level is located at about 2.0 eV above the valence band maximum and corresponds to a totally occupied triplet state responsible for the magnetization. We calculated the excited state properties of the defect. Our results may resolve the controversial assignments of Ni${}_s^{-}$ to different optical centers.

In this paper, we investigate the thermoelectric performance of a double-dot device driven by time-dependently modulated gate voltages. We show that if the modulation frequency $\Omega$ is sufficiently small, not only quantized charge pumping can be realized, but also the heat current flowing in the leads is quantized and exhibits plateaux in units of $\frac{\Omega }{2\pi }{k}_{\mathrm{B}}T\ln 2$. The factor $\ln 2$ stems from the degeneracy of the double-dot states involved in transport. This opens the possibility of using the pumping cycle to transfer heat against a temperature gradient or to extract work from a hot reservoir with Carnot efficiency. However, the performance of a realistic device is limited by dissipative effects due to leakage currents and finite-frequency operation, which we take into account rigorously by means of a generalized master equation approach in the regime where the double dot is weakly coupled to the leads. We show that despite these effects, the efficiency of a double-dot charge pump performing work against a dc source can reach of up to 70$\%$ of the ideal value.

Uranium sulfide belongs to a class of uranium monochalcogenides that crystallize in the rocksalt structure and exhibit ferromagnetism at low temperature. The magnetism is believed to play a role in the low-temperature rhombohedral distortion, possibly due to its large magnetic anisotropy. We have performed electrical and structural characterization along with density-functional theory calculations as functions of pressure to help understand the interplay between structure and magnetism in US. Theoretical calculations suggest that ferromagnetic order is responsible for the small distortion at ambient pressure and low temperature. Under pressure, the Curie temperature is reduced monotonically until it discontinuously disappears near a pressure-induced deformation of the crystal structure. This high-pressure distortion is identical to the one correlated with the onset of magnetic order, but with a larger change in the cell angle. Calculations imply a reduction in the electronic band energy as the driving force for the pressure-induced structure, but the loss of magnetic order associated with this distortion remains a mystery. The high-pressure electronic phase diagram may shed light on the magnetostructural free energy landscape of US.

The powerful terahertz emission from intrinsic Josephson junctions in high-$T_c$ cuprate superconductors has been detected recently. The synchronization of different junctions is enhanced by excitation of the geometrical cavity resonance. A key characteristic of the radiation is its linewidth. In this work, we study the intrinsic linewidth of the radiation near the internal cavity resonance. Surprisingly, this problem was never considered before, neither for a single Josephson junction nor for a stack of the intrinsic Josephson junctions realized in cuprate superconductors. The linewidth appears due to the slow phase diffusion, which is determined by the dissipation and amplitude of the noise. We found that both these parameters are resonantly enhanced when the cavity mode is excited but enhancement of the dissipation dominates leading to the net suppression of diffusion and dramatic narrowing of the linewidth. The line shape changes from Lorentzian to Gaussian when either the Josephson frequency is shifted away from the resonance or the temperature is increased.

We show that the normal state transport properties of nanoscale granular aluminum films, near the metal to insulator transition, present striking similarities with those of Kondo systems. Those include a negative magnetoresistance, a minimum of resistance $R$ at a temperature $T_m$ in metallic films, a logarithmic rise at low temperatures, and a negative curvature of $R\left(T\right)$ at high temperatures. These normal state properties are interpreted in terms of spin-flip scattering of conduction electrons by local magnetic moments, possibly located at the metal/oxide interfaces.