A recent experiment on Nb-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ showed that zero field magnetization appears below the superconducting transition temperature. This gives evidence that the superconducting state breaks time-reversal symmetry spontaneously and is possibly in the chiral topological phase. This is in sharp contrast to the Cu-doped case which is possibly in the nematic phase and breaks rotational symmetry spontaneously. By deriving the free energy of the system from a microscopic model, we show that the magnetic moments of the Nb atoms can be polarized by the chiral Cooper pairs and enlarge the phase space of the chiral topological phase compared to the nematic phase. We further show that the chiral topological phase is a Weyl superconducting phase with bulk nodal points which are connected by surface Majorana arcs.

We consider mixed symmetry superconducting phases in Dirac materials in the odd-parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of a finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by peculiar bulk quasiparticles, with Weyl nodes and nodal lines, and distinctive surface states. These findings are consistent with recent experiments on ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ that report evidence of point nodes, nematicity, and TRSB superconductivity induced by Nb magnetic moments.

A link is established between the spin fermion (SF) model of the cuprates and the approach based on the analogy between the physics of doped Mott insulators in two dimensions and the physics of fermionic ladders. This enables one to use nonperturbative results derived for fermionic ladders to move beyond the large-$N$ approximation in the SF model. It is shown that the paramagnon exchange postulated in the SF model has exactly the right form to facilitate the emergence of the fully gapped $d$-Mott state in the region of the Brillouin zone at the hot spots of the Fermi surface. Hence, the SF model provides an adequate description of the pseudogap.

Numerous experiments have reported discrete symmetry breaking in the high-temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, and time-reversal symmetries. In the absence of translational symmetry breaking or topological order, these conventional order parameters cannot explain the gap in the charged fermion excitation spectrum in the antinodal region. Zhao et al. [L. Zhao, D. H. Torchinsky, H. Chu, V. Ivanov, R. Lifshitz, R. Flint, T. Qi, G. Cao, and D. Hsieh, Nat. Phys. 12, 32 (2016)] and Jeong et al. [J. Jeong, Y. Sidis, A. Louat, V. Brouet, and P. Bourges, Nat. Commun. 8, 15119 (2017)] have also reported inversion and time-reversal symmetry breaking in insulating ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ similar to that in the metallic cuprates, but coexisting with Néel order. We extend an earlier theory of topological order in insulators and metals, in which the topological order combines naturally with the breaking of these conventional discrete symmetries. We find translationally invariant states with topological order coexisting with both Ising-nematic order and spontaneous charge currents. The link between the discrete broken symmetries and the topological-order-induced pseudogap explains why the broken symmetries do not survive in the confining phases without a pseudogap at large doping. Our theory also connects to the O(3) nonlinear sigma model and ${\text{CP}}^1$ descriptions of quantum fluctuations of the Néel order. In this framework, the optimal doping criticality of the cuprates is primarily associated with the loss of topological order.

The WHM-type materials ($W=\mathrm{Zr}/\mathrm{Hf}/\mathrm{La}, H=\mathrm{Si}/\mathrm{Ge}/\mathrm{Sn}/\mathrm{Sb}, M=\mathrm{O}/\mathrm{S}/\mathrm{Se}/\mathrm{Te}$) have been predicted to be a large pool of topological materials. These materials allow for fine tuning of spin-orbit coupling, lattice constant, and structural dimensionality for various combinations of $W, H$, and $M$ elements, thus providing an excellent platform to study how these parameters’ tuning affects topological semimetal state. In this paper, we report high field quantum oscillation studies on $\mathrm{ZrGe}M$ ($M=\mathrm{S},\mathrm{Se}$, and Te), from which we have revealed properties consistent with the theoretically predicted topological semimetal states. From the angular dependence of quantum oscillation frequency, we have also studied the Fermi surface topologies of these materials. Moreover, we have compared Dirac electron behavior between the $\mathrm{ZrGe}M$ and $\mathrm{ZrSi}M$ systems, which reveals deep insights to the tuning of Dirac state by spin-orbit coupling and lattice constants in the WHM system.

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as an extension with truncated interactions. While the ground state wave function takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range $r$ and the interaction strength.

In time-dependent density-functional theory, a family of exchange-correlation kernels, known as long-range-corrected (LRC) kernels, have shown promise in the calculation of excitonic effects in solids. We perform a systematic assessment of existing static LRC kernels (empirical LRC, Bootstrap, and jellium-with-a-gap model) for a range of semiconductors and insulators, focusing on optical spectra and exciton binding energies. We find that no LRC kernel is capable of simultaneously producing good optical spectra and quantitatively accurate exciton binding energies for both semiconductors and insulators. We propose a simple and universal, empirically scaled Bootstrap kernel that yields accurate exciton binding energies for all materials under consideration, with low computational cost.

The thermal properties of three transition metal and rare-earth nitride compounds, ScN, YN, and LuN, have been studied using a first principles approach, in which a $\mathrm{DFT}+U$ treatment is guided by accurate hybrid functional calculations of electronic structure. The phonon dispersions for the three compounds show large longitudinal optic–transverse optic (LO-TO) splitting and soft TO modes. The resulting strong anharmonic scattering between acoustic and TO phonons reduces the lattice thermal conductivities, ${\kappa }_{\mathrm{L}}$, of these compounds. The room temperature ${\kappa }_{\mathrm{L}}$ values of YN and LuN are more than an order of magnitude smaller than that found for the weakly polar III-V compound boron bismuth ($350\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$), in spite of the latter having much larger average atomic mass and smaller acoustic phonon velocities. This paper demonstrates the utility of first principles calculations in understanding the thermal properties of materials, and it highlights the importance of optic phonons in reducing ${\kappa }_{\mathrm{L}}$.

The Aharonov-Bohm (AB) effect in square phosphorene quantum rings, with armchair and zigzag edges, is investigated using the tight-binding method. The energy spectra and wave functions of such rings, obtained as a function of the magnetic flux $\mathrm{\Phi }$ threading the ring, are strongly influenced by the ring width $W$, an in-plane electric field $E_p$, and a side-gating potential $V_g$. Compared to a square dot, the ring shows an enhanced confinement due to its inner edges and an interedge coupling along the zigzag direction, both of which strongly affect the energy spectrum and the wave functions. The energy spectrum that is gapped consists of a regular part, of conduction (valence) band states, that shows the usual AB oscillations in the higher- (lower-) energy region, and of edge states, in the gap, that exhibit no AB oscillations. As the width $W$ decreases, the AB oscillations become more distinct and regular and their period is close to ${\mathrm{\Phi }}_0/2$, where the flux quantum ${\mathrm{\Phi }}_0=h/e$ is the period of an ideal circular ring ($W\to 0$). Both the electric field $E_p$ and the side-gating potential $V_g$ reduce the amplitude of the AB oscillations. The amplitude can be effectively tuned by $E_p$ or $V_g$ and exhibits an anisotropic behavior for different field directions or side-gating configurations.

We have used the scanning Kelvin probe microscopy technique to monitor the charging process of highly resistive granular thin films. The sample is connected to two leads and is separated by an insulator layer from a gate electrode. When a gate voltage is applied, charges enter from the leads and rearrange across the sample. We find very slow processes with characteristic charging times exponentially distributed over a wide range of values, resulting in a logarithmic relaxation to equilibrium. After the gate voltage has been switched off, the system again relaxes logarithmically slowly to the new equilibrium. The results cannot be explained with diffusion models, but most of them can be understood with a hopping percolation model, in which the localization length is shorter than the typical site separation. The technique is very promising for the study of slow phenomena in highly resistive systems and will be able to estimate the conductance of these systems when direct macroscopic measurement techniques are not sensitive enough.

The development of novel reflective optical elements is essential to improve the focusing of neutral atomic beams. The recent availability of commercial thin crystals led to a renewed interest in curved mirrors as reflective elements for He microscopy. We have investigated the reflectivity to incoming He atoms of Cu(111), Ni(111), and Ru(0001) crystals of thickness between 50 and 150 $\mu \mathrm{m}$. The results have been compared with the ones obtained from bulk crystal surfaces. Our study reveals that a 100 $\mu \mathrm{m}$ thick Cu(111) crystal is the best candidate to be employed as a curved mirror, with an absolute reflectivity of 20% and a long-range crystalline order larger than 200 nm. In contrast, much lower reflectivities (3%–14%) have been measured for thin Ni(111) and Ru(0001) crystals. Finally, we show that a thin (100 $\mu \mathrm{m})$ Cu(111) crystal can be bent by an electrostatic field to focus an incoming He beam to a spot of 350 $\mu \mathrm{m}$. Due to the focusing properties of the mirror, a direct beam with less collimation can be used, leading to a larger reflected intensity. The absolute focused intensity is two orders of magnitude larger than previously reported. This represents a big step forward towards achieving the goal of building a high-resolution scanning helium atom microscope.

Using surface x-ray diffraction and scanning tunneling microscopy in combination with first-principles calculations, we have studied the geometric and electronic structure of Cs-deposited ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface kept at room temperature. Two samples were investigated: a single ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystal, whose surface was Ar sputtered and then annealed at $\sim 500{}^{\circ }\mathrm{C}$ for several minutes prior to Cs deposition, and a 13-nm-thick epitaxial ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ film that was not subject to sputtering and was annealed only at $\sim 350{}^{\circ }\mathrm{C}$. In the first case, a considerable fraction of Cs atoms occupy top layer Se atoms sites both on the terraces and along the upper step edges where they form one-dimensional-like structures parallel to the step. In the second case, Cs atoms occupy the $fcc$ hollow site positions. First-principles calculations reveal that Cs atoms prefer to occupy Se positions on the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface only if vacancies are present, which might be created during the crystal growth or during the surface preparation process. Otherwise, Cs atoms prefer to be located in $fcc$ hollow sites in agreement with the experimental finding for the MBE-grown sample.

We report the magnetic and electronic properties of the bilayer ruthenate $\mathrm{S}{\mathrm{r}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$ upon Fe substitution for Ru. We find that $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x\right)}_2{\mathrm{O}}_7$ shows a spin-glass-like phase below 4 K for $x=0.01$ and commensurate E-type antiferromagnetically ordered insulating ground state characterized by the propagation vector ${\mathbf{q}}_{\mathrm{c}}=\left(0.250.250\right)$ for $x\ge 0.03$, respectively, in contrast to the paramagnetic metallic state in the parent compound with strong spin fluctuations occurring at wave vectors $\mathbf{q}=\left(0.0900\right)$ and (0.25 0 0). The observed antiferromagnetic ordering is quasi-two-dimensional with very short correlation length along the $c$ axis, a feature similar to the Mn-doped $\mathrm{S}{\mathrm{r}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$. Our results suggest that this ordered ground state is associated with the intrinsic magnetic instability in the pristine compound, which can be readily tipped by the local magnetic coupling between the $3d$ orbitals of the magnetic dopants and Ru $4d$ orbitals.

Superconductivity in novel bismuth-sulfur superconductors has attracted large research efforts, both experimental and theoretical, but a consensus on the nature of superconductivity in these materials has yet to be reached. Using density functional theory for superconductors, we study the electron-phonon pairing mechanism in ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$. We first confirm the presence of a commensurate charge density wave instability, in accordance with previous studies. Using a recently developed integration scheme for the electron-phonon coupling, we found that its strength is much lower than previously calculated, due to improved density of states calculations. We finally conclude that conventional phonon-mediated pairing cannot explain the high superconducting transition temperatures observed in this material.

It is known that the orbital disordered orthorhombic ($Pnma$) perovskite, $\mathrm{YV}{\mathrm{O}}_3$, undergoes a transition to the $G$-type orbital ordered monoclinic phase $(P{112}_1/a)$ at $T_{G-\mathrm{OO}}\sim 200\mathrm{K}$ followed by a first-order transition to the $C$-type orbital ordered orthorhombic phase ($Pnma$) at $T_S\sim 77\mathrm{K}$. In contrast, using the high-angular-resolution synchrotron x-ray powder diffraction technique, we find that the $C$-type orbital ordered phase appears at $T_N=116\mathrm{K}$ and coexists with the $G$-type monoclinic phase down to $T_S\sim 77\mathrm{K}$. The coexistence of different orbital ordered states in the temperature range $T_S<T<T_N$ is discussed based on large octahedral distortion caused by smaller Y ions present at the $A$ site of the perovskite. Intriguingly, the temperature evolution of the coexistence of the $G$- and $C$-type orbital ordered phases and associated magnetic structures could be responsible for the temperature-induced magnetization reversal observed in the temperature interval $T_S<T<T_N$. We also discuss that the correlation of phase coexistence and magnetization reversal is present in other $R\mathrm{V}{\mathrm{O}}_3$ systems.

We propose an interacting lattice gas model of structural glass characterized by particle distinguishability and site-particle-dependent random nearest-neighboring particle interactions. This incorporates disorder quenched in the configuration space rather than in the physical space. The model exhibits nontrivial energetics while still admitting exact equilibrium states directly constructible at arbitrary temperature and density. The dynamics is defined by activated hopping following standard kinetic Monte Carlo approach without explicit facilitation rule. Kinetic simulations show emergent dynamic facilitation behaviors in the glassy phase in which motions of individual voids are significant only when accelerated by other voids nearby. This provides a microscopic justification for the dynamic facilitation picture of structural glass.

We investigate the energetic stability and the structural and electronic properties of semiconductor/semiconductor and semiconductor/metal 2D van der Waals heterostructures composed by combinations of single layer InSe, bilayer phosphorene (BP), and graphene. For the semiconductor/semiconductor BP/InSe heterostructure, we found that the lowest (highest) unoccupied (occupied) states lie on the InSe (BP) layers, giving rise to a type-II band alignment, with electrons (holes) localized in the InSe (BP) layers. The semiconductor/metal interface composed by a single layer of InSe stacked on graphene (InSe/G) presents a $n$-type Schottky barrier, which can be tuned by applying an external electric field perpendicular to the InSe/G interface ($E_{\perp }^{\mathrm{ext}}$). Upon further increase of $E_{\perp }^{\mathrm{ext}}$, the InSe/G contact becomes Ohmic, promoting a net charge transfer from the graphene sheet to the InSe layer, $n$-type doping. This is in contrast with the other semiconductor/metal van der Waals heterojunction, BP/G, where the BP sheet becomes $p$-type doped as a function of $E_{\perp }^{\mathrm{ext}}$. Exploiting the electron-hole separation in BP/InSe, and the formation of Ohmic contacts at the InSe/G and BP/G interfaces, we propose a $p-n$ junction composed by $p$-type BP and $n$-type InSe, with the graphene acting as electrodes and also as a source of electrons/holes in InSe/BP.

We report the complex dielectric function of the quasi-one-dimensional chalcogenide ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$, which undergoes a structural phase transition presumably associated with exciton condensation below $T_c=326$ K [Y. Wakisaka et al., Phys. Rev. Lett. 103, 026402 (2009); Y. F. Lu et al., Nat. Commun. 8, 14408 (2017)], and of the isostructural ${\mathrm{Ta}}_2{\mathrm{NiS}}_5$, which does not exhibit such a transition. Using spectroscopic ellipsometry, we have detected exciton doublets with pronounced Fano line shapes in both the compounds. The exciton Fano resonances in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ display an order-of-magnitude higher intensity than those in ${\mathrm{Ta}}_2{\mathrm{NiS}}_5$. In conjunction with prior theoretical work [E. Rashba, Sov. Phys. Semicond. 8, 807 (1975)], we attribute this observation to the giant oscillator strength of spatially extended exciton-phonon bound states in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$. The formation of exciton-phonon complexes in ${\mathrm{Ta}}_2{\mathrm{NiS}}_5$ and ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ is confirmed by the pronounced temperature dependence of sharp interband transitions in the optical spectra, the peak energies and widths of which scale with the thermal population of optical phonon modes. The description of the optically excited states in terms of strongly overlapping exciton complexes is in good agreement with the hypothesis of an exciton insulator ground state.

The complete lattice-layer entanglement structure of Bernal-stacked bilayer graphene is obtained for the quantum system described by a tight-binding Hamiltonian which includes mass and bias voltage terms. Through a suitable correspondence with the parity-spin $SU\left(2\right)\otimes SU\left(2\right)$ structure of a Dirac Hamiltonian, when it brings up tensor and pseudovector external field interactions, the lattice-layer degrees of freedom can be mapped into such a parity-spin two-qubit basis which supports the interpretation of the bilayer graphene eigenstates as entangled ones in a lattice-layer basis. The Dirac Hamiltonian mapping structure simply provides the tools for the manipulation of the corresponding eigenstates and eigenenergies of the Bernal-stacked graphene quantum system. The quantum correlational content is then quantified by means of quantum concurrence, in order to have the influence of mass and bias voltage terms quantified, and in order to identify the role of the trigonal warping of energy in the intrinsic entanglement. Our results show that while the mass term actively suppresses the intrinsic quantum entanglement of bilayer eigenstates, the bias voltage term spreads the entanglement in the Brillouin zone around the Dirac points. In addition, the interlayer coupling modifies the symmetry of the lattice-layer quantum concurrence around a given Dirac point. It produces some distortion on the quantum entanglement profile which follows the same pattern of the isoenergy line distortion in the Bernal-stacked bilayer graphene.