We have studied the surface structure and morphology of epitaxial Cr films on Au(001) substrate with Cr thickness ($d_{\mathrm{Cr}}$) below 3 nm. We have characterized the films prepared under various growth conditions by using scanning tunneling microscopy and spectroscopy (STM/STS), low-energy electron diffraction, and Auger electron spectroscopy. The good growth conditions of the Cr(001) films, which have atomically flat terraces without surface segregation of Au and with distinct surface states, are obtained by the following two methods. (I) $d_{\mathrm{Cr}}=3$ nm film realized by two-step growth, i.e., first 1.5 nm of Cr deposited at room temperature ($\sim 290$ K) and an additional 1.5 nm Cr deposition at 570 K and (II) $d_{\mathrm{Cr}}=1.5$ nm film by room temperature growth and subsequently post-annealing at 470 K. The magnetic imaging of (I) $d_{\mathrm{Cr}}=3$ nm Cr(001) film was performed by means of spin-polarized STM/STS. The observed magnetic image indicates that the topological antiferromagnetic (AF) order appears in a series of adjacent terraces and two types of spin frustration caused by screw dislocations lead to modifications of the topological AF order. One type of spin frustration is accompanied by narrow domain walls between two screw dislocations. The other type is a complex spin frustration caused by a cluster of an odd number of screw dislocations. The difference of the two types of spin frustration is explained through a micromagnetic simulation. We have also identified a large spin-frustrated area, consisting of a cluster of multiple number of screw dislocations.

The search for large gap quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators is important both for fundamental and practical interests. The degenerate multiorbitals $p_x,p_y$ in a honeycomb lattice provides a paradigm for the QSH state with a boosted topological gap of the first order in atomic spin-orbit coupling. By using an elementary band representation, we explore the feasibility of this mechanism for QSH in general two-dimensional lattices, and find that the biparticle lattices with $C_{3v}$ or $C_{4v}$ symmetry and degenerate multiorbitals could work. We further provide concrete tight-binding models on honeycomb, kagome, and square lattices to demonstrate the desired topological physics. By introducing ferromagnetism into the QSH state, we extend the mechanism to the QAH state with a boosted gap. The QSH and QAH states can be achieved when the Fermi level is at integer filling only for a honeycomb lattice, but at certain fractional filling for the other lattices. We conclude with a brief discussion on the possible material venues for such a mechanism.

This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress autocorrelation matrix to be fully determined by two spatially isotropic functions: the pressure and torque autocorrelations. The pressure and torque fluctuations being, respectively, normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyperuniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or it is the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.

Relaxor ferroelectrics, which form a peculiar class of functional materials, are often composed of complex perovskites $\mathrm{Pb}\left({BB}^{\prime }\right){\mathrm{O}}_3$, as represented by $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$ where the compositional ordering of Mg and Nb is believed to be essential to its relaxor properties. In this work, analysis using a first-principles-based model shows that, while the electrostatic interactions are important, the nearest neighbor assumption, which was used for metallic alloys, can be adopted to understand the compositional ordering in $\mathrm{Pb}\left({BB}^{\prime }\right){\mathrm{O}}_3$. Numerical simulations with the Kawasaki Monte Carlo method can model the experimentally observed compositional ordering by maximizing the number of the unlike $B\text{−}{B}^{\prime }$ pairs (or the Bethe's parameter), which is the overriding factor that determines the ordering. Subtle points of configuration energy degeneracy are also discussed, which explains the partial disorder inherently present in such systems.

Evolution of magnetism in single crystals of the van der Waals compound $\mathrm{V}{\mathrm{I}}_3$ in external pressure up to 7.3 GPa studied by measuring magnetization and ac magnetic susceptibility is reported. Four magnetic phase transitions, at $T_1=54.5\mathrm{K}, T_2=53\mathrm{K}, T_{\mathrm{C}}=49.5\mathrm{K}$, and $T_{\mathrm{FM}}=26\mathrm{K}$, respectively, have been observed at ambient pressure. The first two have been attributed to the onset of ferromagnetism in specific crystal-surface layers. The bulk ferromagnetism is characterized by the magnetic ordering transition at Curie temperature $T_{\mathrm{C}}$ and the transition between two different ferromagnetic phases $T_{\mathrm{FM}}$, accompanied by a structure transition from monoclinic to triclinic symmetry upon cooling. The pressure effects on magnetic parameters were studied with three independent techniques. $T_{\mathrm{C}}$ was found to be almost unaffected by pressures up to 0.6 GPa whereas $T_{\mathrm{FM}}$ increases rapidly with increasing pressure and reaches $T_{\mathrm{C}}$ at a triple point at ≈ 0.85 GPa. At higher pressures, only one magnetic phase transition is observed moving to higher temperatures with increasing pressure to reach 99 K at 7.3 GPa. In contrast, the low-temperature bulk magnetization is significantly reduced by applying pressure (by more than 50% at 2.5 GPa) suggesting a possible pressure-induced reduction of vanadium magnetic moment. First-principles calculations of $\mathrm{V}{\mathrm{I}}_3$ under pressure allow us to ascribe the evolution of $T_{\mathrm{C}}$ with pressure to the reduction of interplanar distance, including the observed slope change at 0.6 GPa. These calculations also describe the associated band gap closing, showing that with a modest compression the material would become metallic. Overall, the large pressure range covered corresponds to a significant change of interplanar interactions. The obtained data thus allow us to shed light on how does the transition between the three-dimensional (3D) and quasi-2D system affect magnetic interactions in the system.

Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.

We have studied the ${\mathrm{H}}_2\mathrm{O}$ ice VII–ice X phase transition at room temperature by performing three quasicontinuous synchrotron time-resolved x-ray-diffraction experiments in a dynamic diamond anvil cell, reaching pressures of 180 GPa. The dense pressure coverage of our volume data allows us to directly derive the bulk modulus for ${\mathrm{H}}_2\mathrm{O}$ over the entire pressure range. Our data document three major changes in compression behavior in the ranges of 35–40, 50–55, and 90–110 GPa, likely corresponding to the formation of pretransition dynamically disordered ice VII and ice X, and static ice X, respectively. Our results confirm that ice X has a very high bulk modulus.

The high-pressure structural behavior of the noble gas (Ng) clathrate hydrates $\mathrm{Ar}·6.5{\mathrm{H}}_2\mathrm{O}$ and $\mathrm{Xe}·7.2{\mathrm{H}}_2\mathrm{O}$ featuring cubic structures II and I, respectively, was investigated by neutron powder diffraction (using the deuterated analogues) at 95 K. Both hydrates undergo pressure-induced amorphization (PIA), indicated by the disappearance of Bragg diffraction peaks, but at rather different pressures, at 1.4 and above 4.0 GPa, respectively. Amorphous Ar hydrate can be recovered to ambient pressure when annealed at $>1.5\mathrm{GPa}$ and 170 K and is thermally stable up to 120 K. In contrast, it was impossible to retain amorphous Xe hydrate at pressures below 3 GPa. Molecular dynamics (MD) simulations were used to obtain general insight into PIA of Ng hydrates, from Ne to Xe. Without a guest species, both cubic clathrate structures amorphize at 1.2 GPa, which is very similar to hexagonal ice. Filling of large-sized H cages does not provide stability toward amorphization for structure II, whereas filled small-sized dodecahedral D cages shift PIA successively to higher pressures with increasing size of the Ng guest. For structure I, filling of both kinds of cages, large-sized T and small-sized D, acts to stabilize in a cooperative fashion. Xe hydrate represents a special case. In MD, disordering of the guest hydration structure is already seen at around 2.5 GPa. However, the different coordination numbers of the two types of guests in the crystalline cage structure are preserved, and the state is shown to produce a Bragg diffraction pattern. The experimentally observed diffraction up to 4 GPa is attributed to this semicrystalline state.

Because phononic topological insulators have primarily been studied in discrete, graphenelike structures with $C_{6\left(v\right)}$ or $C_{3\left(v\right)}$ hexagonal symmetry, an open question is how to systematically achieve double Dirac cones and topologically nontrivial structures using continuous, nonhexagonal unit cells. Here, we address this challenge by presenting a computational methodology for the inverse design of continuous two-dimensional square phononic metamaterials exhibiting $C_{4\left(v\right)}$ and $C_{2\left(v\right)}$ symmetry. This leads to the systematic design of square unit cell topologies exhibiting a double Dirac degeneracy, which enables topologically protected interface propagation based on the quantum spin Hall effect (QSHE). Numerical simulations prove that helical edge states emerge at the interface between two topologically distinct square phononic metamaterials, which opens the possibility of QSHE-based pseudospin-dependent transport beyond hexagonal lattices.

We investigate the appearance of superconductivity in a model with Peierls electron-phonon coupling for very low carrier concentrations. Superconductivity with very high critical temperatures is found to occur at all carrier concentrations if the electron-phonon coupling is not too weak, with a gap of $s+s^{*}$ symmetry that closes on the Fermi surface for appropriate parameters. The possibility of finding the elusive $p$-type superconductivity is also revealed, although this turns out not to be stable within the approximations we use.

We propose resonating valence bond wave functions for a spin-1 system on the torus that realize a non-Abelian chiral spin liquid. The wave functions take the form of infinite-dimensional matrix product states constructed from conformal blocks of the $\mathrm{SO}{\left(3\right)}_1$ Wess-Zumino-Witten model. This means that they are lattice analogs of the bosonic Moore-Read state introduced in fractional quantum Hall systems. The topological order of this system is revealed by explicit construction of threefold-degenerate ground states and analytical computation of the modular $S$ and $T$ matrices.

We discuss the problem of gauge fixing for strongly correlated electrons coupled to quantum light, described by projected low-energy models such as those obtained within tight-binding methods. Drawing from recent results in the field of quantum optics, we present a general approach to write down a quantum light-matter Hamiltonian in either dipole or Coulomb gauge which is explicitly connected by a unitary transformation, thus ensuring gauge equivalence even after projection. The projected dipole gauge Hamiltonian features a linear light-matter coupling and an instantaneous self-interaction for the electrons, similar to the structure in the full continuum theory. On the other hand, in the Coulomb gauge the photon field enters in a highly nonlinear way, through phase factors that dress the electronic degrees of freedom. We show that our approach generalizes the well-known Peierls approximation, to which it reduces when only local, on-site orbital contributions to light-matter coupling are taken into account. As an application we study a two-orbital model of interacting electrons coupled to a uniform cavity mode, recently studied in the context of excitonic superradiance and associated no-go theorems. Using both gauges we recover the absence of a superradiant phase in the ground state and show that excitations on top of it, described by polariton modes, contain instead nontrivial light-matter entanglement. Our results highlight the importance of treating the nonlinear light-matter interaction of the Coulomb gauge nonperturbatively, to obtain a well-defined ultrastrong coupling limit and to not spoil gauge equivalence.

We develop a closed-form formula to calculate the transient thermal currents flowing through an arbitrary nanoscale phonon device in response to a sudden thermal switch. Our theory provides a solution to the problem in the far-from-equilibrium nonlinear response regime beyond the wide-band-like approximation and Drude regularization. We present calculations in a one-dimensional monatomic chain with Lorentzian-like thermal baths and show that the transient phonon currents are significantly larger than the long-time-limit steady-state phonon current. From the formula's clear mathematical structure, we also show that the transient oscillation periodicity and relaxation time are determined by the poles of the retarded phonon Green's function. In addition, higher temperatures of the thermal baths and stronger coupling between the baths and the central monatomic chain result in higher transient thermal currents. Our results suggest that ultrafast cooling of nanodevices through transient phonon currents is a promising route.

Very recently, a new type of two-dimensional layered material, ${\mathrm{MoSi}}_2{\mathrm{N}}_4$, was fabricated that is semiconducting with weak interlayer interaction, high strength, and excellent stability. We systematically investigate the effect of vertical strain on the electronic structure of ${MA}_2{Z}_4$ ($M=\text{Ti/Cr/Mo}, A=\mathrm{Si}, Z=\text{N/P}$) bilayers. Taking bilayer ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ as an example, our first-principles calculations show that its indirect band gap decreases monotonically as the vertical compressive strain increases. Under a critical strain around 22%, it undergoes a transition from semiconductor to metal. We attribute this to the opposite energy shift of states in different layers, which originates from the built-in electric field induced by the asymmetric charge transfer between two inner sublayers near the interface. Similar semiconductor to metal transitions are observed in other strained ${MA}_2{Z}_4$ bilayers, and the estimated critical pressures to realize such transitions are within the same order as semiconducting transition metal dichalcogenides. The semiconductor to metal transitions in the family of ${MA}_2{Z}_4$ bilayers present interesting possibilities for strain-induced engineering of their electronic properties.

The quest for the topological phases of matter in an aperiodic system has been greatly developed recently. Here we investigate the effects of disorder on topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. For comparison purposes, we also consider the case of a periodic snub-square crystalline lattice, which has the same primitive tiles as the Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott index and the two-terminal conductance, we confirm that the topological phases with disorder share the similar properties in the two systems which possess different symmetry and periodicity. It is shown that the quantum spin Hall states are robust against weak disorder in both the quasicrystalline lattice and the crystalline lattice. More interesting is that topological Anderson insulator phases induced by disorder appear in the two systems. Furthermore, the quantized conductance plateau contributed by the topological Anderson insulator phase is verified by the distribution of local currents.

Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological soft modes even in overconstrained, rigid systems. To do so, we consider non-Hermitian topology based on nonsquare matrices, and design a hyperstatic material in which low-energy modes protected by topology and symmetry appear at interfaces. Our approach presents a novel way of generating softness in robust scale-free architectures suitable for miniaturization to the nanoscale.

Finding large orbital polarization in Ni-based oxides has become a topic of paramount interest in recent years due to the prospect of finding superconductivity. In this work, we investigate the electronic structure of single-crystalline samples of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ and Ni-doped ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ containing $\mathrm{Cu}/{\mathrm{NiO}}_4$ square planar units. Our polarization-dependent x-ray absorption spectroscopy experiments reveal extremely large orbital polarization $(\sim 63\%)$ for ${\mathrm{Ni}}^{2+}$. Cluster calculations and ab initio calculations find that the giant orbital polarization arises due to the low-spin $(S=0)$ configuration with two holes in the Ni $3d_{x^2-y^2}$ orbital, contrary to the expected high-spin $(S=1)$ state from Hund's first rule.

A topological nodal line (NL) semimetal is a kind of special three-dimensional semimetal state with only nodal lines around the Fermi level. It has been revealed that there are basically two types of NLs when spin-orbit coupling is not considered for electronic system: One is dubbed $s$-NLs, protected by a combinational symmetry $S$ of spatial inversion $\left(P\right)$ and time reversal $\left(T\right)$, i.e., $S=PT$; the other one is $m$-NLs, protected by mirror $\left(M\right)$ or glide symmetry, constraining the NL inside certain symmetrical planes. However, a hybrid nodal chain (HNC), composed of linked $s$-NLs and $m$-NLs from the same two crossing bands, has not been well studied so far. Here, we identify by ab initio calculations a new all-$s{p}^2$ hybridized carbon allotrope as a good candidate, which has a unit cell of 24 carbon atoms with $Pnna$ $\left(D_{2h}^6\right)$ symmetry and is termed $\mathrm{oP}\text{−}{\mathrm{C}}_{24}$ carbon. The HNC hosted by $\mathrm{oP}\text{−}{\mathrm{C}}_{24}$ can be simply described by a two-band $\mathit{k}·\mathit{p}$ model, distinguished from the three-band model proposed for another HNC candidate in the TiRhAs family. This kind of HNC is proposed in a real material here and paves the way for further theoretical and experimental investigations.