Very recently, twisted graphene bilayers (TGBs) around the first magic angle $\theta \approx 1.1^{\circ }$ have attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately study a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicates that a moderate heterostrain enables the structural evolution from the small-angle TGB (θ ∼ 1.5°) to the strained magic-angle TGB (θ ∼ 1.1°), exhibiting the characteristic low-energy flat bands. The heterostrain can even drive the system into highly strained tiny-angle TGBs (θ$\ll 1.1$°) with large deformed tetragonal superlattices, where a unique network of topological helical edge states emerges. Furthermore, the predicted domain wall modes, which are strongly localized and result in a hexagon-triangle-mixed frustrated lattice derived from the Kagome lattice, are observed in the strained tiny-angle TGBs.

The efficiency and stability of ${\mathrm{RuO}}_2$ in electrocatalysis has made this material a subject of intense fundamental and industrial interest. The surface functionality is rooted in its electronic and magnetic properties, determined by a complex interplay of lattice-, spin-rotational, and time-reversal symmetries, as well as the competition between Coulomb and kinetic energies. This interplay was predicted to produce a network of Dirac nodal lines (DNLs), where the valence and conduction bands touch along continuous lines in momentum space. Here we uncover direct evidence for three DNLs in ${\mathrm{RuO}}_2$ by angle-resolved photoemission spectroscopy. These DNLs give rise to a flat-band surface state that is readily tuned by the electrostatic environment, and that presents an intriguing platform for exotic correlation phenomena. Our findings support high spin-Hall conductivities and bulk magnetism in ${\mathrm{RuO}}_2$, and are likely related to its catalytic properties.

Using a combination of analytical arguments and state-of-the-art diagrammatic Monte Carlo simulations, we show that the corrections to the dispersion in interacting Weyl semimetals are determined by the ultraviolet cutoff and the inverse screening length. If both of these are finite, then the diagrammatic series is convergent even in the low-temperature limit, which implies that the semimetallic phase remains stable. Meanwhile, the absence of a UV cutoff or screening results in logarithmic divergences at zero temperature. These results highlight the crucial impact of Coulomb interactions and screening, mediated, e.g., through the presence of parasitic bands, which are ubiquitous effects in real-world materials. Also, despite sizable corrections from Coulomb forces, the contribution from the frequency-dependent part of the self-energy remains extremely small, thus giving rise to a system of effectively almost free fermions with a strongly renormalized dispersion.

Understanding different approaches to confining massless Dirac fermions in graphene is of keen interest to researchers; it is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization, and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene $p\text{−}n$ boundaries with an angle $\sim {34}^{\circ }$. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in the graphene wedge into Landau levels (LLs). The spatial confinement of the wedge affects the Landau quantization, which enables us to experimentally measure the spatial extent of the wave functions of the LLs. The magnetic fields induce a sudden and large increase in energy of the quasibound states because of a π Berry phase jump of the massless Dirac fermions in graphene. Such behavior is the hallmark of the “Klein tunneling” in graphene. Our experiment demonstrated that the angled wedge is a unique system with the critical magnetic fields for the π Berry phase jump depending on the distance from the summit of the wedge.

The weak intrinsic spin-orbit coupling in graphene can be greatly enhanced by proximity coupling. Here, we report on the proximity-induced spin-orbit coupling in graphene transferred by hexagonal boron nitride (hBN) onto the topological insulator ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ (BSTS) which was grown on a hBN substrate by vapor solid synthesis. Phase coherent transport measurements, revealing weak localization, allow us to extract the carrier density-dependent phase coherence length $l_{\varphi }$. While $l_{\varphi }$ increases with increasing carrier density in the hBN/graphene/hBN reference sample, it decreases in graphene/BSTS due to the proximity coupling of BSTS to graphene. The latter behavior results from D'yakonov-Perel'-type spin scattering in graphene with a large proximity-induced spin-orbit coupling strength of at least 2.5 meV.

Surface functionalization emerges as an alternative pathway for electronic structure engineering in two-dimensional (2D) systems. We explore a hybrid heterostructure built from a 2D transition-metal dichalcogenide atop a layer of photochromic self-assembled azobenzene molecules. This setup can modify carrier transport through the 2D nanosheet by an effective photoactived gating control, achieved through trans to cis isomerization of the azobenzene in close contact with the 2D nanosheet. We show theoretically that this behavior can be ascribed to a tunable gating mechanism. We use a combination of atomistic calculations of the local effective potential profile with simulations of the electron scattering by such potential in a massive Dirac Hamiltonian formalism. We find that different isomers induce a local perturbation with drastically different features that explain well the experimental behavior.

In recent years, there have been conflicting reports regarding the ultrafast photoconductive response of films of single walled carbon nanotubes (CNTs), which apparently exhibit photoconductivities that can differ even in sign. Here, we observe explicitly that the THz photoconductivity of CNT films is a highly variable quantity which correlates with the length of the CNTs, while the chirality distribution has little influence. Moreover, by comparing the photoinduced change in THz conductivity with heat-induced changes, we show that both occur primarily due to heat-generated modification of the Drude electron relaxation rate, resulting in a broadening of the plasmonic resonance present in finite-length metallic and doped semiconducting CNTs. This clarifies the nature of the photoresponse of CNT films and demonstrates the need to carefully consider the geometry of the CNTs, specifically the length, when considering them for application in optoelectronic devices.

We present a machine-learning approach to a long-standing issue in quantum many-body physics, namely, analytic continuation. This notorious ill-conditioned problem of obtaining spectral function from an imaginary time Green's function has been a focus of new method developments for past decades. Here we demonstrate the usefulness of modern machine-learning techniques including convolutional neural networks and the variants of a stochastic gradient descent optimizer. The machine-learning continuation kernel is successfully realized without any “domain knowledge,” which means that any physical “prior” is not utilized in the kernel construction and the neural networks “learn” the knowledge solely from “training.” The outstanding performance is achieved for both insulating and metallic band structure. Our machine-learning-based approach not only provides the more accurate spectrum than the conventional methods in terms of peak positions and heights, but is also more robust against the noise which is the required key feature for any continuation technique to be successful. Furthermore, its computation speed is ${10}^4\text{–}{10}^5$ times faster than the maximum entropy method.

We prove the existence of higher-order topological insulators with protected chiral hinge modes in quasi-two-dimensional systems made out of coupled layers stacked in an inversion-symmetric manner. In particular, we show that a homogeneous external magnetic field slightly tilted away from the stacking direction drives alternating $p$- and $n$-doped honeycomb sheets into a higher-order topological phase, characterized by a nontrivial three-dimensional ${\mathbb{Z}}_2$ invariant. We identify graphene, silicene, and phosphorene multilayers as potential material platforms for the experimental detection of this second-order topological insulating phase.

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small “magic” twist angles has been linked to the existence of nearly flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moiré superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed $\left(p_x,p_y\right)$ two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component ($d\text{−}\mathrm{wave}$) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-coupling regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-type insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferromagnetic and antiferromagnetic orders with different types of nematic and magnetic orbital orders. Overall, our work provides a solid framework for further investigations of the phase diagram of the two-orbital extended Hubbard model in both strong- and weak-coupling regimes.

In this paper, we generalized the Peschel-Emery line of the interacting transverse field Ising model to a model based on three-state clock variables. Along this line, the model has exactly degenerate ground states, which can be written as product states. In addition, we present operators that transform these ground states into each other. Such operators are also presented for the Peschel-Emery case. We numerically show that the generalized model is gapped. Furthermore, we study the spin-$S$ generalization of interacting Ising model and show that along a Peschel-Emery line they also have degenerate ground states. We discuss some examples of excited states that can be obtained exactly for all these models.

We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is handled with strong-coupling perturbation theory which encodes the information about Mott transition physics into a rich dynamical local self-energy. The local nature of the self-energy allows us to combine it with kernel polynomial and transfer matrix methods which consequently enables us to study lattices with millions of sites. The transfer matrix method, which in the ribbon geometry is essentially free from finite-size errors, can be employed to perform finite-size scaling on the width of the ribbon. This enables us to rule out the possibility of metallic phase between the Mott and Anderson insulating phases which has been claimed in the literature. Therefore, we find a direct transition between Anderson and Mott insulators when the disorder strength $W$ is comparable to the Hubbard interaction $U$. For a fixed disorder strength $W$, we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions $U$, the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.

A nonlocal density functional for the kinetic pressure tensor of a Fermi gas is derived. The functional is designed to reconcile the quantum hydrodynamic model with the microscopic approaches, both for homogeneous equilibrium and linear dynamic configurations. The derivation paves the way to improving and implementing further time-nonlocal functionals. The present approximation is systematically tested in and beyond the linear regime for the Fermi gas, as well as for some small sodium clusters, proving that it is quantitatively superior to some other density functionals.

With density functional theory we have performed molecular dynamics simulations of ZrC, which displayed spontaneous carbon Frenkel pair formation at a temperature of $3200\mathrm{K}$, some 500° below the melting point. To understand this behavior, rarely seen in equilibrium simulations, we quenched and examined a set of lattices containing a Frenkel pair. Five metastable structures were found, and their formation energies and electronic properties were studied. Their thermal generation was found to be facilitated by a reduction of between 0.7 and 1.5 eV in formation energy due to thermal expansion of the lattice. With input from a quasiharmonic description of the defect-free energy of formation, an ideal solution model was used to estimate lower bounds on their concentration as a function of temperature and stoichiometry. At 3000 K (0.81 of the melting temperature) their concentration was estimated to be 1.2% per mole in a stoichiometric crystal, and 0.3% per mole in a crystal with 10% per mole of constitutional vacancies. Their contribution to heat capacity, thermal expansion, and bulk modulus was estimated.

${}^{59}\mathrm{Co}$ and ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements in external magnetic and zero magnetic fields have been performed to investigate the magnetic properties of the A-type antiferromagnetic (AFM) ${\mathrm{CaCo}}_2{\mathrm{P}}_2$. NMR data, especially the nuclear spin lattice relaxation rates $1/T_1$ exhibiting a clear peak, provide clear evidence for the AFM transition at a Néel temperature of $T_{\mathrm{N}}\sim 110\mathrm{K}$. The magnetic fluctuations in the paramagnetic state were found to be three-dimensional ferromagnetic, suggesting ferromagnetic interaction between Co spins in the $\mathit{ab}$ plane characterizes the spin correlations in the paramagnetic state. In the AFM state below $T_{\mathrm{N}}$, we have observed ${}^{59}\mathrm{Co}$ and ${}^{31}\mathrm{P}$ NMR signals under zero magnetic field. From ${}^{59}\mathrm{Co}$ NMR data, the ordered magnetic moments of Co are found to be in $ab$ plane and are estimated to be 0.35 ${\mu }_{\mathrm{B}}$ at 4.2 K. Furthermore, the external field dependence of ${}^{59}\mathrm{Co}$ NMR spectrum in the AFM state suggests a very weak magnetic anisotropy of the Co ions and also provides microscopic evidence of canting the Co-ordered moments along the external magnetic field directions. The magnetic state of the Co ions in ${\mathrm{CaCo}}_2{\mathrm{P}}_2$ is well explained by the local-moment picture in the AFM state, although the system is metallic, as seen by $1/T_{1}T=\mathrm{constant}$ behavior.

In type-II superconductors, the macroscopic response of vortex matter to an external perturbation depends on the local interaction of flux lines with the pinning landscape (pinscape). The (Campbell) penetration depth ${\lambda }_{\mathrm{C}}$ of an ac field perturbation is often associated with a phenomenological pinning curvature. However, this basic approach is unable to capture thermal hysteresis effects observed in a variety of superconductors. The recently developed framework of strong-pinning theory has established a quantitative relationship between the microscopic pinscape and macroscopic observables. Specifically, it identifies history-dependent vortex arrangements as the primary source for thermal hysteresis in the Campbell response. In this work, we show that this interpretation is well-suited to capture the experimental results of the clean superconductor $\mathrm{Nb}{\mathrm{Se}}_2$, as observed through Campbell response (linear ac susceptibility) and small-angle neutron scattering measurements. Furthermore, we exploit the hysteretic Campbell response upon thermal cycling to extract the temperature dependence of microscopic pinning parameters from bulk measurements, specifically the pinning force and pinning length. This spectroscopic tool may stimulate further pinscape characterization in other superconducting systems.

We study the effect of quenched disorder on the semimetal-superconductor quantum phase transition in a model of two-dimensional Dirac semimetal with $N$ flavors of two-component Dirac fermions, using perturbative renormalization group methods at one-loop order in a double epsilon expansion. For $N\ge 2$ we find that the Harris-stable clean critical behavior gives way, past a certain critical disorder strength, to a finite-disorder critical point characterized by non-Gaussian critical exponents, a noninteger dynamic critical exponent $z>1$, and a finite Yukawa coupling between Dirac fermions and bosonic order parameter fluctuations. For $N\ge 7$ the disordered quantum critical point is described by a renormalization group fixed point of stable-focus type and exhibits oscillatory corrections to scaling.

In the context of describing electrons in solids as a fluid in the hydrodynamic regime, we consider a flow of electrons in a channel of finite width, i.e., a Poiseuille flow. The electrons are accelerated by a constant electric field. We develop the appropriate relativistic hydrodynamic formalism in 2+1 dimensions and show that the fluid has a finite dc conductivity due to boundary-induced momentum relaxation, even in the absence of impurities. We use methods involving the AdS/CFT correspondence to examine the system in the strong-coupling regime. We calculate and study velocity profiles across the channel, from which we obtain the differential resistance $dV/dI$. We find that $dV/dI$ decreases with increasing current $I$ as expected for a Poiseuille flow, also at strong coupling and in the relativistic velocity regime. Moreover, we vary the coupling strength by varying $\eta /s$, the ratio of shear viscosity over entropy density. We find that $dV/dI$ decreases when the coupling is increased. We also find that strongly coupled fluids are more likely to become ultrarelativistic and turbulent. These conclusions are insensitive to the presence of impurities. In particular, we predict that in channels which are clearly in the hydrodynamic regime already at small currents, the DC channel resistance strongly depends on $\eta /s$.

We report the existence of two competing mechanisms in the current-driven electrical breakdown of vanadium sesquioxide (${\mathrm{V}}_2{\mathrm{O}}_3$) and vanadium dioxide ($\mathrm{V}{\mathrm{O}}_2$) nanodevices. Our experiments and simulations show that the competition between a purely electronic (PE) mechanism and an electrothermal (ET) mechanism, suppressed in nanoscale devices, explains the current-driven insulator-to-metal phase transition (IMT). We find that the relative contribution of PE and ET effects is dictated by thermal coupling and resistivity, a discovery which disambiguates a long-standing controversy surrounding the physical nature of the current-driven IMT in vanadium oxides. Furthermore, we show that the electrothermally driven IMT occurs through a nanoscopic surface-confined filament. This nanoconfined filament has a very large thermal gradient, thus generating a large Seebeck-effect electric field.