We study analytically and numerically the condensation of a driven-dissipative exciton-polariton system using symmetric nonresonant pumping geometries. We show that the lowest condensation threshold solution carries a definite parity as a consequence of the symmetric excitation profile. At higher pump intensities competition between the two parities can result in critical quenching of one and saturation of the other. Using long pump channels, we show that the competition of the condensate parities gives rise to a different type of topologically stable defect propagating indefinitely along the condensate. The defects display repulsive interactions and are characterized by a sustained wave packet carrying a pair of opposite parity domain walls in the condensate channel.

We present low-temperature magnetotransport measurements on graphene rings encapsulated in hexagonal boron nitride. We investigate phase-coherent transport and show Aharonov-Bohm (AB) oscillations in quasiballistic graphene rings with hard confinement. In particular, we report on the observation of $h/e,h/2e$, and $h/3e$ conductance oscillations. Moreover we show signatures of magnetic focusing effects at small magnetic fields confirming ballistic transport. We perform tight-binding calculations which allow us to reproduce all significant features of our experimental findings and enable a deeper understanding of the underlying physics. Finally, we report on the observation of the AB conductance oscillations in the quantum Hall regime at reasonable high magnetic fields, where we find regions with enhanced AB oscillation visibility with values up to 0.7%. These oscillations are well explained by taking disorder into account allowing for a coexistence of hard- and soft-wall confinement.

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling $t_{\perp }$. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one to two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. The DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.

We report magnetotransport and de Haas–van Alphen (dHvA) effect studies on ${\mathrm{MoP}}_2$ single crystals, predicted to be a type-$\mathrm{II}$ Weyl semimetal with four pairs of robust Weyl points located below the Fermi level and long Fermi arcs. The temperature dependence of resistivity shows a peak before saturation, which does not move with magnetic field. Large nonsaturating magnetoresistance (MR) was observed, and the field dependence of MR exhibits a crossover from semiclassical weak-field $B^2$ dependence to the high-field linear-field dependence, indicating the presence of Dirac linear energy dispersion. In addition, a systematic violation of Kohler's rule was observed, consistent with multiband electronic transport. Strong spin-orbit coupling splitting has an effect on dHvA measurements whereas the angular-dependent dHvA orbit frequencies agree well with the calculated Fermi surface. The cyclotron effective mass $\sim 1.6m_e$ indicates the bands might be trivial, possibly since the Weyl points are located below the Fermi level.

We use density functional calculations to show that heterovalent cation-order sequences enable control over band-gap variations up to several eV and band-gap closure in the bulk band insulator ${\mathrm{LaSrAlO}}_4$. The band-gap control originates from the internal electric fields induced by the digital chemical order, which induces picoscale band bending; the electric-field magnitude is mainly governed by the inequivalent charged monoxide layers afforded by the layered crystal habit. Charge transfer and ionic relaxations across these layers play secondary roles. This understanding is used to construct and validate a descriptor that captures the layer-charge variation and to predict changes in the electronic gap in layered oxides exhibiting antisite defects and in other chemistries.

Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-2 and four period-8 cycles, similar to the Bott periodicity found for topological insulators and superconductors without spatial symmetries. With the help of the dimensional reduction scheme, the classification in arbitrary dimensions $d\ge 1$ can be obtained from the classification in one dimension, for which we present a derivation based on relative homotopy groups and exact sequences to classify one-dimensional insulators and superconductors with reflection symmetry. The resulting classification is fully consistent with a comprehensive classification obtained recently by Shiozaki and Sato [Phys. Rev. B 90, 165114 (2014)]. The use of a scattering-matrix-inspired method allows us to address the second descendant ${\mathbb{Z}}_2$ phase, for which the topological nontrivial phase was previously reported to be vulnerable to perturbations that break translation symmetry.

The growth of superconducting order after an interaction quench in a hexagonal lattice is studied. The cases of both time-reversal (TR) preserving graphene, as well as the TR broken Haldane model, are explored. Spin singlet superconducting order is studied where the $s,d+id$, and $d-id$ wave orders are the irreducible representations of the hexagonal lattice. For small quenches, the $d$-wave order parameter grows the fastest, a result also expected when the system is in thermal equilibrium. For the TR symmetry preserving case, the growth rate of the two $d$-wave orders is identical, while the TR-broken case prefers one of the chiral $d$-wave orders over the other, leading to a TR broken topological superconductor. As the interaction quench becomes larger, a smooth crossover is found where eventually the growth rate of the $s$ wave becomes the largest. Thus for large interaction quenches, the $s$ wave is preferred over the $d$ wave for both TR preserving and TR broken systems. This result is explained in terms of the high energy quasiparticles responsible for the dynamics as the interaction quench amplitude grows. The results are relevant for time-resolved measurements that can probe the symmetry of the superconducting fluctuations in a transient regime.

We explore the malleability of ultrasmall metal nanoparticles by means of ab initio calculations. It is revealed that, when strained, such nanoparticles exhibit complex behavior, including bifurcation between slow and fast quakes of their atomic structure, despite being few-body systems. We show the bifurcation to arise from the collapse of the nanoparticle's stiffness and a broken soft-mode symmetry, and that whether a slow or fast quake occurs can be controlled by varying the amplitude of the externally applied strains. We predict that while energy is released abruptly in a fast quake, surprisingly it continues to build up during a slow quake, and that, in common with slow-slip geological earthquakes, the slow nanoparticle quake is a silent precursor to a fast “seismic” quake. We show that electrical conductance and force measurements can detect and distinguish between slow and fast quakes, opening the way for experiments and potential applications of these phenomena.

Magnetic topological semimetals have drawn significant interest since they can combine band topology with intrinsic magnetic order. Here, we propose that ideal Weyl semimetal features can coexist with a ferromagnetic (FM) ground state in a class of compounds with centrosymmetric tetragonal structures. In this magnetic system with inversion symmetry, the direction of magnetization is able to manipulate the symmetry protected band structures from a node-line type to a Weyl one in the presence of spin-orbital coupling. The FM node-line semimetal phase is protected by mirror symmetry with the reflection-invariant plane perpendicular to the magnetic order. Within mirror symmetry breaking due to magnetization along other directions, the gapless node-line loop will degenerate to only one pair of Weyl points protected by rotational symmetry along the magnetic axis, which is largely separated in momentum space. Such a FM Weyl semimetal phase offers a nice platform with a minimum number of Weyl points in a condensed matter system. These findings provide several realistic candidates for the investigation of topological semimetals with time-reversal symmetry breaking, especially demonstrating the use of system symmetry as a powerful recipe for discovering FM Weyl semimetals with attractive features.

Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide a condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder, the Fermi arc gradually loses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. The predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can be directly observed in angle-resolved photoemission spectroscopy (ARPES) and Fourier transformed scanning tunneling microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom, and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of ${\mathbb{Z}}_2$ lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the ${\mathbb{Z}}_2$ slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors, Luttinger liquids, and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem.

We have investigated unusual phase transitions that were triggered by chemical doping in $\mathrm{C}{\mathrm{a}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$. Our experiments showed that doping with a few percent of Mn ($>4\%$) can change the quasi-two-dimensional metallic state of $\mathrm{C}{\mathrm{a}}_3\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_7$ into a Mott insulating state with a G-type antiferromagnetic order, but this Mott state cannot be induced by Fe doping. By combining these results with first-principles calculations, we show that lattice-orbital coupling (LOC) plays an important role in the Mott transition. Interestingly, the transition temperature $T_{\mathrm{MIT}}$ is found to be predetermined by a structural parameter denoted by $c/\sqrt{ab}$ at temperatures far above Néel temperature $T_{\mathrm{N}}$. This LOC-assisted Mott transition clearly contrasts with the band-filling picture. It is addressed that this type of Mott transition originates in the strong scattering centers formed by specific $3d$ dopants. The dopant-scattering picture is then applied to explain the puzzling doping effects that occur in other ruthenates and $3d$ oxides. Our findings will advance the general understanding of how the unusual properties of $4d$ correlated systems are governed by the complex interplay that occurs among the charge, spin, lattice, and orbital degrees of freedom.

Shift-current transients are obtained for near-band-gap excitation of bulk GaAs by numerical solutions of the semiconductor Bloch equations in a basis obtained from a 14-band k$·$p model of the band structure. This approach provides a transparent description of the optically induced excitations in terms of interband, intersubband, and intraband excitations which enables a clear distinction between different contributions to the shift-current transients and fully includes resonant as well as off-resonant processes. Using a geodesic grid in reciprocal space in our numerical solutions, we are able to include the electron-hole Coulomb attraction in combination with our anisotropic three-dimensional band structure. We obtain an excitonic absorption peak and an enhancement of the continuum absorption and demonstrate that the excitonic wave function contains a significant amount of anisotropy. Optical excitation at the excitonic resonance generates shift-current transients of significant strength; however, due to the electron-hole attraction the shift distance is smaller than for above-band-gap excitation. We thus demonstrate that our approach is able to provide important information on the ultrafast electron dynamics on the atomic scale.

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the ($1+1$)-dimensional system as well as ($3+1$)-dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore the pumped particle number is quantized by the topological reason. Finally, we study the topological temporal pump in $3+1$ dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.

Motivated by recent experiments [Science 355, 1192 (2017); Nat. Nanotechnol. 12, 430 (2017)], we present here an extensive theoretical analysis of the thermal conductance of atomic-size contacts made of three different metals, namely gold (Au), platinum (Pt), and aluminum (Al). The main goal of this work is to elucidate the role of phonons in the thermal transport through these atomic contacts as well as to study the validity of the Wiedemann-Franz law, which relates the electrical and the thermal conductance. For this purpose, we have employed two different custom-developed theoretical approaches. The first one is a transport method based on density functional theory (DFT) that allows one to accurately compute the contributions of both electrons and phonons to the thermal transport in few-atom-thick contacts. The second technique is based on a combination of classical molecular dynamics (MD) simulations and a tight-binding model that enables the efficient calculation of the electronic contribution to the thermal conductance of atomic contacts of larger size. Our DFT-based calculations show that the thermal conductance of few-atom contacts of Au and Pt is dominated by electrons, with phonons giving a contribution typically below 10% of the total thermal conductance, depending on the contact geometry. For these two metals we find that the small deviations from the Wiedemann-Franz law, reported experimentally, largely stem from phonons. In the case of Al contacts we predict that the phononic contribution can be considerably larger with up to 40% of the total thermal conductance. We show that these differences in the phononic contribution across metals originate mainly from their distinct Debye energies. On the other hand, our MD-based calculations demonstrate that the electronic contribution to the thermal conductance follows very closely the Wiedemann-Franz law, irrespective of the material and the contact size. Finally, the ensemble of our results consistently shows that the reported observation of quantized thermal transport at room temperature is restricted to few-atom contacts of Au, a monovalent metal in which the transport is dominated by the $s$ valence orbitals. In the case of multivalent metals like Pt and Al this quantization is statistically absent due to the fact that additional orbitals contribute to the transport with conduction channels that have intermediate transmissions between 0 and 1, even in the case of single-atom contacts.

The interlayer sliding behaviors of hexagonal boron nitride ($h$-BN) were investigated via a density functional theory approach with dispersion interaction included. It was found that the self-consistent screening effect (SCS) and the polarizability contractions had significant influences on London dispersion forces, which are responsible for not only the stacking modes but also for the sliding behaviors of $h$-BN. In consideration of the ionic characteristics of $h$-BN, surprisingly, the calculated dispersion force was found to dominate the electrostatic interaction along a minimum-energy sliding pathway and make a pronounced contribution ($\sim 35\%)$ to the barrier during the constrained sliding. This study demonstrates that the SCS and polarizability contractions play important roles in the sliding behaviors of $h$-BN and that the long-range dispersion interaction should be carefully treated, even in systems with ionic characteristics.

We study interfacial magnetocrystalline anisotropies in various Fe/semiconductor heterostructures by means of first-principles calculations. We find that many of those systems show perpendicular magnetic anisotropy (PMA) with a positive value of the interfacial anisotropy constant $K_{\mathrm{i}}$. In particular, the ${\mathrm{Fe}/\mathrm{CuInSe}}_2$ interface has a large $K_{\mathrm{i}}$ of $\sim 2.3\mathrm{mJ}/{\mathrm{m}}^2$, which is about 1.6 times larger than that of Fe/MgO known as a typical system with relatively large PMA. We also find that the values of $K_{\mathrm{i}}$ in almost all the systems studied in this work follow the well-known Bruno's relation, which indicates that minority-spin states around the Fermi level provide dominant contributions to the interfacial magnetocrystalline anisotropies. Detailed analyses of the local density of states and wave-vector-resolved anisotropy energy clarify that the large $K_{\mathrm{i}}$ in ${\mathrm{Fe}/\mathrm{CuInSe}}_2$ is attributed to the preferable $3d$-orbital configurations around the Fermi level in the minority-spin states of the interfacial Fe atoms. Moreover, we have shown that the locations of interfacial Se atoms are the key for such orbital configurations of the interfacial Fe atoms.

Superconductivity occurs in the proximity of other competing orders in a wide variety of materials. Such competing phases may reveal themselves when superconductivity is locally suppressed by a magnetic field in the core of a vortex. We explore the competition between superconductivity and charge density wave order in the attractive Hubbard model on a square lattice. Using Bogoliubov–de Gennes mean-field theory, we study how vortex structures form and evolve as the magnetic flux is tuned. Each vortex seeds a charge density wave region whose size is determined by the energy cost of the competing phase. The vortices form a lattice whose lattice parameter shrinks with increasing flux. Eventually, their charge-ordered cores overlap, leading to a field-driven coexistence phase exhibiting both macroscopic charge order and superconductivity—a “supersolid.” Ultimately, superconductivity disappears via a first-order phase transition into a purely charge-ordered state. We demonstrate that the Hubbard model maps to a strong-coupling field theory with a constant-squared-sum constraint. We argue that such a constraint necessarily leads to ordered-vortex cores and field-driven coexistence. The coexistence phase can be interpreted as a crystalline arrangement of meron defects in a pseudospin description. We construct a phase diagram using $t^{\prime }$, the next-nearest-neighbor hopping, to tune the competition between phases.