We present general quantum mechanical expressions for higher-order moments, cumulants, and spectra of continuously measured quantum systems with applications in spin noise spectroscopy, quantum transport, and measurement theory in general. Starting from the so-called stochastic master equation of continuous measurement theory, we find that the leading orders of the fluctuating detector output $z\left(t\right)$ with respect to the measurement strength $\beta$ are a white shot noise background, a constant measurement offset, and the leading order quantum noise of the measured operator $A$. Starting from quantum expressions for the multitime moments $\langle z\left(t_n\right)\cdots z\left(t_1\right)\rangle$ we derive three- and four-time cumulants that are valid in all orders of $\beta$ covering the full regime between the weak- and strong-measurement limit (Zeno limit). Intriguingly, quantum expressions for the cumulants were found that exhibit the same simple structure as those for the moments after introduction of only a slightly modified system propagator. Very compact expressions for the cumulant-based third- and fourth-order spectra (bispectrum and trispectrum) follow naturally. We illustrate the usefulness of higher-order spectra by treating a real-world two-spin system with strong hyperfine interaction. Moreover, spin noise spectroscopy is shown to have the potential for investigating the transition from weak measurements to the famous quantum Zeno regime for realistic probe laser intensities.

Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just a few atoms thick and its very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi-one-dimensional systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a boron nitride substrate affects the electronic properties of graphene nanoribbons. We consider both armchair and zigzag nanoribbons. Our results show that for some stacking configurations the boron nitride can significantly affect the electronic structure of the ribbons. In particular, for zigzag nanoribbons, due to the lock between spin and sublattice degree of freedom at the edges, the hexagonal boron nitride can induce a very strong spin splitting of the spin-polarized, edge states. We find that such spin splitting can be as high as 40 meV.

Ab initio nonequilibrium Keldysh formalism based on an $N$-order renormalization technique is used to compute $I\left(V\right)$ ballistic electron emission microscopy characteristics at the Au/Ge(001) interface. Such a formalism quantitatively reproduces precise experimental measurements under ultrahigh vacuum and low-temperature conditions. At $T=0$ K, the ballistic current follows the law ${(V-V_{\mathrm{SB}})}^{2.1}$, $V_{\mathrm{SB}}$ being the Schottky barrier. At $T>0$ K, temperature effects become significant near the onset and must be taken into account to identify an accurate value for $V_{\mathrm{SB}}$ from a best-fit procedure. We find two values for $V_{\mathrm{SB}}$, 0.67 and 0.75 eV, which we associate with two different atomic registries at the interface.

Topological states of matter in non-Hermitian systems have attracted a lot of attention due to their intriguing dynamical and transport properties. In this paper, we propose a periodically driven non-Hermitian lattice model in one dimension, which features rich Floquet topological phases. The topological phase diagram of the model is derived analytically. Each of its non-Hermitian Floquet topological phases is characterized by a pair of integer winding numbers, counting the number of real zero- and $\pi$-quasienergy edge states at the boundaries of the lattice. Non-Hermiticity-induced Floquet topological phases with unlimited winding numbers are found, which allow arbitrarily many real zero- and $\pi$-quasienergy edge states to appear in the complex quasienergy bulk gaps in a well-controlled manner. We further suggest probing the topological winding numbers of the system by dynamically imaging the stroboscopic spin textures of its bulk states.

The Burgers distortion is a two-stage transition between bcc and hcp structures. Refractory metal elements from the Sc and Ti columns of the periodic table (bcc/hcp elements) form bcc structures at high temperatures but transition to hcp at low temperatures via the Burgers distortion. Elements of the V and Cr columns, in contrast, remain bcc at all temperatures. The energy landscape of bcc/hcp elements exhibits an alternating slide instability, while the normal bcc elements remain stable as bcc structures. This instability is verified by the presence of unstable elastic constants and vibrational modes for bcc/hcp elements, while those elastic constants and modes are stable in bcc elements. We show that a pseudogap opening in the density of states at the Fermi level drives the Burgers distortion in bcc/hcp elements, suggesting the transition is of the Jahn-Teller-Peierls type. The pseudogap lies below the Fermi level for regular bcc elements in the V and Cr columns of the periodic table. The wave vector ${\mathbf{k}}_S$ when the gap opens relates to the reciprocal lattice vector $\mathbf{G}=\left(1\frac{1}{2}\frac{1}{2}\right)$ of the distorted bcc structure as ${\mathbf{k}}_S=\frac{1}{2}\mathbf{G}$. The bcc binary alloys containing both bcc/hcp and bcc elements exhibit a similar instability but stabilize part way through the bcc to hcp transition.

Magnetic skyrmions have significant potential for applications in storage and logic devices, but the ability to control skyrmion motion is key to their success. To realize controlled skyrmion motion, vertical spin current-driven methods employing, e.g., the spin Hall or inverse spin galvanic effect, are efficient; thus, magnetic heterostructures featuring large spin-orbit torques are appealing. In this paper, we report on the observation of room-temperature magnetic skyrmions in Pt/Co/W multilayers. The interfacial Dzyaloshinskii-Moriya interaction was estimated to be $0.19\pm 0.05\mathrm{mJ}/{\mathrm{m}}^2$ based on the asymmetric domain-wall motion occurring upon the application of in-plane magnetic fields. The evolution of the magnetic structures from labyrinth domains to skyrmions with diameters of around 145 nm under magnetic fields was observed by performing Lorentz transmission electron microscopy. The skyrmion nucleation fields could be tuned by varying the repetition number. Large spin Hall angle systems such as Pt/Co/W multilayers are appealing for achieving current-driven skyrmion motion in future racetrack and logic applications.

We study the ground state and low-energy subgap excitations of a finite wire of a time-reversal-invariant topological superconductor (TRITOPS) with spin-orbit coupling. We solve the problem analytically for a long chain of a specific one-dimensional lattice model in the electron-hole symmetric configuration and numerically for other cases of the same model. We present results for the spin density of excitations in long chains with an odd number of particles. The total spin projection along the axis of the spin-orbit coupling $S_z=\pm 1/2$ is distributed with fractions $\pm 1/4$ localized at both ends and shows even-odd alternation along the sites of the chain. We calculate the localization length of these excitations and find that it can be well approximated by a simple analytical expression. We show that the energy $E$ of the lowest subgap excitations of the finite chain defines tunneling and entanglement between end states. We discuss the effect of a Zeeman coupling ${\mathrm{\Delta }}_Z$ on one of the ends of the chain only. For ${\mathrm{\Delta }}_Z<E$, the energy difference of excitations with opposite spin orientation is ${\mathrm{\Delta }}_Z/2$, consistent with a spin projection $\pm 1/4$. We argue that these physical features are not model dependent and can be experimentally observed in TRITOPS wires under appropriate conditions.

It was recently reported in experiments that at temperatures below 2500 K liquid nitrogen (N) remains molecular up to 120 GPa [Phys. Rev. Lett. 119, 235701 (2017)], which contradicts a liquid-liquid transition at 88 GPa and 2000 K predicted by PBE-GGA density functional. To clarify this, we perform extensive first principles molecular dynamics using SCAN meta-GGA density functional, which captures the intermediate-range part of the van der Waals interaction better than PBE-GGA. It is found that SCAN gives more accurate bond energy and length of an isolated ${\mathrm{N}}_2$ molecule than PBE. SCAN, as well as PBE, is capable of reproducing the first-order molecular-to-polymeric phase transition, but in contrast to PBE, it predicts a wider stability range for fluid ${\mathrm{N}}_2$. The boundary of this range is 15 GPa higher than the one predicted with PBE, which is in closer agreement with experiments. In addition, SCAN predicts a higher amount of threefold coordinated atoms in the polymeric phase than PBE, which is expected from experiments in amorphous N. These improvements indicate that SCAN is more accurate than PBE in predicting the phase transition from molecular to polymeric fluid N.

We studied single crystals of orthorhombic ${\mathrm{Sr}}_2{\mathrm{VO}}_4$ containing spin-singlet dimers of ${\mathrm{V}}^{4+}\left(3d^1\right)$ and those with Ti or Nb substituted for V. We found that both Ti and Nb dopings induce the evolution of a Curie-Weiss component in the magnetic susceptibility, but the rate of evolution with doping is several times higher for Nb doping. We also found that Nb doping induces the conduction of $d$ electrons. These results can be explained by the hybridization of the Nb $4d$ states with the $3d$ states of the neighboring V ions, possibly causing rearrangement of the $d$ electron in the doubly degenerate $e$ states in the V ion.

Cobalt $L$-edge x-ray absorption spectra (XAS) and x-ray magnetic circular dichroism (XMCD) of ${\mathrm{CoS}}_2$ have been measured at low temperature (4 K) in order to characterize the electronic and magnetic structure with a significant improvement in resolution as compared with previous measurements. The branching ratio of $L_3$ and $L_2$ x-ray absorption near-edge spectra was found to be consistent with a low-spin configuration ($S=1/2$). A total magnetic moment $〈m〉=0.78{\mu }_B$/Co atom with the orbital part $〈m_l〉=0.049{\mu }_B$ has been obtained from the XMCD signal, consistent with the nearly half-metallic character of ${\mathrm{CoS}}_2$ and with the itinerant nature of the ferromagnetism. The behavior under pressure of ${\mathrm{CoS}}_2$ was studied by Co $K$-edge XAS and XMCD experiments performed up to a pressure of about 30 GPa using diamond-anvil cell at a temperature of 10 K. No evidence of structural phase transition was observed, while the intensity of the XMCD signal was found to decrease continuously for increasing pressures, becoming negligible in the $8\sim 10$ GPa pressure range, a fact consistent with the collapse of itinerant ferromagnetic ordering. The gradual change in the electronic and magnetic structure upon application of pressure was also monitored by the near-edge XAS evolution, found to be in agreement with full multiple-scattering calculations under uniform contraction of distances, and by the blue-shift of the $K$-edge energy. The Co $K$-edge energy was found to shift to higher energies (up to 0.64 eV at 30 GPa) and a change of slope was observed at pressures around 5 GPa that may correspond to the disappearance of half-metallicity, in agreement with previous studies.

We show that superconducting correlations in the presence of nonzero condensate velocity can mediate the peculiar interaction between localized spins that breaks the global inversion symmetry of magnetic moments. The proposed interaction mechanism is capable of removing fundamental degeneracies between topologically distinct magnetic textures. For the generic system of three magnetic impurities in the current-carrying superconductor, we find the energy term proportional to spin chirality. In realistic superconductor/ferromagnetic/superconductor setups we reveal significant energy differences between various magnetic textures with opposite chiralities. We calculate Josephson energies of junctions through left- and right-handed magnetic helices as well as through the magnetic skyrmions with opposite topological charges. Relative energy shifts between otherwise degenerate magnetic textures in these setups are regulated by the externally controlled Josephson phase difference. The suggested low-dissipative manipulation with the skyrmion position in a racetrack geometry can be used for advanced spintronics applications.

We study the dynamical process of equilibration of topological properties in quantum many-body systems undergoing a parameter quench between two topologically inequivalent Hamiltonians. This scenario is motivated by recent experiments on ultracold-atomic gases, where a trivial initial state is prepared before the Hamiltonian is ramped into a topological insulator phase. While the many-body wave function must stay topologically trivial in the coherent postquench dynamics, here we show how the topological properties of the single-particle density matrix dynamically change and equilibrate in the presence of interactions. In this process, the single-particle density matrix goes through a characteristic level crossing as a function of time, which plays an analogous role to the gap closing of a Hamiltonian in an equilibrium topological quantum phase transition. As an exact case study exemplifying this mechanism, we numerically solve the quench dynamics of an interacting one-dimensional topological insulator.

The local $Z_N$ quantized Berry phase for the $\mathrm{SU}\left(N\right)$ antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local $Z_2$ Berry phase for SU(2) symmetry, has a direct correspondence to the number of singlet pairs spanning a particular bond, and is effective as a tool to characterize and classify the various symmetry-protected topological phases of one-dimensional $\mathrm{SU}\left(N\right)$ spin systems. We extend the path-integral quantum Monte Carlo method for the $Z_2$ Berry phase in order to calculate the $Z_N$ Berry phase numerically. We demonstrate our method by calculating the $Z_4$ Berry phase for the bond-alternating $\mathrm{SU}\left(4\right)$ antiferromagnetic Heisenberg chain, which is represented by the Young diagram of four columns.

We present a fragment-based many-body Green's function method suitable for treating large molecular systems in heterogeneous polarizable environments. The Green's function for a total system is approximated from fragment Green's functions and is expanded up to two-body terms. The screened Coulomb potential is approximated from the sum of intrafragment density-response functions, with interfragment polarization terms being neglected. The approximations for the Green's function and screened Coulomb potential lead to a many-body expansion of the self-energy. This expansion is essentially equivalent to the many-body expansion of the Fock matrix in the fragment molecular orbital method. To handle large molecular systems, the present implementation relies on the Coulomb hole plus screened exchange (COHSEX) approximation for the $GW$ self-energy. The accuracy of the FMO-COHSEX method was demonstrated in comparison to conventional COHSEX results for organic molecular aggregates. We confirmed that the present fragmentation approximation can provide reasonably accurate results, and mean absolute errors for quasiparticle energies of less than 0.1 eV have been achieved for valence orbitals. We also assessed the accuracy of the COHSEX approximation to describe the effects of molecular aggregation of electronic states, by comparing them with the $GW$ method. The COHSEX approximation has been shown to successfully describe the induced polarization and dispersion effects. As an illustrative application of the present method, we considered the electronic states of the pentacene thin film, which contains 1476 atoms. We investigated the impact of the induced polarization effect in the heterogeneous environment, highlighting the gap renormalization and the polarization-induced localization. This application shows that the present fragment-based method is useful for studying electronic structures of molecular aggregates in complex environments.

The dynamic polarization of nuclear spins interacting with resident electrons under resonant excitation of trions is studied in a nominally undoped GaAs/(Al,Ga)As quantum well. Unlike in common time-resolved pump-probe techniques, we used a single-beam approach in which the excitation light is modulated between the circular and linear polarization states. The time-integrated intensity of the excitation laser reflected from the sample surface, proportional to the optical generation rate and changing due to the pumping of the resident electrons, is detected. Polarized electrons, on the other hand, transfer their spin to the lattice nuclei via the hyperfine interaction. Exciting the sample with a train of pulses in an external magnetic field leads to resonant spin amplification observed when the Larmor precession frequency is synchronized with the laser pulse repetition rate. A buildup of the nuclear spin polarization causes a shifting of the resonant spin amplification peaks since the resulting nuclear field alters the strength of the external magnetic field experienced by the electrons. It was established that the nuclear spin polarization time $T_1$ is temperature dependent and, owing to the electron localization at lower temperatures, becomes shorter. “Locking” of the nuclear (Overhauser) field in the oblique external magnetic field, related to the anisotropy of the electron $g$ factor, was observed. The $g$ factor ratio between the in-plane ($g_{\parallel }$) and out-of-plane ($g_{\perp }$) components was estimated to be $g_{\perp }/g_{\parallel }=1.3$.

We study transport across either a potential or a magnetic barrier which is placed on the top surface of a three-dimensional thin topological insulator (TI). For such thin TIs, the top and bottom surfaces interact via a coupling $\lambda$ which influences the transport properties of junctions constructed out of them. We find that for junctions hosting a potential barrier, the differential conductance oscillates with the barrier strength. The period of these oscillations doubles as the coupling $\lambda$ changes from small values to a value close to the energy of the incident electrons. In contrast, for junctions with a magnetic barrier, the conductance approaches a nonzero constant as the barrier strength is increased. This feature is in contrast to the case of transport across a single TI surface where the conductance approaches zero as the strength of a magnetic barrier is increased. We also study the spin currents for these two kinds of barriers; in both cases, the spin current is found to have opposite signs on the top and bottom surfaces. Thus this system can be used to split applied charge currents to spin currents with opposite spin orientations which can be collected by applying opposite spin-polarized leads to the two surfaces. We show that several of these features of transport across finite width barriers can be understood analytically by studying the $\delta$-function barrier limit. We discuss experiments which may test our theory.

Motivated by the recent development of fast and ultrasensitive thermometry in nanoscale systems, we investigate quantum calorimetric detection of individual heat pulses in the sub-meV energy range. We propose a hybrid superconducting injector-calorimeter setup, with the energy of injected pulses carried by tunneling electrons. It is shown that the superconductor constitutes a versatile injector, with tunable tunnel rates and energies. Treating all heat transfer events microscopically, we analyze the statistics of the calorimeter temperature fluctuations and derive conditions for an accurate measurement of the heat pulse energies. Our results pave the way for fundamental quantum thermodynamics experiments, including calorimetric detection of single microwave photons.

Using the example of a two-dimensional macroscopic model glass in which the interparticle forces can be precisely measured, we obtain strong hints for resolving a controversy concerning the origin of the anomalous enhancement of the vibrational spectrum in glasses (boson peak). Whereas many authors attribute this anomaly to the structural disorder, some other authors claim that the short-range order, leading to washed-out Van Hove singularities, would cause the boson-peak anomaly. As in our model system, the disorder-induced and short-range-order-induced features can be completely separated, we are able to discuss the controversy about the boson peak in real glasses in a new light. Our findings suggest that the interpretation of the boson peak in terms of short-range order only, might result from a coincidence of the two phenomena in the materials studied. In general, as we show, the two phenomena both exist, but are two completely separate entities.