For a many-body system of arbitrary dimension, we consider fermionic ground states of noninteracting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $\mathrm{\Delta }$ between the number of occupied symmetric and antisymmetric single-particle states is a topological invariant in this case. We prove lower bounds on the configurational and the number entropy based on this invariant. Entanglement entropies are particularly important for identifying topological phases protected by spatial symmetries because they lack gapless boundary modes in general. In topological crystalline insulators, the topological invariant $\mathrm{\Delta }$ and the entropy bounds can be directly determined from high-symmetry points in the Brillouin zone.

The dynamic balance between pair creation and annihilation processes takes a crucial role to the topological superconductivity in the Kitaev model. Here we study the effect of spatial separation of creation and annihilation terms, i.e., sources and drains of pair are arranged alternatively. In this regard, a non-Hermitian Hamiltonian is naturally considered, which may possess complex energy branches. However, when the Bardeen-Cooper-Schrieffer pair excitation is only considered, the spectrum in such a subspace is fully real. In particular, the Zak phases extracted from the pair wave function are quantized and therefore able to characterize the different phases regardless of the breaking of time-reversal symmetry. For open chain system, the corresponding Majorana lattice is investigated. We find that although there are complex modes, all the edge modes have zero energy and obey the bulk-boundary correspondence. This results in the Kramer-type degeneracy of both the real and complex levels as a signature of the topologically nontrivial phase.

Here we present an analysis of the evolution of Majorana corner modes realizing in a two-dimensional higher-order topological superconductor (HOTSC) on a square lattice under the influence of local Coulomb repulsion. Both weak- and strong-interaction regimes are studied. It is shown that in the homogeneous system, the weak repulsion widens the region of the topologically nontrivial phase on the phase diagram. The open-boundary effect, resulting in spatial inhomogeneity of the system, leads to the appearance of the ground-state crossover as the repulsion intensity increases. Before the crossover, concentration correlators are $C_4$ symmetric and spin independent, and the corner states have energies that are determined by the overlap of the excitation wave functions localized at the different corners. After the crossover, the concentration correlators are spin dependent and possess the spontaneously broken symmetry. In turn, the corner excitation energy is size independent and defined by the Coulomb repulsion intensity with a quadratic law. In the strong-repulsion regime we derive the effective HOTSC Hamiltonian in the atomic representation and found a rich variety of interactions induced by virtual processes between the lower and upper Hubbard subbands. It is shown that Majorana corner modes still can be realized in the limit of the infinite repulsion, although the boundaries of the topologically nontrivial phase are strongly renormalized by Hubbard corrections.

Reading out the parity degree of freedom of Majorana bound states is key to demonstrating their non-Abelian exchange properties. Here, we present a low-energy model describing localized edge states in a two-arm device. We study parity-to-charge conversion based on coupling the superconductor bound states to a quantum dot whose charge is read out by a sensor. The dynamics of the system, including the readout device, is analyzed in full using a quantum-jump approach. We show how the resulting signal and signal-to-noise ratio differentiates between local Majorana and Andreev bound states.

We apply digitized quantum annealing (QA) and quantum approximate optimization algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At variance with the usual QAOA applications to MaxCut, or to quantum spin-chains ground-state preparation, here the classical cost function is characterized by highly nonlocal multispin interactions. Yet, we provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem, and we prove numerically an enhanced performance of QAOA over traditional QA. We also investigate on the role of the classical cost-function landscape geometry in this problem. By artificially breaking this geometrical structure, we show that the detrimental effect of a gap-closing transition, encountered in QA, is also negatively affecting the performance of our QAOA implementation.

Ultrafast laser irradiation of metals can elevate the temperature of electrons to the same order as the Fermi temperature while the lattice remains cold. In this transient and highly nonequilibrium regime, the material properties can undergo drastic modifications, revealing insights into the physical phenomena of the condensed state that are otherwise not evident under equilibrium conditions. However, a clear description of these phenomena, even for elemental metals, remains greatly unexplored partly due to the limitations imposed by the phenomenological treatment of electron-phonon scattering with simplified assumptions for these highly nonequilibrium regimes. In this work, using recent advancements in first-principles calculations, we provide a detailed understanding of hot electron dynamics in a free-electron-like metal (aluminum) and a noble metal (gold) to demonstrate the important role played by the electronic structure in dictating their transport properties at elevated electron temperatures. By performing parameter-free density functional theory calculations of the electron-temperature-dependent heat capacities, electron-phonon coupling, electron mean-free paths, and thermal conductivities, we show that semiempirical and free-electron estimations can lead to erroneous predictions, especially for the case of gold where the excitation of the low-lying $d$ bands can drastically modify the transport properties. We find that the diffusive mean-free paths of electrons in gold can be increased from $\sim 35\mathrm{nm}$ at ambient conditions to $\sim 70\mathrm{nm}$ at electron temperatures of $k_{\mathrm{B}}{T}_e=6\mathrm{eV}$ as a result of drastically reduced electron-phonon scattering. In contrast, we find that the mean-free paths of electrons in aluminum are relatively insensitive to high electron temperature perturbations mainly resulting from the unchanged electron-phonon scattering even at elevated electron temperatures. This ultimately results in a much greater increase in the thermal conductivity of gold at electron temperatures of $\sim 20000$ K, where it increases by more than two orders of magnitude. However, in aluminum, the thermal conductivity increase at the elevated electron temperatures is relatively not as pronounced (which increases by a factor of $\sim 70$). Our results shed light on the microscopic understanding of hot electron dynamics in metals and is crucial for a plethora of applications such as in plasmonic devices.

In pump-probe spectroscopies, THz pulses are used to quench a system, which is subsequently probed by either a THz or optical pulse. In contrast, third-harmonic generation experiments employ a single multicycle driving pulse and measure the induced third harmonic. In this work, we analyze a spectroscopy setup where both a quench and a drive are applied and two-dimensional spectra as a function of time and quench-drive delay are recorded. We calculate the time evolution of the nonlinear current generated in the superconductor within an Anderson-pseudospin framework and characterize all experimental signatures using a quasiequilibrium approach. We analyze the superconducting response in Fourier space with respect to both the frequencies corresponding to the real time and the quench-drive delay time. In particular, we show the presence of a transient modulation of higher harmonics, induced by a wave mixing process of the drive with the quench pulse, which probes both quasiparticle and collective excitations of the superconducting condensate.

In a recent work by Schrodi et al. [Phys. Rev. B 104, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi et al. Our Monte Carlo results for these parameters suggest that unconventional pairing correlations do not exceed their noninteracting values at any carrier concentration we have checked. Instead, strong charge-density-wave correlations persist at the lowest accessible temperatures for dilute and nearly half-filled bands. Lastly, we present arguments for how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the presence of Fermi surface nesting.

The theory of bulk orbital magnetization has been formulated both in reciprocal space based on Berry curvature and related quantities, and in real space in terms of the spatial average of a quantum mechanical local marker. Here we consider a three-dimensional antiferromagnetic material having a vanishing bulk but a nonzero surface orbital magnetization. We ask whether the surface-normal component of the surface magnetization is well defined, and if so, how to compute it. As the physical observable corresponding to this quantity, we identify the macroscopic current running along a hinge shared by two facets. However, the hinge current only constrains the difference of the surface magnetizations on the adjoined facets, leaving a potential ambiguity. By performing a symmetry analysis, we find that only crystals exhibiting a pseudoscalar symmetry admit well-defined magnetizations at their surfaces at the classical level. We then explore the possibility of computing surface magnetization via a coarse-graining procedure applied to a quantum local marker. We show that multiple expressions for the local marker exist, and apply constraints to filter out potentially meaningful candidates. Using several tight-binding models as our theoretical test bed and several potential markers, we compute surface magnetizations for slab geometries and compare their predictions with explicit calculations of the macroscopic hinge currents of rod geometries. We find that only a particular form of the marker consistently predicts the correct hinge currents.

The one-dimensional Rice-Mele lattice consisting of two-site unit cells enables topological charge pumping at low enough temperatures. We show here that energy pumping is feasible in this system. We analyze energy polarization using the second-quantization formalism and connect it to intercell energy current by the relevant continuity equation. Following this formulation, we numerically evaluate the energy current pumped in an adiabatic cycle when the system parameters vary periodically and slowly with time. Unlike the pumped charge, the pumped energy is entirely temperature independent at half-filling. The global Berry phase for all bands and the related topological phase transitions during the pumping cycle account for the energy pumping. The present paper paves the way for manipulating energy current without electric and thermal biases.

The orbital magnetoelectric effect (OME) generically refers to the appearance of an orbital magnetization induced by an applied electric field. Here, we show that nanoribbons of transition metal dichalcogenides (TMDs) with zigzag edges may exhibit a sizable OME activated by an electric field applied along the ribbons' axis. We examine nanoribbons extracted from a monolayer (1L) and a bilayer (2L) of ${\mathrm{MoS}}_2$ in the trigonal structural phase. Transverse profiles of the induced orbital angular momentum accumulations are calculated to first order in the longitudinally applied electric field. Our results show that close to the nanoribbon's edge-state crossings energy, the orbital angular momentum accumulations take place mainly around the ribbons' edges. They have two contributions: one arising from the orbital Hall effect (OHE) and the other consisting in the OME. The former is transversely antisymmetric with respect to the principal axis of the nanoribbon, whereas the latter is symmetric and hence responsible for the resultant orbital magnetization induced in the system. We found that the orbital accumulation originating from the OHE for the 1L nanoribbon is approximately half that of a 2L nanoribbon. Furthermore, while the OME can reach fairly high values in 1L-TMD nanoribbons, it vanishes in the 2L ones that preserve spatial inversion symmetry. The microscopic features that justify our findings are also discussed.

We investigate the ability of selective cavity coupling to a topological chain for tailoring the connectivity of Majorana fermions. We show how topological qubits (TQs), associated with nonlocal Majorana fermion pairing, can be displaced from the edges to the bulk of a topological chain through selective access to light-matter interaction with specific physical sites. In particular, we present a comprehensive density matrix renormalization group study of ground-state features in different chain-cavity coupling geometries, and we validate analytical insights in the strong-coupling regime. This type of Majorana fermion correlation generation process comes with emergent cavity photon features. Moreover, by considering the time evolution after a sudden quench of the cavity-matter coupling strength, we show that the development of high nontrivial matter (Majorana) correlations leaves behind measurable nonclassical photon imprints in the cavity. Innovative ways to dynamically generate TQ nonlocal correlations in topological chains of arbitrary length are thus provided, opening alternative routes to controllable long-range entanglement in hybrid photonic solid-state systems.

The self-screening error in the random-phase approximation and the $GW$ approximation (GWA) is a well-known issue and has received attention in recent years with several methods for a correction being proposed. Here, we apply two of these, a self-screening and a so-called self-polarization correction scheme, to model calculations to examine their applicability. We also apply a local form of the self-screening correction to ab initio calculations of real materials. We find indications for the self-polarization scheme to be the more appropriate choice of correction for localized states, while we additionally observe that it suffers from causality violations in the strongly correlated regime. The self-screening correction, on the other hand, significantly improves the description in more delocalized states. It is found to provide a notable reduction in the remaining GWA error when calculating the band gaps of several semiconductors, indicating a physical explanation for a part of the remaining discrepancy in one-shot $GW$ compared with experiment, while leaving the localized semicore $d$ states mostly unaffected.

We study the anomalous Hall effect (AHE) in tilted Weyl metals with weak Gaussian disorder under the Kubo-Streda formalism in this work. To separate the three different contributions, namely, the intrinsic, side-jump, and skew-scattering contributions, it is usually considered necessary to go to the eigenstate (chiral) basis of the Kubo-Streda formula. However, it is more straightforward to compute the total Hall current in the spin basis. For this reason, we develop a systematic and transparent scheme to separate the three different contributions in the spin basis for relativistic systems by building a one-to-one correspondence between the Feynman diagrams of the different mechanisms in the chiral basis and the products of the symmetric and antisymmetric parts of the polarization operator in the spin basis. We obtained the three contributions of the AHE in tilted Weyl metals by this scheme and found that the side-jump contribution exceeds both the intrinsic and skew-scattering contributions for the low-energy effective Hamiltonian. We compared the anomalous Hall current obtained from our scheme with the results from the semiclassical Boltzmann equation approach under the relaxation time approximation and found that the results from the two approaches agree with each other in the leading order of the tilting velocity.

Proton incorporation through ionic liquid gating (ILG) has become an efficient strategy to manipulate the novel ground-state properties in complex oxides. However, the mechanisms of proton evolution and their correlations with other degrees of freedom in quantum material systems are still unclear. Herein, we provide insights into the correlated interactions among different lattice-spin-orbital-spin degrees of freedom in spinel ${\mathrm{NiCo}}_2{\mathrm{O}}_4$ (NCO) films with a complex local electronic configuration and coordination environments. Our results reveal that the Ni ions near the Fermi level show the prior ${\mathrm{Ni}}^{3+}\to {\mathrm{Ni}}^{2+}$ response, whereas the Co ions at different octahedral and tetrahedral sites exhibit a stepwise ${\mathrm{Co}}^{3+}\to {\mathrm{Co}}^{2+}$ evolution. The gradual evolutions reflected in both structure and electronic configuration aspects determine the different electronic conducting mechanisms as well as the variation of the magnetic ground states in the protonated NCO films. Our systematic structure-property investigations shed light on the fundamental understanding of the strongly correlated nature in quantum materials and the manipulation of quantum materials with desired functionalities through the ILG approach.