The interaction of electrons with atomic motion critically influences charge transport properties in molecular conducting junctions and quantum dot systems, and it is responsible for a plethora of transport phenomena. Nevertheless, theoretical tools are still limited to treat simple model junctions in specific parameter regimes. In this paper, which forms the first paper of a series, we put forward a generalized input-output method (GIOM) for studying charge transport in molecular junctions accounting for strong electron-vibration interactions and including electronic and phononic environments. The method radically expands the scope of the input-output theory, which was originally put forward to treat quantum optic problems. Based on the GIOM, we derive a Langevin-type equation of motion for system operators, which possess a great generality and accuracy, and permits the derivation of a stationary charge current expression involving only two types of transfer rates. Furthermore, we devise the so-called polaron transport in electronic resonance approximation, which allows us to feasibly simulate electron dynamics in generic tight-binding models with strong electron-vibration interactions.

We apply our generalized input-output method (GIOM), introduced in the previous paper of this series, to prototype molecular junction models describing vibrationally coupled electron transport. In short junctions where analytic treatments are available, we show that the charge current obtained by the GIOM reduces to known limits and reasonably agrees with exact numerical simulations (when available). For extended junctions, we numerically reveal that the current displays a turnover from phonon-assisted to phonon-suppressed transport as a function of electronic and vibrational parameters. As an additional application, we consider a cavity-coupled molecular junction. Here we identify a cavity-induced suppression of charge current in the single-site case, and observe the coexistence of phononic and photonic sidebands in the current-voltage characteristics when both strong light-matter interaction and electron-vibration coupling are present. Together with the first paper of this series, we demonstrate that the input-output framework, which is normally employed in quantum optics, can serve as a powerful and feasible tool in the realm of electron transport junctions.

The existence of strong trigonal warping around the K point for the low-energy electronic states in multilayer ($N\ge 2$) graphene films and graphite is well established. It is responsible for phenomena such as Lifshitz transitions and anisotropic ballistic transport. The absolute orientation of the trigonal warping with respect to the center of the Brillouin zone is, however, not agreed upon. Here, we use quasiparticle scattering experiments on a gated bilayer graphene/hexagonal boron nitride heterostructure to settle this disagreement. We compare Fourier transforms of scattering interference maps acquired at various energies away from the charge neutrality point with tight-binding-based joint density of states simulations. This comparison enables unambiguous determination of the trigonal warping orientation for bilayer graphene low-energy states. Our experimental technique is promising for quasidirectly studying fine features of the band structure of gated two-dimensional materials such as topological transitions, interlayer hybridization, and moiré minibands.

We report the electronic transport features of $\mathrm{HfT}{\mathrm{e}}_5$ under external magnetic field. We observe a series of plateaus in Hall resistance ${\rho }_{xy}$ as magnetic field increases until it reaches the quantum limit at 1–2 Tesla. At the plateau regions, the longitudinal resistance ${\rho }_{xx}$ exhibits local minima. Although ${\rho }_{xx}$ is still nonzero, its value becomes much smaller than ${\rho }_{xy}$ at the last few plateaus. By mapping the Fermi surface via measuring the Shubonikov–de Haas oscillation, we find that the strength of Hall plateau is proportional to the Fermi wavelength, suggesting that its formation may be attributed to the gap opening from the interaction driven Fermi surface instability. By comparing the bulk band structures of $\mathrm{ZrT}{\mathrm{e}}_5$ and $\mathrm{HfT}{\mathrm{e}}_5$, we find that there exists an extra pocket near the Fermi level of $\mathrm{HfT}{\mathrm{e}}_5$, which may lead to the finite but nonzero longitudinal conductance.

We present the electronic and structural properties of monolayer ${\mathrm{WSe}}_2$ grown by pulsed-laser deposition on monolayer graphene (MLG) on SiC. The spin splitting in the ${\mathrm{WSe}}_2$ valence band at $\overline{\mathrm{K}}$ was ${\mathrm{\Delta }}_{\mathrm{SO}}=0.469\pm 0.008$ eV, as determined by angle-resolved photoemission spectroscopy. Synchrotron-based grazing-incidence in-plane x-ray diffraction (XRD) revealed the in-plane lattice constant of monolayer ${\mathrm{WSe}}_2$ to be $a_{{\mathrm{WSe}}_2}=3.2757\pm 0.0008$ Å. This indicates a lattice compression of $-0.19$% relative to bulk ${\mathrm{WSe}}_2$. By using the experimentally determined graphene lattice constant ($a_{\mathrm{MLG}}=2.4575\pm 0.0007$ Å), we found that a $3\times 3$ unit cell of the slightly compressed ${\mathrm{WSe}}_2$ is perfectly commensurate with a $4\times 4$ graphene lattice with a mismatch below 0.03%, which could explain why the monolayer ${\mathrm{WSe}}_2$ is compressed on MLG. From XRD and first-principles calculations, we conclude that the observed size of strain will affect ${\mathrm{\Delta }}_{\mathrm{SO}}$ only on the order of a few meV. In addition, angle-resolved, ultraviolet, and x-ray photoelectron spectroscopies shed light on the band alignment between ${\mathrm{WSe}}_2$ and MLG/SiC and indicate electron transfer from graphene to the ${\mathrm{WSe}}_2$ monolayer. As further revealed by atomic force microscopy, the ${\mathrm{WSe}}_2$ island size depends on the number of carbon layers on top of the SiC substrate. This suggests that the epitaxy of ${\mathrm{WSe}}_2$ favors the weak van der Waals interactions with graphene, while it is perturbed by the influence of the SiC substrate and its carbon buffer layer.

Knabe's theorem lower bounds the spectral gap of a one-dimensional frustration-free local Hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gap threshold for Hamiltonians that are gapless in the thermodynamic limit, showing that the local spectral gap must scale inverse linearly with the length of the region for such systems. Recent works have further improved upon this threshold, tightening it in the one-dimensional case and extending it to higher dimensions. Here, we show a local spectral gap threshold for frustration-free Hamiltonians on a finite-dimensional lattice that is optimal up to a constant factor that depends on the dimension of the lattice. Our proof is based on the detectability lemma framework and uses the notion of a coarse-grained Hamiltonian (introduced in [Anshu et al., Phys. Rev. B 93, 205142]) as a link connecting the (global) spectral gap and the local spectral gap.

Here we analyze the divergences of the irreducible vertex function in dynamical mean field theory, which may indicate either a nonphysical breakdown of the perturbation theory or a response to some physical phenomenon. To investigate this question, we construct a quasiparticle vertex from the diverging irreducible vertex functions. This vertex describes the scattering between quasiparticles and quasiholes in a Fermi liquid. We show that the quasparticle vertex does not diverge in the charge channel, wherein the irreducible vertex does diverge; and we show that the quasiparticle vertex does diverge in the spin channel, wherein the irreducible vertex does not diverge. This divergence occurs at the Mott transition, wherein the Fermi-liquid theory breaks down. Both the half filled Hubbard and Anderson lattices are investigated. In general, our results support that the divergences of the irreducible vertex function do not indicate a nonphysical failure of the perturbation theory. Instead, the divergences are the mathematical consequence of inverting a matrix (the local charge susceptibility) which accumulates increasingly negative diagonal elements as the Hubbard interaction suppresses charge fluctuations. Indeed, we find that the first divergences of the irreducible vertex in both Hubbard and Anderson lattices occurs near the maximum magnitude of the (negative) vertex-connected part of the charge susceptibility.

Realizing remarkable tunability in optical properties without sacrificing speed is critical to obtain all optical ultrafast devices. In this work, we investigate the ultrafast temporal behavior of optically tunable epsilon-near-zero (ENZ) metamaterials, operating in the visible spectral range. To perform this the ultrafast dynamics of the hot electrons is acquired by femtosecond pump-probe spectroscopy and studied based on a two-temperature model (2TM). We show that pumping with femtosecond pulses changes the effective permittivity of the metamaterial by more than $400\%$. This significant modulation is more pronounced in the ENZ region and we confirm this by the 2TM. The realized ultrafast modulation in effective permittivity, along with the ultrashort relaxation time of 3.3 ps, opens another avenue towards ultrafast photonic applications.

We study the influence of quantum dot symmetry on the Rabi frequency and phonon-induced spin relaxation rate in a single-electron GaAs spin qubit. We find that anisotropic dependence on the magnetic field direction is independent of the choice of the gating potential. Also, we discover that relative orientation of the quantum dot, with respect to the crystallographic frame, is relevant in systems with ${\mathbf{C}}_{1\mathrm{v}}$, ${\mathbf{C}}_{2\mathrm{v}}$, or ${\mathbf{C}}_n$ ($n\ne 4r$) symmetry. To demonstrate the important impact of the gating potential shape on the spin qubit lifetime, we compare the effects of an infinite-wall equilateral triangle, square, and rectangular confinement with the known results for the harmonic potential. In the studied cases, enhanced spin qubit lifetime is revealed, reaching almost six orders of magnitude increase for the equilateral triangle gating.

Recent experimental realizations of the topological semimetal states in several monolayer systems are very attractive because of their exotic quantum phenomena and technological applications. Based on first-principles density-functional theory calculations including spin-orbit coupling, we here explore the drastically different two-dimensional (2D) topological semimetal states in three monolayers, ${\mathrm{Cu}}_2\mathrm{Ge}$, ${\mathrm{Fe}}_2\mathrm{Ge}$, and ${\mathrm{Fe}}_2\mathrm{Sn}$, which are isostructural with a combination of the honeycomb Cu or Fe lattice and the triangular Ge or Sn lattice. We find that (i) the nonmagnetic (NM) ${\mathrm{Cu}}_2\mathrm{Ge}$ monolayer with a planar geometry exhibits the massive Dirac nodal lines, (ii) the ferromagnetic (FM) ${\mathrm{Fe}}_2\mathrm{Ge}$ monolayer with a buckled geometry exhibits the massive Weyl points, and (iii) the FM ${\mathrm{Fe}}_2\mathrm{Sn}$ monolayer with a planar geometry and an out-of-plane magnetic easy axis exhibits the massless Weyl nodal lines. It is therefore revealed that mirror symmetry cannot protect the fourfold-degenerate Dirac nodal lines in the NM ${\mathrm{Cu}}_2\mathrm{Ge}$ monolayer but preserves the doubly degenerate Weyl nodal lines in the FM ${\mathrm{Fe}}_2\mathrm{Sn}$ monolayer. Our findings demonstrate that the interplay of crystal symmetry, magnetic easy axis, and band topology is of importance for tailoring various 2D topological states in ${\mathrm{Cu}}_2\mathrm{Ge}$, ${\mathrm{Fe}}_2\mathrm{Ge}$, and ${\mathrm{Fe}}_2\mathrm{Sn}$ monolayers.

Converting information into work has, during the past decade, gained renewed interest as it gives insight into the relation between information theory and thermodynamics. Here, we theoretically investigate an implementation of Maxwell's demon in a double quantum dot and demonstrate how heat can be converted into work using only information. This is accomplished by continuously monitoring the charge state of the quantum dots and transferring electrons against a voltage bias using a feedback scheme. We investigate the electrical work produced by the demon and find a non-Gaussian work distribution. To illustrate the effect of a realistic charge detection scheme, we develop a model taking into account noise as well as a finite delay time and show that an experimental realization is feasible with present day technology. Depending on the accuracy of the measurement, the system is operated as an implementation of Maxwell's demon or a single-electron pump.

We determined the lattice dynamics of metastable, surface-stabilized $\alpha$-phase ${\mathrm{FeSi}}_2$ nanoislands epitaxially grown on the Si(111) surface with average heights and widths ranging from 1.5 to 20 nm and 18 to 72 nm, respectively. The crystallographic orientation, surface morphology, and local crystal structure of the nanoislands were investigated by reflection high-energy electron diffraction, atomic force microscopy, and x-ray absorption spectroscopy. The Fe-partial phonon density of states (PDOS), obtained by nuclear inelastic scattering, exhibits a pronounced damping and broadening of the spectral features with decreasing average island height. First-principles calculations of the polarization-projected Si- and Fe-partial phonon dispersions and PDOS enable the disentanglement of the contribution of the $xy$- and $z$-polarized phonons to the experimental PDOS. Modeling of the experimental data with the theoretical results unveils an enhanced damping of the $z$-polarized phonons for islands with average sizes below 10 nm. This phenomenon is attributed to the fact that the low-energy $z$-polarized phonons couple to the low-energy surface/interface vibrational modes. The thermodynamic and elastic properties obtained from the experimental data show a pronounced size-dependent behavior.

Using first-principle calculations, we systematically study strain tuning of the electronic properties of two-dimensional graphitic carbon nitride nanosheets with empirical formula $C_n{N}_m$. We found the following: (i) the ferromagnetic ordered state in the metal-free systems $(n,m)=(4,3)$, (10,9), and (14,12) remains stable in the presence of strain of about $6\%$. However, the system (9,7) loses its ferromagnetic ordering when increasing strain. This is due to the presence of topological defects in the (9,7) system, which eliminates the asymmetry between spin up and spin down of the $p_z$ orbitals when strain is applied. (ii) By applying uniaxial strain, a band gap opens in systems which are initially gapless. (iii) In semiconducting systems which have an initial gap of about 1 eV, the band gap is closed with applying uniaxial strain.

We derive a set of rules for transforming integrals over the time contour met in the theory of nonequilibrium Green's functions (NEGF) into usual integrals over the real and imaginary times for the case when the system's Hamiltonian is different on each track. This situation is encountered, e.g., in the influence functional formalism of the path integrals theory when integrating over all trajectories associated with a part of a system.

We report on the study of the thermal dynamics of square artificial spin ice, probed by means of temperature- and frequency-dependent ac susceptibility. Pronounced influence of the interisland coupling strength was found on the frequency response of the samples. Through the subsequent analysis of the frequency- and coupling-dependent freezing temperatures, we discuss the phenomenological parameters obtained in the framework of the Vogel-Fulcher-Tammann law in terms of the samples' microscopic features. The high sensitivity and robust signal to noise ratio of ac susceptibility validate the latter as a promising and simple experimental technique for resolving the dynamics and temperature driven dynamics crossovers for the case of artificial spin ice.

It is argued that an analog of a supersymmetric quantum mechanical spectrum can be realized in a Josephson junction formed by a topological insulator. These Andreev bound states can be studied by means of a circuit quantum electrodynamics setup. At the same time the equilibrium Josephson current has a more complicated analytical structure and is not expressed in terms of the Andreev states by a standard formula.

Complex quantum coupling phenomena of halide perovskites are examined through ab initio calculations and exact diagonalization of model Hamiltonians to formulate a set of fundamental guiding rules to engineer the band gap through strain. The band-gap tuning in halides is crucial for photovoltaic applications and for establishing nontrivial electronic states. Using ${\mathrm{CsSnI}}_3$ as the prototype material, we show that in the cubic phase, the band gap reduces irrespective of the nature of strain. However, for the tetragonal phase, it reduces with tensile strain and increases with compressive strain, while the reverse is the case for the orthorhombic phase. The reduction can give rise to negative band gap in the cubic and tetragonal phases leading to normal to topological insulator phase transition. Also, these halides tend to form a stability plateau in a space spanned by strain and octahedral rotation. In this plateau, with negligible cost to the total energy, the band gap can be varied in a range of 1 eV. Furthermore, we present a descriptor model for the perovskite to simulate their band gap with strain and rotation. Analysis of band topology through model Hamiltonians led to the conceptualization of topological influencers that provide a quantitative measure of the contribution of each chemical bonding towards establishing a normal or topological insulator phase. On the technical aspect, we show that a four orbital based basis set ($\text{Sn}-\{s,p\}$ for ${\mathrm{CsSnI}}_3$) is sufficient to construct the model Hamiltonian which can explain the electronic structure of each polymorph of halide perovskites.

We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and twisted double bilayer (TDBG) graphene under perpendicular pressure. An approach has been proposed to obtain the equilibrium in-plane structural deformation and out-of-plane corrugation in moiré superlattices under pressure. We find that the in-plane relaxation becomes much stronger under higher pressure, while the corrugation height in each layer is maintained. A comparison between the band structures of relaxed and rigid structures demonstrates that not only the gaps on the electron and hole sides (${\mathrm{\Delta }}_e$ and ${\mathrm{\Delta }}_h$) are significantly underestimated without relaxation, but also the detailed dispersions of the middle bands of rigid structures are rather different from those of relaxed systems. ${\mathrm{\Delta }}_e$ and ${\mathrm{\Delta }}_h$ in TBG reach maximum values around critical pressures with the narrowest middle bands. Topological transitions occur in TDBG under pressure with the middle valence and conduction bands in one valley touching and their Chern numbers transferred to each other. The pressure can also tune the gap at the neutrality point of TDBG, which becomes closed for a pressure range and reopened under higher pressure. The behavior of the electronic structure of superlattices under pressure is sensitive to the twist angle $\theta$ with the critical pressures generally increasing with $\theta$.

We present an ab initio $GW$ self-energy calculation of the electronic structure of ${\mathrm{LaNiO}}_2$. With respect to density-functional theory, we find that in $GW$ the La $4f$ states undergo an important $+2$ eV upward shift from the Fermi level, while the O $2p$ states are pulled down by $-1.5$ eV, thus reinforcing the charge-transfer character of this material. However, $GW$ many-body effects leave the $d$-like bands at the Fermi level almost unaffected, so that the Fermi-surface topology is preserved, unlike in cuprates.