We investigate a systematic statistical bias found in full configuration quantum Monte Carlo (FCIQMC) that originates from controlling a walker population with a fluctuating shift parameter. This bias can become the dominant error when the sign problem is absent, e.g., in bosonic systems. FCIQMC is a powerful statistical method for obtaining information about the ground state of a sparse and abstract matrix. We show that, when the sign problem is absent, the shift estimator has the nice property of providing an upper bound for the exact ground-state energy and all projected energy estimators, while a variational estimator is still an upper bound to the exact energy with substantially reduced bias. A scalar model of the general FCIQMC population dynamics leads to an exactly solvable Itô stochastic differential equation. It provides further insights into the nature of the bias and gives accurate analytical predictions for delayed cross-covariance and autocovariance functions of the shift energy estimator and the walker number. The model provides a toehold on finding a cure for the population control bias. We provide evidence for nonuniversal power-law scaling of the population control bias with walker number in the Bose-Hubbard model for various estimators of the ground-state energy based on the shift or on projected energies. For the specific case of the noninteracting Bose-Hubbard Hamiltonian we obtain a full analytical prediction for the bias of the shift energy estimator.

We study the topological properties and the topological phase transitions therein of a semi-Dirac Haldane model on a honeycomb lattice in the presence of an extended range (third neighbor) hopping. While in the absence of third-neighbor hopping $t_3$ the system exhibits a gapless electronic spectrum, its presence creates an energy gap in the dispersion. However, the nature of the spectral gap, that is, whether it is trivial or topological, needs to be ascertained. We find that the answer depends on the value of $t_3$ and its interplay with the value of the on-site potential that breaks the sublattice symmetry, namely, the Semenoff mass $\mathrm{\Delta }$. To elucidate our findings on the topological phases, we demonstrate two kinds of phase diagrams using the available parameter space, one in which the phases are shown in the $\mathrm{\Delta }\text{−}{t}_3$ plane and one in a more familiar $\mathrm{\Delta }\text{−}\varphi$ plane ($\varphi$ is the Haldane flux). The phase diagrams depict the presence of Chern insulating lobes comprising Chern numbers $\pm 2$ and $\pm 1$ for a certain range of values for $t_3$, along with trivial insulating regions (zero Chern number). Thus, there are phase transitions from one topological regime to another which are characterized by abrupt changes in the values of the Chern number. To support the existence of the topological phases, we compute counterpropagating chiral edge modes in a ribbon geometry. Finally, the anomalous Hall conductivity obtained by us shows plateaus at either $e^2/h$ or $2e^2/h$ corresponding to these topological phases.

We report an investigation of the microscopic mechanism of hydrogen penetration and migration in the conversion process of the buffer layer on SiC into quasi-freestanding graphene. By systematically observing the initial stage, we found that hydrogen intercalation initiates locally and simultaneously throughout the terrace, followed by the expansion of the intercalated area, resulting in full graphenization of the buffer layer over the SiC surface. This suggests that hydrogen can penetrate the buffer layer. In addition, we found that the steps on the SiC surface can act as a migration barrier, hindering the migration of hydrogen at the interface across the steps. This series of experimental results provides important insights into the fundamental mechanism of hydrogen intercalation and may help to pave the way toward graphene electronics.

We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ell =0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.

We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an $H$ theorem for the nonlinear Landau kinetic equation.

${\mathrm{Li}}_2{\mathrm{RuO}}_3$ (LRO) forms a valence bond crystal at room temperature. It undergoes a high temperature phase transition that involves structural, magnetic, and electronic changes leading to an exotic valence bond liquid state. The orbital degrees of freedom are thought to be fundamental to the evolution of LRO properties across the phase transition. We report temperature dependent broadband $\left(100–26000\mathrm{c}{\mathrm{m}}^{–1}\right)$ reflectance measurements on single crystals of LRO to elucidate structural and transport properties. Specifically, the phonon and electronic properties of LRO were investigated through the phase transition. We report that above the transition temperature $(T_{\mathrm{c}}\approx 500\mathrm{K})$, the optical band gap closes for electrons in the $d_{\mathrm{xz}}/d_{\mathrm{yz}}$ orbitals, but the $d_{\mathrm{xy}}$ electrons remain gapped. This behavior at high temperature can be associated with an orbital selective metallic state which to our knowledge has not been previously reported in LRO.

Finding disentangled representation plays a predominant role in the success of modern deep learning applications, but the results lack a straightforward explanation. Here we apply the information bottleneck method and its $\beta$-variational-autoencoder (VAE) implementation to find the disentangled low-dimensional representation of classical models. For the Ising model, our results reveal a deep connection between the disentangled features and the physical order parameters, and the widely used Bernoulli decoder is found to be learning a mean-field Hamiltonian at fixed temperature. This analogy motivates us to extend the application of $\beta$-VAE to more complex classical models with nonbinary variables using a different decoder neural network and propose a modified architecture ${\beta }^2$-VAE to enforce thermal fluctuations in generated samples. Our work provides a way to design a physics-informed algorithm that can yield learned features in potential correspondence with real physical properties.

The proposed topological Kondo insulator ${\mathrm{SmB}}_6$ hosts a bulk Kondo hybridization gap that stems from strong electronic correlations and a metallic surface state whose effective mass remains disputed. Thermopower and scanning tunneling spectroscopy measurements argue for heavy surface states that also stem from strong correlations, whereas quantum oscillation and angle-resolved photoemission measurements reveal light effective masses that would be consistent with a Kondo breakdown scenario at the surface. Here we investigate the evolution of the surface state via electrical and thermoelectric transport measurements under hydrostatic pressure, a clean symmetry-preserving tuning parameter that suppresses the Kondo gap and increases the valence of Sm from ∼2.6+ towards a 3+ magnetic metallic state. Electrical resistivity measurements reveal that the surface carrier density increases with increasing pressure, whereas thermopower measurements show an unchanged Fermi energy under pressure. As a result, the effective mass of the surface state charge carriers linearly increases with pressure as the Sm valence approaches 3+. Our results are consistent with the presence of correlation-driven surface states in ${\mathrm{SmB}}_6$ and suggest that the surface Kondo effect persists under pressure to 2 GPa.

The Bose-Einstein condensation of excitons into a single quantum state is known as exciton condensation. Exciton condensation, which potentially supports the frictionless flow of energy, has recently been realized in graphene bilayers and van der Waals heterostructures. Here we show that exciton condensates can be predicted from a combination of reduced density matrix theory and cumulant theory. We show that exciton condensation occurs if and only if there exists a large eigenvalue in the cumulant part of the particle-hole reduced density matrix. In the thermodynamic limit we show that the large eigenvalue is bounded from above by the number of excitons. In contrast to the eigenvalues of the particle-hole matrix, the large eigenvalue of the cumulant matrix has the advantage of providing a size-extensive measure of the extent of condensation. Here we apply this signature to predict exciton condensation in both the Lipkin model and molecular stacks of benzene. The computational signature has applications to the prediction of exciton condensation in both molecules and materials.

Topological nodal surface semimetals are a class of materials characterized by degenerate conduction and valence bands on closed nodal surfaces in the Brillouin zone that are protected by crystalline symmetries. These materials attract considerable attention for exhibiting intriguing, topologically driven quantum phenomena that are fundamentally interesting and practically useful. Here we identify by systematic ab initio calculations and topological quantum chemistry analysis prominent topological nodal surface semimetal states in ${\mathrm{Sr}}_5{X}_3(X$ = As, Sb, Bi) compounds in hexagonal $P{6}_3/mcm$ ($D_{6h}^3$) symmetry. These nodal surface states comprise degenerate the highest occupied band and the lowest unoccupied band that overlap in a single band at the $k_z=\pm \pi$ plane and are protected by time-reversal and nonsymmorphic twofold screw rotation symmetry. Topological quantum chemistry theory analysis reveals a twofold band degeneracy without spin-orbit coupling at the high-symmetry and generic $\mathit{k}$ points located at the $k_z=\pm \pi$ plane, which is formed by the bands of (${\mathrm{A}}_1\oplus {\mathrm{B}}_2)@6g$ band representations. Since the compounds studied here have been already experimentally synthesized, the present results have an immediate impact on the experimental detection and characterization of the theoretically predicted topological physics.

We study the consequences of the approximately trigonal ($D_{3d}$) point symmetry of the transition metal ($M$) site in two-dimensional van der Waals ${MX}_2$ dihalides and ${MX}_3$ trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal $d$ shell, which is best represented by $d$ orbitals that describe the trigonal rather than $O_h$ symmetry. The ligand-ligand bond length differences (rather than metal-ligand) take the role of a Jahn-Teller-like mode and in combination with interlayer distances and dimensionality effects tune the crystal field splittings and bandwidths. These effects, in turn, are amplified by electronic correlation effects—leading to crystal field splittings of the order of 0.1–1 eV between the singlet and the lowest orbital doublet—as opposed to the often assumed degenerate $3t_{2g}$ states. Our calculations explain why most of the materials in this family are insulating, and why these considerations have to be taken into account in realistic models of them. Further, orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ${\mathrm{ZrI}}_2$ and ${\mathrm{CuCl}}_2$ as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analyzing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and $p\text{−}d$ orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states, and we provide a simple framework and numerical tool for others. Our paper establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Our analysis shows that trigonal symmetry and its breaking is a key feature of the two-dimensional halides that needs to be accounted for in search of novel electronic states in materials ranging from ${\mathrm{CrI}}_3$ to $\alpha \text{−}{\mathrm{RuCl}}_3$.

Being used in optoelectronic devices as ultrathin conductor-insulator junctions, detailed investigations are needed about how exactly $h$-BN and graphene hybridize. Here we present a comprehensive ab initio study of hot carrier dynamics governed by electron-phonon scattering at the $h$-BN/graphene interface, using graphite (bulk), monolayer, and bilayer graphene as benchmark materials. In contrast to monolayer graphene, all multilayer structures possess low-energy optical phonon modes that facilitate carrier thermalization. We find that the $h$-BN/graphene interface represents an exception with a comparatively weak coupling between low-energy optical phonons and electrons. As a consequence, the thermalization bottleneck effect, known from graphene, survives hybridization with $h$-BN, but is substantially reduced in all other bilayer and multilayer cases considered. In addition, we show that the quantum confinement in bilayer graphene does not have a significant influence on the thermalization time compared to graphite and that bilayer graphene can hence serve as a minimal model for the bulk counterpart.

We demonstrate a unique approach to test the signature of the nodal-line physics by thermodynamic methods. By measuring magnetic susceptibility in ZrSiS we found an intriguing temperature-driven crossover from dia- to paramagnetic behavior. We show that the anomalous behavior represents a real thermodynamic signature of the underlying nodal-line physics through the means of chemical pressure (isovalent substitution of Zr for Hf), quantum oscillations, and theoretical modeling. The anomalous part of the susceptibility is orbital by nature, and it arises due to the vicinity of the Fermi level to a degeneracy point created by the crossing of two nodal lines. Furthermore, an unexpected Lifshitz topological transition at the degeneracy point is revealed by tuning the Fermi level. The present findings in ZrSiS give an attractive starting point for various nodal-line physics-related phenomena to be tested by thermodynamic methods in other related materials.

Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.

The complex magnetic structures, spin reorientation, and associated exchange interactions have been investigated in ${\mathrm{Er}}_{0.5}{\mathrm{Dy}}_{0.5}{\mathrm{FeO}}_3$ using bulk magnetization, neutron diffraction, specific heat measurements, and density functional theory calculations. The ${\mathrm{Fe}}^{3+}$ spins order as G-type antiferromagnet structure depicted by ${\mathrm{\Gamma }}_4(G_x$, $A_y$, $F_z$) irreducible representation below 700 K, similar to its end compounds. The bulk magnetization data indicate occurrence of the spin-reorientation and rare-earth magnetic moments' polarization below $\sim 75$ K and 10 K, respectively. The neutron diffraction studies confirm an “incomplete” ${\mathrm{\Gamma }}_4\to {\mathrm{\Gamma }}_2(F_x$, $C_y$, $G_z$) spin-reorientation initiated $\le 75$ K. Although the relative volume fraction of the two magnetic structures varies with decreasing temperature, both coexist even at 1.5 K. Below 10 K, the polarization of ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ moments in a $c_y^R$ arrangement develops, which gradually increases with decreasing temperature. At 2 K, magnetic structure associated with $c_z^R$ arrangement of ${\mathrm{Er}}^{3+}/{\mathrm{Dy}}^{3+}$ moments also appears. At 1.5 K, while the rare-earth magnetic moments show a $c_y^R+c_z^R$-type arrangement, the ${\mathrm{Fe}}^{3+}$ spins are represented by a combination of a ${\mathrm{\Gamma }}_2+{\mathrm{\Gamma }}_4$ ($G_z,G_x$) arrangement. A clear signature of the magnetic structure with ${\mathrm{\Gamma }}_1(G_y$) representation, symmetrically compatible with the $c_z^R$-type arrangement of rare-earth moments, is not confirmed from the refinement of the neutron diffraction data. The observed Schottky anomaly at 2.5 K suggests that the “rare-earth ordering” is induced by polarization due to ${\mathrm{Fe}}^{3+}$ spins. The ${\mathrm{Er}}^{3+}-{\mathrm{Fe}}^{3+}$ and ${\mathrm{Er}}^{3+}-{\mathrm{Dy}}^{3+}$ exchange interactions, obtained from first principle calculations, indicate that these interactions primarily cause the complicated spin reorientation and $c_y^R$ rare-earth ordering in the system, respectively, while the dipolar interactions between rare-earth moments result in the $c_z^R$ type rare-earth ordering at 2 K.

In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this top-down approach, $(d-1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a bottom-up approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit of a periodic lattice of coupled $(d-1)$-dimensional Majorana modes. We illustrate this idea by considering one-dimensional proximitized superconductors with spatially modulated potential or magnetic fields. The ensuing inhomogeneous topological state exhibits one-dimensional counterpropagating Majorana modes with finite dispersion, and with a Majorana gap that can be controlled by external fields. In the massless case, the Majorana modes have opposite Majorana polarizations and pseudospins, are conformally invariant, and realize centrally extended quantum mechanical supersymmetry. The supersymmetry exhibits spontaneous partial breaking. Consequently, the massless Majorana fermion can be identified as a Goldstino, i.e., the Nambu-Goldstone fermion associated with the spontaneously broken supersymmetry.

In order to study the effects of Mn substitution on the superconducting and magnetic ground state of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ $(T_c=35 \mathrm{K})$, members of the $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by elemental analysis, thermodynamic, and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as $x$ is increased from 0 to 0.036. For $x$ values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kinklike features allow for the determination of the transition temperature $T^{*}$ that increases as Mn substitution increases. A temperature-composition $\left(T\text{−}x\right)$ phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature $T^{*}$ appearing near 26 K for $x\sim 0.017$ and rising slowly up to 33 K for $x\sim 0.036$. In addition to the creation of the $T\text{−}x$ phase diagram for $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$, specific-heat data are used to track the jump in specific heat at $T_c$; the $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ data do not follow the scaling of $\mathrm{\Delta }{C}_p$ with $T_c^3$ as many of the other Fe-based superconducting systems do. These data suggest that, as magnetic pair breaking is present, the jump in $C_p$ for a given $T_c$ is reduced. Elastoresistivity coefficients $2m_{66}$ and $m_{11}-m_{12}$ as a function of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$. This may indicate that the magnetic order in Mn-substituted system may be still the same as $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$. Superconductivity of $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_4{\mathrm{As}}_4$ is also studied as a function of magnetic field. A clear change in $H_{c2}^{\prime }(T)/T_c$, where $H_{c2}^{\prime }(T)$ is $d{H}_{c2}(T)/dT$, at $x\sim 0.015$ is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also show the changes near $x=0.015$, again consistent with Fermi-surface changes associated with the magnetic ordering seen for higher-$x$ values.

We examined the magnetoresistance with applied magnetic field in the $ab$ plane for ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Mn}}_2{\mathrm{As}}_2$ with $x=0–0.30$, which exhibits a unique antiferromagnetic order with the simultaneous breaking of spatial-inversion and time-reversal symmetries. By investigating the temperature and magnetic-field strength/direction dependence of the magnetoresistance in detail, we found there are three main contributions to the magnetoresistance. One is due to an external field effect inducing cyclotron motion of electron and Zeeman splitting. This is most prominent at $x=0$ and 0.15. The second one is a spin fluctuation related negative magnetoresistance. This becomes large at a ferromagnetic transition temperature of 100 K at $x=0.25$. The third one is the spin-orbit coupling related effects, which leads to an in-plane anisotropy of magnetoresistance. We also argue that anisotropic magnetoresistance can be understood in terms of the magnetoelectric effect arising from the odd-parity magnetic-multipole ordering.