The in-plane magnetoconductance of the strongly interacting two-dimensional electron system in a silicon MOSFET (metal-oxide-semiconductor-field-effect transistor) exhibits an unmistakable kink at a well-defined electron density, $n_k$. The kink at $n_k$ is near, but not at the critical density $n_c$ determined from resistivity measurements, and the density at which $n_k$ occurs varies with temperature. These features are inconsistent with expectations for a quantum phase transition. We suggest instead that this is a percolation transition and present a detailed model based on the formation of a mixed insulating and metallic phase within which a metal-insulator transition takes place by percolation.

Ultrathin Pb and Ge films deposited on Ag(111) surfaces have been investigated and compared. We found that at 1/3 ML, both films formed surface alloys, ${\mathrm{Ag}}_2\mathrm{Pb}$ and ${\mathrm{Ag}}_2\mathrm{Ge}$, with $\sqrt{3}\times \sqrt{3}R{30}^{\circ }$ and $\frac{19}{20}\sqrt{3}\times \frac{19}{20}\sqrt{3}R{30}^{\circ }$ structures on Ag(111) but the surface electronic structures exhibit a most evident difference at the Ag(111) surface zone boundary ${\overline{M}}_{\mathrm{Ag}\left(111\right)}$, where the single band and the splitting ones were observed, respectively. Up to 1 ML, ${\mathrm{Ag}}_2\mathrm{Ge}$ subsequently develops into germanene with a striped phase and then a quasifreestanding phase, as previously reported [Lin et al., Phys. Rev. Mater. 2, 024003 (2018)], while ${\mathrm{Ag}}_2\mathrm{Pb}$ evolves to a dense Pb(111) phase that also reveals splitting bands at ${\overline{M}}_{\mathrm{Ag}\left(111\right)}$. We discover that the larger (smaller) atomic size of a Pb (Ge) atom with respect to an Ag atom causes the commensurate (incommensurate) interfaces and further demonstrate that the splitting bands of ${\mathrm{Ag}}_2\mathrm{Ge}$ surface alloy and 1-ML Pb film originated from the commonly incommensurate interface with Ag(111), which mediates umklapp scattering by inducing the mirror image of the pristine ${\mathrm{Ag}}_2\mathrm{Ge}$ and Pb(111) bands relative to ${\overline{M}}_{\mathrm{Ag}\left(111\right)}.$

We develop a microscopic theory of the Coulomb drag effect in a hybrid system consisting of spatially separated two-dimensional quantum gases of degenerate electrons and indirect excitons. Considering both the normal-phase and condensate regimes of the exciton subsystem, we investigate the transmobility of the system being the kinetic coefficient, which couples the static electric field applied to the electron layer with the particle density current (flux) in the exciton subsystem. The temperature dependence of the transmobility and its dependence on the interlayer separation are studied. It is shown that exciton-exciton interaction plays a dramatic role. If the exciton gas is in the normal phase, then the screening of interlayer interaction by the exciton subsystem results in an exponential damping of the transmobility with the decrease of temperature, while at low temperatures, the interactions result in a robust bosonic transport due to the emergence of the Bogoliubov quasiparticles.

We present a theoretical study of photocarrier dynamics in graphene due to electron-phonon (EP) interactions. Using the relaxation-time approximation (RTA) with parameters determined from density functional theory (DFT) and a complementary explicitly solvable model, we show that the photocarrier thermalization time changes by orders of magnitude, when the excitation energy is reduced from 1 eV to the 100 meV range. In detail the ultrafast thermalization at low temperatures takes place on a femtosecond timescale via optical phonon emission, but slows down to picoseconds once excitation energies become comparable with these optical phonon energy quanta. In the latter regime thermalization times exhibit a pronounced dependence on temperature. Our DFT-based model includes all the inter- and intraband transitions due to EP scattering. Thanks to the high melting point of graphene we extend our studies up to 2000 K and show that such high temperatures reduce the photocarrier thermalization time through phonon absorption.

Electronic tunability in crystals with weakly bound layers can be achieved through layer stacking order. One such example is ${\mathrm{MoTe}}_2$, where the low-temperature orthorhombic $T_d$ phase is topological and host to Weyl quasiparticles. The transition mechanism to the nontrivial topology is elucidated by single-crystal neutron diffraction. Upon cooling from the monoclinic $1T^{\prime }$ to the $T_d$ phase, diffuse scattering accompanies the transition, arising from random, in-plane layer displacements, and dissipates upon entering the $T_d$ phase. Diffuse scattering is observed only in the $H0L$ plane due to irreversible layer shifts along the $c$ axis that break the centrosymmetry of the monoclinic lattice.

We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast Walsh-Hadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities (e.g., energy and/or particle number) we observe a slowing down of the dynamics as the transition into the many-body localized phase is approached. More specifically, our data are consistent with a subballistic spread of entanglement and a stretched-exponential decay of an autocorrelation function, with their associated exponents reflecting slow dynamics near the transition for a fixed system size. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and cannot rule out that the slow dynamics is a finite-size effect. Furthermore, we observe examples of nonmonotonic dependence of the exponents with time, with the dynamics initially slowing down but accelerating again at even larger times, consistent with the slow dynamics being a crossover phenomenon with a localized critical point.

We use machine learning to enable large-scale molecular dynamics (MD) of a correlated electron model under the Gutzwiller approximation scheme. This model exhibits a Mott transition as a function of on-site Coulomb repulsion $U$. The repeated solution of the Gutzwiller self-consistency equations would be prohibitively expensive for large-scale MD simulations. We show that machine learning models of the Gutzwiller potential energy can be remarkably accurate. The models, which are trained with $N=33$ atoms, enable highly accurate MD simulations at much larger scales ($N\gtrsim {10}^3$). We investigate the physics of the smooth Mott crossover in the fluid phase.

We show that in quantum Hall systems at half filling, edge potentials alone can drive transitions between the Pfaffian and anti-Pfaffian topological phases. We conjecture this is true in realistic systems even in the presence of bulk interactions that weakly break the particle-hole symmetry. The strong effects of edge potentials could be understood from different topological shifts of competing phases at half filling, manifested on the disk geometry as the variation of orbital numbers at a fixed number of particles. In particular, we show analytically that the particle-hole conjugation of Hamiltonians on the disk is equivalent to the tuning of edge potentials, which allows us to explicitly demonstrate the phase transition numerically. The importance of edge potentials in various experimental contexts, including the recently discovered particle-hole symmetric phase, is also discussed.

For an isotropic single-band system, it is well known that the semiclassical Boltzmann transport theory within the relaxation time approximation and the Kubo formula with the vertex corrections provide the same result with the $(1-cos\theta )$ factor in the inverse transport relaxation time. In anisotropic multiband systems, the semiclassical Boltzmann transport equation is generalized to coupled integral equations relating transport relaxation times at different angles in different bands. Using the Kubo formula, we study the vertex corrections to the dc conductivity in anisotropic multiband systems, and we derive the relation satisfied by the transport relaxation time for both elastic and inelastic scatterings, verifying that the result is consistent with the semiclassical approach.

We report a comprehensive experimental investigation on the magnetic anisotropy in bulk single crystals of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$, a quasi-two-dimensional ferromagnet belonging to the family of magnetic layered transition metal trichalcogenides that have recently attracted a great deal of interest with regard to the fundamental and applied aspects of two-dimensional magnetism. For this purpose electron spin resonance (ESR) and ferromagnetic resonance (FMR) measurements have been carried out over a wide frequency and temperature range. A gradual change in the angular dependence of the ESR linewidth at temperatures above the ferromagnetic transition temperature $T_{\mathrm{c}}$ reveals the development of two-dimensional spin correlations in the vicinity of $T_{\mathrm{c}}$ thereby proving the intrinsically low-dimensional character of spin dynamics in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. Angular and frequency dependent measurements in the ferromagnetic phase clearly show an easy-axis-type anisotropy of this compound. Furthermore, these experiments are compared with simulations based on a phenomenological approach, which takes into account results of static magnetization measurements as well as high temperature $g$ factors obtained from ESR spectroscopy in the paramagnetic phase. As a result the determined magnetocrystalline anisotropy energy density (MAE) $K_U$ is $(0.48\pm 0.02)\times {10}^6$ erg/${\mathrm{cm}}^3$. This analysis is complemented by density functional calculations which yield the experimental MAE value for a particular value of the electronic correlation strength $U$. The analysis of the electronic structure reveals that the low-lying conduction band carries almost completely spin-polarized, quasihomogeneous, two-dimensional states.

Ultrathin films of $\beta$-tungsten $\left(\beta \text{−}\mathrm{W}\right)$ is attracting extensive attentions because of its promising application in spintronics due to giant spin Hall effect and its fundamental interest in superconductivity. By means of first-principles calculations, we have elucidated its nontrivial topological nature with multiple Dirac nodal lines in the $\beta \text{−}\mathrm{W}$ metal when spin-orbit coupling (SOC) is ignored. The analysis of electronic structures reveal that its topology is associated with the band inversion between the $d_{xz}+d_{yz}$ and $d_{z^2}$ orbitals at the $M$ point in its Brillouin zone. By switching on the SOC, these Dirac nodal lines become gapped, as accompanied with the occurrence of 24 massive Dirac fermions at the energy of 87 meV below the Fermi level. Different from the exact gapless Dirac fermions with the linear band crossings, we have identified that these massive Dirac fermions all open a tiny gap of 7 meV. In addition, we have observed the topologically protected nontrivial surface arc states connecting these massive Dirac fermions. The existence of these massive Dirac fermions in the $\beta \text{−}\mathrm{W}$ phase would be important to understand its giant spin Hall effect according to a recent study [Nature 555, 638 (2018)] where massive Dirac fermions were identified to generate Berry-curvature-induced Hall conductivity.

We report here a giant zero-point energy renormalization of 273 meV in the direct band gap at $\mathbf{K}$ in the Brillouin zone and a 571 meV of blueshifting in the position of the doubly-degenerate brightest excitonic peak in monolayer hexagonal boron nitride. The nonradiative exciton linewidth is found to be 97 meV at 0 K with a large coupling strength of 1.1 eV. This linewidth is found to be mainly dominated by the scattering from the longitudinal optical phonons near the degenerate LO-TO mode, with negligible contributions from other lower branches. Additionally, the band gap has a temperature dependent slope of $-0.53$ meV ${\mathrm{K}}^{-1}$, which we found to be in excellent agreement with the reported experimental data on large diameter boron nitride nanotubes. We obtained our results by solving a coupled electron-hole Bethe-Salpeter equation which includes the lattice vibrational dynamics, purely using an ab initio approach.

Unique properties of plasmons in two-dimensional electron systems (2DESs) have been studied for many years. Existing theoretical approaches allow for analytical study of the properties of ungated and gated plasmons in two fundamental, ideal cases—the 2DES in a dielectric environment and under an infinite metallic gate, respectively. Here we introduce an analytical theory of the interaction of gated and ungated plasmons in partly gated 2DES. Generally, a finite-width gate is formed by a metallic strip placed over an infinite plane hosting 2D electrons. Our solution, in particular, describes the propagating plasmon modes with their charge density having $N$ nodes under the gate. In this regard, a new mode with $N=0$ has been found in addition to the gapped modes with $N=1,2,\cdots$ previously derived from numerical calculations. Unexpectedly, this fundamental plasmon mode has been found to differ substantially from the rest. In fact, it is characterized by gapless square root dispersion and represents a hybrid of gated and ungated plasmons. In contrast to the higher modes, the currents and lateral fields of the fundamental mode are localized mainly to the outside area in the vicinity of the gate. Heretofore, such a “near-gate plasmon” has never been considered.

The recent discoveries of two-dimensional (2D) ferromagnetic insulators ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and ${\mathrm{CrI}}_3$ [Gong et al., Nature (London) 546, 265 (2017); Huang et al., Nature (London) 546, 270 (2017).] offer unprecedented opportunities for exploration of exotic new quantum phenomena. Here we use first-principles approaches to carry out a comparative study of the 2D heterostructures of germanene/${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and germanene/${\mathrm{CrI}}_3$, resulting in a predictive design of a highly appealing high-temperature quantum anomalous Hall effect (QAHE) system. We show that germanene-passivated ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ becomes topologically nontrivial, and can harbor the QAHE at $\sim 30$ K; in contrast, germanene-passivated ${\mathrm{CrI}}_3$ becomes a topologically trivial ferromagnetic metal. We rationalize these results based on the different interfacial couplings in the two systems, much stronger for the former because of effective Ge-Ge and Ge-Te bondings. We further show that both silicene/${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$/Ge(111) can also harbor QAHEs, offering broader opportunities for potential experimental realization of a high-temperature QAHE.

Understanding the crystal field of lanthanide complexes is pivotal for the testing of Stevens operator equivalents and the development of lanthanide-based molecular magnets. Intense theoretical investigation is aimed at the determination of the Hamiltonian parameters, but accurate experimental tests often suffer from overparametrization. Because of this, clear-cut experimental determinations are missing even high-symmetry environments. Here we present a detailed study of the crystal-field parameters of Pr(III) ions in a high-symmetry environment, using the cyano-based molecular magnetic material $\mathrm{Pr}\left[\mathrm{Co}{\left(\mathrm{CN}\right)}_6\right]·5{\mathrm{H}}_2\mathrm{O}$. The problem of multiple solutions is considered with particular detail, and we show how unequivocal determination of the parameters becomes possible only by combining different spectroscopic and magnetometric techniques. Eventually we compare the solution with fitting methodologies that are commonly employed and we highlight the level of information that can be gained by such procedures.

Exchange bias occurs in field-cooled antiferromagnet/ferromagnet systems and can most often be explained in terms of uncompensated magnetic moments at the interface that are pinned in their orientation during field cooling. The presence of spin-flop coupling is often associated with spin-compensated interfaces. Here, we report exchange bias in complex oxide heterostructures of antiferromagnetic ${\mathrm{LaFeO}}_3$ and thin layers of ferromagnetic $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ with several intriguing features. The exchange bias does not require field cooling but can also be obtained by applying a setting field at elevated temperature. Furthermore, the exchange bias is positive for setting fields up to 3 T, and its magnitude is strongly dependent on the setting-field strength. X-ray magnetic linear dichroism measurements show a predominantly perpendicular spin configuration at the interface. We discuss the possibility of the exchange bias being driven by a net moment from spin canting in the antiferromagnet due to Dzyaloshinkii-Moriya interactions.

Spin-valve structures in which a change of magnetic configuration is responsible for magnetoresistance led to impressive advances in spintronics, focusing on magnetically storing and sensing information. However, this mature technology also offers versatile control of magnetic textures with usually neglected underlying fringing fields to enable entirely different applications by realizing topologically nontrivial states. Together with proximity-induced superconductivity in a two-dimensional electron gas with a large $g$ factor, these fringing fields realized in commercially available spin valves provide Zeeman splitting, synthetic spin-orbit coupling, and confinement, needed for Majorana bound states (MBS). Detailed support for the existence and control of MBS is obtained by combining accurate micromagnetic simulation of fringing fields used as an input in the Bogoliubov–de Gennes equation to calculate low-energy spectrum, wave-function localization, and local charge neutrality. A generalized condition for a quantum phase transition in these structures provides valuable guidance for the MBS evolution and implementing reconfigurable effective topological wires.

The bound states that can occur in a superfluid vortex have recently called for attention owing to the capability of detecting them experimentally. However, a detailed theoretical account for the presence of these vortex bound states is still lacking for all temperatures in the superfluid phase and couplings along the BCS-BEC crossover. Here, we fill this gap and present a systematic theoretical study based on the Bogoliubov–de Gennes equations for the bound states that occur over the two characteristic (inner and outer) spatial ranges in which the extension of a superfluid vortex can be partitioned. It is found that the total number of bound states decreases from the BCS (weak-coupling) side of the crossover toward the intermediate-coupling region where they are still present, whereas the bound states disappear upon entering the BEC (strong-coupling) side. A scaling relation is also obtained that connects the number of bound states in the inner spatial range of the vortex to the depth and width of the vortex itself. A criterion is finally provided in terms of the local density of states, to distinguish where a given fermionic superfluid is located in the coupling-temperature phase diagram of the BCS-BEC crossover.

We theoretically investigate effects of lattice distortions on the spin ordering of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, local lattice distortions originating from the site vibration are taken into account to yield effective spin interactions via the spin-lattice coupling (SLC). The breathing lattice alternation is characterized by the ratio of the nearest-neighbor interaction for large tetrahedra to that for small ones, $J^{\prime }/J$. It is found by Monte Carlo simulations that the system exhibits a first-order transition into four different types of collinear magnetic ordered states. In the uniform case ($J^{\prime }/J=1$), the state realized at stronger SLC is cubic-symmetric characterized by the $(1/2,1/2,1/2)$ magnetic Bragg peaks, while the one at weaker SLC is tetragonal-symmetric characterized by the (1,1,0) ones. With increasing the breathing distortion (decreasing $J^{\prime }/J$), the ordering pattern of the $(1/2,1/2,1/2)$ state becomes noncubic with its magnetic Bragg reflections almost unchanged, while the (1,1,0) state is robust. The noncubic state peculiar to the breathing pyrochlores is further categorized into two types. We demonstrate that these two noncubic orderings result in the massive degeneracy of the ground state and that the associated residual entropy per spin takes characteristic values of $\simeq \frac{ln\left(4\right)}{16}{k}_{\mathrm{B}}$ and $\simeq \frac{ln\left(6\right)}{16}{k}_{\mathrm{B}}$. Experimental implications of the results are discussed.