We develop a supervised machine learning algorithm that is able to learn topological phases of finite condensed-matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector ensembling procedure. We combine our algorithm with decision trees and random forests to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from bulk lattice data in real space and show how the Shannon information entropy of ensembles of lattice eigenvectors can be used to retrieve a signal detailing how topological information is distributed in the bulk. We further use insights obtained from these information entropy signatures to engineer global topological features from real-space lattice data that still carry most of the topological information in the lattice, while greatly diminishing the size of feature space, thus effectively amounting to a topological lattice compression. Finally, we explore the theoretical possibility of interpreting the information entropy topological signatures in terms of emergent information entropy wave functions, which lead us to Heisenberg and Hirschman uncertainty relations for topological phase transitions. The discovery of Shannon information entropy signals associated with topological phase transitions from the analysis of data from several thousand SSH systems illustrates how model explainability in machine learning can advance the research of exotic quantum materials with properties that may power future technological applications such as qubit engineering for quantum computing.

In this work we show the existence of closure domains in ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ thin films featuring a striped magnetic pattern and study the effect of the magnetic domain arrangement on the magnetotransport properties. By means of x-ray resonant magnetic scattering, we experimentally demonstrate the presence of such closure domains and also estimate their sizes and relative contribution to surface magnetization. Magnetotransport experiments show that the behavior of the magnetoresistance depends on the measurement geometry as well as on the temperature. When the electric current flows perpendicular to the stripe direction, the resistivity decreases when a magnetic field is applied along the stripe direction (negative magnetoresistance) in all the studied temperature range. Transport calculations in the Ohmic regime indicate that the main source is the anisotropic magnetoresistance. In the case of current flowing parallel to the stripe domains, the magnetoresistance changes sign, being positive at room temperature and negative at 100 K. An intrinsic magnetoresistant contribution arising from the domain walls appears as the most plausible explanation for the observed behavior. We have put in evidence the importance of using x-ray resonant magnetic scattering for the determination of thin-film properties related with the magnetic structure.

We theoretically study the magnetic response of a superconductor/ferromagnet/normal-metal strip in an in-plane Fulde-Ferrell (FF) state. We show that unlike an ordinary superconducting strip, the FF strip can be switched from diamagnetic to paramagnetic and then back to a diamagnetic state by increasing the perpendicular magnetic field. Being in a paramagnetic state, the FF strip exhibits a magnetic field driven second-order phase transition from the FF state to the ordinary state without spatial modulation along the strip. We argue that the global paramagnetic response is connected with a peculiar dependence of the sheet superconducting current density on supervelocity in the FF state, and it exists in the nonlinear regime.

By measuring the polarization changes in terahertz, infrared, and visible radiation over an extended energy range (3–2330 meV), we observe symmetry breaking in cuprate high-temperature superconductors over wide energy, doping, and temperature ranges. We measure the polarization rotation $\left(\mathrm{Re}\left[{\theta }_{\mathrm{F}}\right]\right)$ and ellipticity $\left(\mathrm{Im}\left[{\theta }_{\mathrm{F}}\right]\right)$ of transmitted radiation through thin films as the sample is rotated. We observe a twofold rotational symmetry in ${\theta }_{\mathrm{F}}$, which is associated with linear dichroism (LD) and occurs when electromagnetic radiation polarized along one direction is absorbed more strongly than radiation polarized in the perpendicular direction. Such polarization anisotropies can be generally associated with symmetry breakings. We measure the amplitude of the LD signal and study its temperature, energy, and doping dependence. The LD signal shows a resonant behavior with a peak in the few hundred meV range, which is coincident with the midinfrared optical feature that has been associated with the formation of the pseudogap state. The strongest LD signal is found in underdoped films, although it is also observed in optimally and overdoped samples. The LD signal is consistent with an electronic nematic order which is decoupled from the crystallographic axes as well as novel magnetoelectric effects.

Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [Phys. Rev. B 93, 014203 (2016)] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions—so-called “bubbles”—resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states, we demonstrate the stability of many-body localization with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in the Bose-Hubbard model.

Quasicrystals can be described as projections of sections of higher dimensional periodic lattices into real space. The image of the lattice points in the projected-out dimensions, called the perpendicular space, carries valuable information about the local structure of the real space lattice. In this paper, we use perpendicular space projections to analyze the elementary excitations of a quasicrystal. In particular, we consider the vertex tight-binding model on the two-dimensional Penrose lattice and investigate the properties of strictly localized states using their perpendicular space images. Our method reproduces the previously reported frequencies for the six types of localized states in this model. We also calculate the overlaps between different localized states and show that the number of type-five and type-six localized states which are independent from the four other types is a factor of golden ratio $\tau =(1+\sqrt{5})/2$ higher than previously reported values. Two orientations of the same type-five or type-six which are supported around the same site are shown to be linearly dependent with the addition of other types. We also show through exhaustion of all lattice sites in perpendicular space that any point in the Penrose lattice is either in the support of at least one localized state or is forbidden by local geometry to host a strictly localized state.

Using high resolution superconducting quantum interference device magnetometry we have made detailed measurements of the waiting time effect of the thermoremanent magnetization (TRM) decays on a single-crystal $\mathrm{Cu}\mathrm{Mn}(6\%)$ spin-glass sample near $T_g$. We have systematically mapped the rapid decrease of the characteristic timescale ${\mathrm{tw}}_{\mathrm{eff}}$, approaching $T_g$ from below, for waiting times ranging from 100 to 100 000 s. Using ${\mathrm{tw}}_{\mathrm{eff}}$ to determine the length scale of the growth of correlations during the waiting time, ${\xi }_{\mathrm{TRM}}$ (observed in both numerical studies and experiment), we observe both growth of ${\xi }_{\mathrm{TRM}}$ in the spin-glass phase and then a rapid reduction very close to $T_g$. We interpret this reduction in ${\xi }_{\mathrm{TRM}}$, for all waiting times, as being governed by the critical correlation length scale ${\xi }_{\mathrm{crit}}=a{(T-T_c)}^{-\nu }$.

X-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) spectroscopy were applied at the Ge (Ga) $L_{2,3}$ edge to unravel the spin-resolved unoccupied electronic states of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (Ga). Complicated spectral features were observed in both XAS and XMCD spectra. For their interpretation, we compared the experimental XAS and XMCD spectra with the calculated Ge (Ga) $4s$ and $4d$ orbital partial density of states. The comparison enabled a qualitative explanation of the XMCD spectra as the difference between the majority- and minority-spin unoccupied density of states summed over the $4s$ and $4d$ orbitals. Our finding provides a new approach to uncover the spin-split partial density of states above the Fermi level.

Second magnetization peak (SMP) in hole-doped cuprates and iron pnictide superconductors has been widely explored. However, similar feature in the family of electron-doped cuprates is not common. Here, we report the vortex dynamics study in the single crystal of an electron-doped cuprate ${\mathrm{Pr}}_{0.87}{\mathrm{LaCe}}_{0.13}{\mathrm{CuO}}_4$ superconductor using dc magnetization measurements. A second magnetization peak feature in the isothermal $M\left(H\right)$ was observed for $H\parallel ab$ planes. On the other hand, no such feature was observed for the $H\parallel c$ axis in the crystal. Using magnetic relaxation data, a detailed analysis of activation pinning energy via collective creep theory suggests an elastic to plastic creep crossover across the SMP. Moreover, for the $H\parallel ab$, a peak in the temperature dependence of critical current density is also observed near 7 K, which is likely be related to a dimensional crossover [three-dimensional–two dimensional (3D-2D)] associated with the emergence of Josephson vortices at low temperatures. The anisotropy parameter obtained $\gamma \approx 8–11$ indicates the 3D nature of vortex lattice mainly for the $H\parallel c$ axis. The $H-T$ phase diagrams for $H\parallel c$ and $H\parallel ab$ are presented.

The intriguing electronic phase diagram involving charge density wave (CDW) transitions in the $\mathrm{Ta}{\mathrm{S}}_2$ system has been widely investigated over the past decade, especially for the $1T$ and $2H$ phases. $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$, regarded as the natural heterostructure that combines the characteristics of $1T$ and $2H\text{−}\mathrm{Ta}{\mathrm{S}}_2$, has also been the focus recently, due to the prospects for fundamental research and device applications. Here, we have systematically investigated the electrical transport properties of $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$ single crystals combined with the band structure calculations and found that the low-temperature phase of candidate chiral superconductor $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$ ($T_c\sim 3.5$ K) at normal state is not the simple CDW but exhibits a strong magnetic field dependence. The most significant result is the emergence of the large magnetoresistance (MR), which may originate from the high mobility of holes and partial compensation. In addition, the symmetry of MR under the low magnetic field has also changed significantly in $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$, which is closely related to the CDW structures formed in the $H$ layers at 22 K. The results are conducive to the understanding of the mechanism of MR appearing in layered CDW compounds, and the presence of MR in $4H_b\text{−}\mathrm{Ta}{\mathrm{S}}_2$ suggests the potential applications for functional devices in the future.

We report transport properties in a ternary compound MoAlB single crystal. It shows a metallic behavior with a residual resistivity ratio of $\rho$(300 K)/$\rho$(2 K)=40. After applied magnetic fields, the resistivity shows a quick upturn and saturates to a plateau as the temperature decreasing. At 2 K, the magnetoresistance (MR) increases quadratically with the magnetic field and reaches up to $1650\%$ ($B=14$ T) without saturation. The two-band fitting of the Hall conductivity suggests that the unsaturated large quadratic MR in MoAlB was originated from the carriers' compensation with high mobility (${\mu }_h=7104{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and ${\mu }_e=1432{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$). The angle dependence of the ${\rho }_{xx}$ shows significant anisotropy. Furthermore, pronounced Shubnikov-de Haas (SdH) oscillations are observed in both magnetoresistivity and Hall resistivity. We analyzed these quantum oscillations carefully and revealed several small Fermi surfaces with the light cyclotron masses in MoAlB. The angle dependence of SdH oscillations reveals quasi-two-dimensional Fermi surface structure in MoAlB.

We design efficient controlled-rotation gates with arbitrary angle acting on three-spin encoded qubits for exchange-only quantum computation. Two pulse sequence constructions are given. The first is motivated by an analytic derivation of the efficient Fong-Wandzura sequence for an exact cnot gate. This derivation, briefly reviewed here, is based on elevating short sequences of swap pulses to an entangling two-qubit gate. To go beyond cnot, we apply a similar elevation to a modified short sequence consisting of swaps and one pulse of arbitrary duration. This results in two-qubit sequences that carry out controlled-rotation gates of arbitrary angle. The second construction streamlines a class of arbitrary cphase gates established earlier. Both constructions are based on building two-qubit sequences out of subsequences with special properties that render each step of the construction analytically tractable.

We theoretically investigate the valley-dependent transmission of particles through a combined electric and magnetic barrier in the $\alpha -T_3$ model which interpolates between the honeycomb and the dice lattices. We show that the combination of the Fabry-Pérot interferences and the magnetic field leads to a perfect transmission for one valley and a suppression of the transmission for the other valley. When only one of the barriers (magnetic or electric) is present, no valley-polarized current can be produced. By tuning the Fermi energy, this valley-dependent peculiar behavior can be used for valley filtering. Our results show that highly efficient valley filtering with maximum polarization can be achieved by controlling the value of the magnetic field and the electric barrier height and width.

Recently, holey graphene (HG) was synthesized successfully at atomic precision with regard to hole size and shape, which indicates that HG has interesting physical and chemical properties for energy and environmental applications. The shaping of the pores also transforms semimetallic graphene into semiconductor HG, which opens new doors for its use in electronic applications. We investigated systematically the structural, electronic, optical, and thermoelectric properties of HG structure using first-principles calculations. HG was found to have a direct band gap of 0.65 eV (PBE functional) and 0.95 eV (HSE06 functional); the HSE06 functional is in good agreement with experimental results. For the optical properties, we used single-shot $G_0{W}_0$ calculations by solving the Bethe-Salpeter equation to determine the intralayer excitonic effects. From the absorption spectrum, we obtained an optical gap of 1.28 eV and a weak excitonic binding energy of 80 meV. We found large values of thermopower of 1662.59 $\mu \mathrm{V}$/K and a better electronic figure of merit, ${ZT}_e$, of 1.13 from the investigated thermoelectric properties. Our investigations exhibit strong and broad optical absorption in the visible light region, which makes monolayer HG a promising candidate for optoelectronic and thermoelectric applications.

The high-frequency transport of a two-dimensional (2D) electron system was investigated by measuring the rf power transmitted through a pair of emitter/detector $\mathsf{T}$-shaped antennas capacitively coupled to the 2D channel. The frequency range covered amounted to 10–100 MHz. The distinctive feature of such a setup is that neither were Ohmic contacts formed to the electron system, nor were metallic pads deposited on the sample surface. We demonstrate that in such an arrangement the microwave-induced resistance oscillations could be observed in case the sample was additionally excited by a microwave radiation of 60–100 GHz frequencies. The amplitude of the first oscillation is clearly comparable to the amplitude of the Shubnikov–de Haas oscillations resolved at relatively high magnetic fields. Furthermore, introducing Ohmic contacts to the 2D channel or pads deposited directly on the sample surface did not alter significantly the amplitude of the detected microwave-induced resistance oscillations.

We observe that in a strongly interacting two-dimensional electron system in ultraclean SiGe/Si/SiGe quantum wells, the resistivity on the metallic side near the metal-insulator transition increases with decreasing temperature, reaches a maximum at some temperature, and then decreases by more than one order of magnitude. We scale the resistivity data in line with expectations for the transport of strongly correlated Fermi systems and find a nearly perfect agreement with theory over a wide range of electron densities.

We study high-harmonic generation in two-dimensional electron systems with Rashba and Dresselhaus spin-orbit coupling and derive harmonic generation selection rules with the help of group theory. Based on the band structures of these minimal models and explicit simulations we reveal how the spin-orbit parameters control the cutoff energy in the high-harmonic spectrum. We also show that the magnetic field and polarization dependence of this spectrum provides information on the magnitude of the Rashba and Dresselhaus spin-orbit coupling parameters. The shape of the Fermi surface can be deduced at least qualitatively and if only one type of spin-orbit coupling is present, the coupling strength can be determined.

A tunable gap in the topological surface state is of great interest for novel spintronic devices and applications in quantum computing. Here, we study the surface electronic structure and magnetic properties of the Gd-doped topological insulator $\mathrm{Tl}{\mathrm{Bi}}_{0.9}{\mathrm{Gd}}_{0.1}{\mathrm{Se}}_2$. Utilizing superconducting quantum interference device magnetometry, we show paramagnetic behavior down to 2 K. Combining spin- and angle-resolved photoemission spectroscopy with different polarizations of light, we demonstrate that the topological surface state is characterized by the Dirac cone with a helical spin structure and confirm its localization within the bulk band gap. By using different light sources in photoemission spectroscopy, various Dirac-point gap values were observed: 50 meV for $h\nu =18\mathrm{eV}$ and 20 meV for $h\nu =6.3\mathrm{eV}$. Here, we discuss the gap observation by the angle-resolved photoemission spectroscopy method as a consequence of the scattering processes. Simulating the corresponding spectral function, we demonstrate that the asymmetric energy-distribution curve of the surface state leads to an overestimation of the corresponding gap value. We speculate that 20 meV in our case is a trustworthy value and attribute this gap to be originated by scattering both on magnetic and charge impurities provided by Gd atoms and surface defects. Given the complexity and importance of scattering processes in the topological surface state together with our observations of distinctive photoemission asymmetry, we believe our results are important for research of the massive Dirac fermions in novel quantum materials.

Studying the local moment and $5f$-electron occupations sheds insight into the electronic behavior in actinide materials. X-ray absorption spectroscopy (XAS) has been a powerful tool to reveal the valence electronic structure when assisted with theoretical calculations. However, the analysis currently taken in the community on the branching ratio of the XAS spectra generally does not account for the hybridization effects between local $f$ orbitals and conduction states. In this paper, we discuss an approach which employs the density functional theory plus Gutzwiller rotationally invariant slave boson method to obtain a local Hamiltonian for the single-impurity Anderson model, and calculates the XAS spectra by the exact diagonalization (ED) method. A customized numerical routine was implemented for the ED XAS part of the calculation. By applying this technique to the recently discovered $5f$-electron topological Kondo insulator $\mathrm{Pu}{\mathrm{B}}_4$, we determined the signature of $5f$-electronic correlation effects in the theoretical x-ray spectra. We found that the Pu $5f-6d$ hybridization effect provides an extra channel to mix the $j=5/2$ and $7/2$ orbitals in the $5f$ valence. As a consequence, the resulting electron occupation number and spin-orbit coupling strength deviate from the intermediate-coupling regime.