In this work we present a comprehensive analysis of collective electronic fluctuations and their effect on single-particle properties of the Hubbard model. Our approach is based on a standard dual fermion and boson scheme with the interaction truncated at the two-particle level. Within this framework we compare various approximations that differ in the set of diagrams (ladder vs exact diagrammatic Monte Carlo), and/or in the form of the four-point interaction vertex (exact vs partially bosonized). This allows to evaluate the effect of all components of the four-point vertex function on the electronic self-energy. In particular, we observe that contributions that are not accounted for by the partially bosonized approximation for the vertex have only a minor effect on electronic degrees of freedom in a broad range of model parameters. In addition, we find that in the regime, where the ladder dual fermion approximation provides an accurate solution of the problem, the leading contribution to the self-energy is given by the longitudinal bosonic modes. This can be explained by the fact that contributions of transverse particle-hole and particle-particle modes partially cancel each other. Our results justify the applicability of the recently introduced dual triply irreducible local expansion (D-TRILEX) method that represents one of the simplest consistent diagrammatic extensions of the dynamical mean-field theory. We find that the self-consistent D-TRILEX approach is reasonably accurate also in challenging regimes of the Hubbard model, even where the dynamical mean-field theory does not provide the optimal local reference point (impurity problem) for the diagrammatic expansion.

Twisted bilayer graphene (TBG) exhibits many fascinating electronic and transport properties. Here we analyze the nonlinear optical response in TBG in the terahertz regime. By considering an effective two-band model with a simplified interlayer tunnel, we write the time-dependent wave function in terms of generalized Floquet states consisting of multiple high-order harmonics. A two-component spinor recursion relation is solved up to terms in the third order of the applied field. The third-order conductivity of TBG with different twist angles is obtained. For small twist angles the Kerr effect dominates over the high harmonic processes, while for large twist angles, the high harmonic processes completely dominate the nonlinear response. We attribute this phenomenon to the band dispersion sensitive transition probability in low- and high-energy regimes. The frequency- and temperature-dependent critical field is also presented. The critical field is insensitive to the temperature, indicating that the nonlinear response persists at room temperature.

The chiral Hamiltonian for twisted graphene bilayers is written as a $2\times 2$ matrix operator by a renormalization of the Hamiltonian that takes into account the particle-hole symmetry. This results in an effective Hamiltonian written in terms of Pauli matrices with three contributions: a kinetic term, a confinement potential, and a non-Abelian gauge field. The action of the proposed renormalization maps zero-mode flat bands into ground states. On each graphene layer, modes near zero energy have an antibonding nature in a triangular lattice. This leads to a phase-frustration effect associated with massive degeneration and makes flat-band modes similar to confined modes observed in other bipartite lattices. At magic angles, it is shown that the intralayer frustration is exactly zero. Surprisingly, the proposed Hamiltonian renormalization suggests that flat bands at magic angles are akin to floppy-mode bands in flexible crystals or glasses, making an unexpected connection between rigidity topological theory and twisted two-dimensional superconductor systems.

We calculate the conductance spectra of a Co atom adsorbed on Cu(111), considering the Co $3d$ orbitals within a correlated multiple configurations model interacting through the substrate band with the Co $4s$ orbital, which is treated in a mean-field-like approximation. By symmetry, only the $d_{z^2}$ orbital couples with the $s$ orbital through the Cu bands, and the interference between both conduction channels introduces a zero-bias anomaly in the conductance spectra. We find that, while the Kondo resonance is mainly determined by the interaction of the Co $d$ orbitals with the bulk states of the Cu(111) surface, a proper description of the contribution given by the coupling with the localized surface states to the Anderson widths is crucial to describe the interference line shape. We find that the coupling of the Co $4s$ orbital with the Shockley surface states is responsible for two main features observed in the measured conductance spectra, the dip shape around the Fermi energy and the resonance structure at the surface state low band edge.

In pure ferroelastics, the coupling existing under applied electric field between spontaneous strain and electric polarization is shown theoretically to transform the paraelastic and ferroelastic phases into polarized phases. This effect is rooted in the existence in the zero-field crystal structure of most ferroelastics of polarizable crystallographic sites forming an antiferroelectric array of dipoles. Under high fields the polar ferroelastic phase can become ferroelectric across a first-order isostructural transition, which exhibits a double hysteresis loop.

Two-dimensional (2D) multiferroics have attracted considerable interest since the recent discovery of 2D ferroelectricity and ferromagnetism in van der Waals materials. Here we show the universality of 2D multiferroics in the Ca-based double-perovskite bilayer system and the transition of magnetization that is dependent on the ferroelectric switching paths by combining symmetry analysis and first-principles calculation. We demonstrate that although both the switching of rotation and tilt distortion can lead to polarization reversal, only the latter can cause a change in the direction of magnetization. The breaking of the inversion symmetry correlation between the initial and final polarization states is the key to achieve the transition of magnetization caused by polarization reversal. The ferroelectric switching that reverses tilt distortion via multistep switching generally has the lowest energy barrier, providing the feasibility of controlling magnetization by an electric field.

We carry out density functional theory (DFT) calculations to explore the antiferromagnetic (AFM) spin cycloid in multiferroic ${\mathrm{BiFeO}}_3$ of the $R3c$ ground state structure. We calculate the energy dispersion $E\left(\mathbf{q}\right)$ of cycloidal spin spirals along the high symmetry directions of the pseudo-cubic unit cell and find a flat AFM spin spiral (or cycloid) ground state with a periodicity of $\sim 80$ nm, which is in good agreement with experiments. To investigate which structural distortion of the $R3c$ phase is the driving mechanism for the stabilization of this cycloid, we further study three artificial phases: cubic, $R\overline{3}c$, and $R3m$. In all cases, we find a large exchange frustration. The comparison between these phases provides detailed insight about how polarization and octahedral antiphase tilting affect the different magnetic interactions and the magnetic ground state in ${\mathrm{BiFeO}}_3$. In $R3c{\mathrm{BiFeO}}_3$, the magnetic ground state is driven by a competition between the frustrated exchange stemming from the hybridization between the elements Bi, Fe, O and the Dzyaloshinskii-Moriya (DM) interaction due to the Fe-Bi ferroelectric displacement. The cycloid appears to be stable because the anisotropy energy in $R3c{\mathrm{BiFeO}}_3$ is relatively small to enforce a collinear order.

We report a mechanical point-contact spectroscopy study on the single crystalline ${\mathrm{NbGe}}_2$ with a superconducting transition temperature $T_c=2.0$–2.1 K. The differential conductance curves at 0.3 K can be well fitted by a single-gap $s$-wave Blonder-Tinkham-Klapwijk model and the temperature-dependent gap follows a standard Bardeen-Cooper-Schrieffer behavior, yielding ${\mathrm{\Delta }}_0\sim 0.32$ meV and $2{\mathrm{\Delta }}_0/k_{\text{B}}{T}_c=3.62$ in the weak-coupling limit. In magnetic field, the superconducting gap at 0.3 K remains constant up to $H_{c1}\sim 150$ Oe and gradually decreases until $H_{c2}\sim 350$ Oe, indicating ${\mathrm{NbGe}}_2$ is going through a transition from a type-I to type-II (possible type-II/1) superconductor at low temperature.

We studied the nature of Yu-Shiba-Rusinov (YSR) bound states in response to the potential scattering $U$ by tuning the electron density at the Fermi energy. By comparing two systems, Mn-phthalocyanine molecules on Pb(111) and Co atoms on PbSe/Pb(111), we demonstrate that the sign of $U$ can be unambiguously determined by varying the electron density at the Fermi energy. We further show that $U$ competes with the exchange interaction $JS$ in the formation of YSR bound states. Our work provides insights into the interactions between magnetic atoms and superconductors at a fundamental level.

Non-Hermitian (NH) systems with aperiodic order display phase transitions that are beyond the paradigm of Hermitian physics. This motivates the search for exactly solvable models, where localization-delocalization phase transitions, mobility edges in complex plane, and their topological nature can be unraveled. Here, we present an exactly solvable model of quasicrystal, which is a nonpertrurbative NH extension of a famous integrable model of quantum chaos proposed by Grempel et al. [Phys. Rev. Lett. 49, 833 (1982)] and dubbed the Maryland model. Contrary to the Hermitian Maryland model, its NH extension shows a richer scenario, with a localization-delocalization phase transition via topological mobility edges in complex energy plane.

We compute spin-orbit torques (SOTs) in strained PtMnSb from first principles. We consider both tetragonal strain and shear strain. We find a strong linear dependence of the field-like SOTs on these strains, while the antidamping SOT is only moderately sensitive to shear strain and even insensitive to tetragonal strain. We also study the dependence of the SOT on the magnetization direction. In order to obtain analytical expressions suitable for fitting our numerical ab initio results we derive a general expansion of the SOT in terms of all response tensors that are allowed by crystal symmetry. Our expansion includes also higher-order terms beyond the usually considered lowest order. We find that the dependence on the strain is much smaller for the higher-order terms than for the lowest order terms. In order to judge the sensitivity of the SOT to the exchange correlation potential we compute the SOT in both GGA and LDA. We find that the higher-order terms depend significantly on the exchange-correlation potential, while the lowest order terms are insensitive to it. Since the higher-order terms are small in comparison to the lowest order terms the total SOT is insensitive to the exchange correlation potential in strained PtMnSb.

Stimulated by recent works highlighting the indispensable role of Coulomb interactions in the formation of helical chains and chiral electronic order in the elemental chalcogens, we explore the $p$-orbital Hubbard model on a one-dimensional helical chain. By solving it in the Hartree approximation we find a stable ground state with a period-3 orbital density wave. We establish that the precise form of the emerging order strongly depends on the Hubbard interaction strength. In the strong-coupling limit, the Coulomb interactions support an orbital density wave that is qualitatively different from that in the weak-coupling regime. We identify the phase transition separating these two orbital ordered phases and show that realistic values for the interorbital Coulomb repulsion in elemental chalcogens place them in the weak-coupling phase, in agreement with observations of the order in the elemental chalcogens.

We study a hybrid structure, comprising a single-level quantum dot attached to a topological superconducting nanowire, analyzing dynamical transfer of the Majorana quasiparticle onto the normal region. Motivated by the recent experimental realization of such a heterostructure and its investigation under stationary conditions [Schneider et al., Nat. Commun. 11, 4707 (2020)] where the quantum dot energy level can be tuned by gate potential, we examine how much time is needed for the Majorana mode to leak into the normal region. We estimate that for typical hybrid structures this dynamical process would take about 20 ns. We propose a feasible empirical protocol for its detection by means of the time-resolved Andreev tunneling spectroscopy.

We study the hot electron energy-loss rate (ELR) induced by acoustic $P^{\mathrm{ac}}$ and optical $P^{\mathrm{op}}$ phonons, in two-dimensional transition-metal dichalcogenides (TMDCs), in presence of quantizing magnetic field $B$, including the hot-phonon effect. At the low-temperature regime, the ELR is found to display a quantum oscillations with their amplitude being found to increase with the increase of the magnetic field. The unscreened TA phonon due to deformation potential (DP) coupling is dominant over the other screened acoustic phonon contributions. In the extreme Bloch-Grüneisen (BG) region, the ELR displays a pronounced $P^{\mathrm{ac}}\propto T^4\left(T^6\right)$ temperature dependence for unscreened TA-DP phonons (other screened mechanisms). When the temperature increases, $T_e>T_{\mathrm{BG}}$, the ELR shows a linear $P^{\mathrm{ac}}\propto T$ behavior in the equipartition region. At higher temperatures, there is a crossover from $P^{\mathrm{ac}}$ dominated ELR to $P^{\mathrm{op}}$ by zeroth-order DP coupling dominated ELR with the cross-over temperature being about $T_e\sim 50\mathrm{K}$. The hot phonon effect is demonstrated to reduce ELR significantly. The effect of the magnetic field is found to enhance the ELR significantly, making $B$ as its another tuning knob. Among the four TMDC materials, ${\mathrm{MoS}}_2$ (${\mathrm{MoSe}}_2$) displays the biggest ELR due to acoustic (optical) phonon scattering while ${\mathrm{WSe}}_2$ (${\mathrm{WS}}_2$) shows the smallest ELR. Our results for the ${\mathrm{MoS}}_2$ material are compared with those of the zero-field ELR.

We describe a crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization in arbitrary dimensions. The bulk polarization response is constructed by coupling the system to geometric deformations of the underlying crystalline order, represented by local lattice vectors—the elasticity tetrads. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat bands are a consequence of the bulk-boundary correspondence of polarized topological media, and contrary to related nodal line semimetal phases also containing surface flat bands, they span the entire surface Brillouin zone. We also present an example Hamiltonian exhibiting a Lifshitz transition from the nodal line phase to the TI phase with polarization. In addition, we discuss a general classification of three-dimensional (3D) crystalline TI phases and invariants in terms of the elasticity tetrads. The phase with polarization naturally arises from this classification as a dual to the previously better-known 3D TI phase exhibiting quantum (spin) Hall effect. Besides polarization, another implication of the large surface flat band is the susceptibility to interaction effects such as superconductivity: The mean-field critical temperature is proportional to the size of the flat bands, and this type of system may hence exhibit superconductivity with a very high critical temperature.

We propose a hybrid approach which employs the dynamical mean field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent $\mathrm{DFT}+\mathrm{DMFT}$ scheme in a basis of maximally localized Wannier orbitals using wien2k, wien2wannier, and the DMFT impurity solver w2dynamics. As a test-bed material we apply the method to ${\mathrm{SrVO}}_3$ and report a significant improvement as compared to previous $d+p$ calculations. In particular, the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle in $\mathrm{DFT}+\mathrm{DMFT}$ before, and has unwelcomed consequences for the $d\text{−}p$ hybridization as well as for the correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation bypasses the uncertainty of the “double-counting” problem of $\mathrm{DFT}+\mathrm{DMFT}$ and yields very similar quasiparticle renormalized bands on the “DFT” and “DMFT” side.

We discover two distinct topological pathways through which the pentagonal Cairo tiling (P5), a structural model for single-layer $A{B}_2$ pyrite materials, respectively transforms into a crystalline rhombus-hexagon (C46) and random rhombus-pentagon-hexagon (R456) tilings, by continuously introducing Stone-Wales (SW) topological defects. We find these topological transformations are controlled by the orientation correlations among neighboring $B-B$ bonds and exhibit a phenomenological analogy of the (anti)ferromagnetic-to-paramagnetic transition in two-state Ising systems. Unlike the SW defects in hexagonal two-dimensional (2D) materials such as graphene, which cause distortions, the defects in pentagonal 2D materials preserve the shape and symmetry of the fundamental cell of P5 tiling and are associated with a minimal energy cost, making the intermediate R456 tilings realizable metastable states at room temperature. Moreover, the intermediate structures along the two pathways are neither crystals nor quasicrystals, and yet these random tilings preserve the hyperuniformity of the P5 or C46 crystal (i.e., the infinite-wavelength normalized density fluctuations are completely suppressed) and can be viewed as 2D analogs of disordered Barlow packings in three dimensions. The resulting 2D materials possess metallike electronic properties, making them promising candidates for forming Schottky barriers with the semiconducting P5 material.

We analyze the statistical characteristics of quasinonequilibrium two-dimensional electron-hole plasmas in graphene layers (GLs) and graphene bilayers (GBLs) and evaluate their heat capacity. The GL heat capacity of the weakly pumped intrinsic or weakly doped GLs normalized by the Boltzmann constant is equal to $c_{\text{GL}}\simeq 6.58$. With varying carrier temperature the intrinsic GBL carrier heat capacity $c_{\text{GBL}}$ changes from $c_{\text{GBL}}\simeq 2.37$ at $T\lesssim 300$ K to $c_{\text{GBL}}\simeq 6.58$ at elevated temperatures. These values are markedly different from the heat capacity of classical two-dimensional carriers with $c=1$. The obtained results can be useful for the optimization of different GL- and GBL-based high-speed devices.

Few-layer selenium and tellurium films have been recently prepared, and they provide a new platform to explore novel properties of two-dimensional (2D) elemental materials. In this work, we have performed a systematic first-principles study on the electronic, linear, and nonlinear optical (NLO) properties of atomically thin selenium and tellurium films within the density-functional theory with the generalized gradient approximation plus scissors correction using the band gaps from the relativistic hybrid Heyd-Scuseria-Ernzerhof functional calculations. The underlying atomic structures of these materials are determined theoretically using the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Interestingly, we find that few-layer Se and Te possess large second-harmonic generation (SHG), linear electro-optic effect, and bulk photovoltaic effect. In particular, trilayer (TL) Te possesses large SHG coefficient, being more than 65 times larger than that of GaN, a widely used NLO material. Bilayer (BL) Te has huge static SHG coefficient ${\chi }_{xyy}^{\left(2\right)}\left(0\right)$, being more than 100 times larger than that of GaN. Furthermore, monolayer (ML) Se possesses large SHG coefficient with ${\chi }_{xyy}^{\left(2\right)}$ being six times larger than that of GaN. Both ML Se and BL Te possess large linear electro-optic coefficients $r_{xyy}\left(0\right)$ and $r_{yzx}\left(0\right)$, which is about six times and five times larger than that of bulk GaN polytypes, respectively. Moreover, we predict that TL Te exhibits strong bulk photovoltaic effect (BPVE) with shift current conductivity of $\sim 440\mu \mathrm{A}$/${\mathrm{V}}^2$, being greater than that of GeS, a polar system with the largest BPVE found so far. Although the shift current conductivities of bulk and 2D Se are comparable, the shift current conductivities of TL Te are five times larger than those of bulk Te. Finally, an analysis of the calculated electronic band structures indicates that the strong NLO responses of 2D Se and Te materials are primarily derived from their low-dimensional structures with high anisotropy, directional covalent bonding, lone-pair electrons, and relatively small band gaps. These findings provide a practical strategy to search for excellent NLO and BPVE materials.