Effective Two-band Model Research Articles

Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction.

Recent advances in creating moiré periods of two-dimensional heterostructures enable diverse and compatible tunability to modulate the conventional proximity effect involving superconductivity, magnetism, and topology. Here, by constructing a MnTe/NbSe2 heterojunction via molecular beam epitaxy growth, we report on a moiré-enhanced multiband superconductivity by low-temperature scanning tunneling microscopy/spectroscopy measurements. We observe a distinct double-gap superconducting spectrum on monolayer MnTe that is absent on the NbSe2 substrate. The subgap character exhibits a moiré-related oscillation in real space, which can be well described by an effective two-band model. The restored two-gap feature and its rapid suppression under a small magnetic field are speculated to be mediated by the moiré superlattice, which is closely related to the enhanced interband coupling strength of quasiparticle scattering. Our work paves the way for engineering proximitized properties of heterostructures by a moiré landscape with spatial modulations.

Nematic Excitonic Insulator in Transition Metal Dichalcogenide Moiré Heterobilayers.

We study the effect of interelectron Coulomb interactions on the displacement field induced topological phase transition in transition metal dichalcogenide moiré heterobilayers. We find a nematic excitonic insulator phase that breaks the moiré superlattice's threefold rotational symmetry and preempts the topological phase transition in both AA and AB stacked heterobilayers when the interlayer tunneling is weak, or when the Coulomb interaction is not strongly screened. The nematicity originates from the frustration between the nontrivial spatial structure of the interlayer tunneling, which is crucial to the existence of the topological Chern band, and the interlayer coherence induced by the Coulomb interaction that favors uniformity in layer pseudospin orientations. We construct a unified effective two-band model that captures the physics near the band inversion and applies to both AA and AB stacked heterobilayers. Within the two-band model the competition between the nematic excitonic insulator phase and the Chern insulator phase can be understood as the switching of the energetic order between the s-wave and the p-wave excitons upon increasing the interlayer tunneling.

Hubbard Subbands and Superconductivity in the Infinite-Layer Nickelate

An effective two-dimensional two-band model for infinite-layer nickelates consists of bands obtained from $d_{x^2-y^2}$ and $s$--like orbitals. We investigate whether it could be mapped onto a single-band Hubbard model and the filling of Hubbard bands. We find that both one-band physics and a Kondo-lattice regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the filling of the itinerant $s$-band. Next we investigate one-particle excitations by changing the screening. First, for weak screening the strong correlations push electrons out of the $s$-band so that the undoped nickelate is similar to a cuprate. Second, for strong screening the $s$ and $d_{x^2-y^2}$ bands are both partly filled and weakly couple. Particularly in this latter regime mapping to a one-band model gives significant spectral weight transfer between the Hubbard subbands. Finally we point out that the superconducting phases may have either $d$-wave or $s$-wave symmetry.

Antiferromagnetic fluctuations and dominant dxy -wave pairing symmetry in nickelate-based superconductors

Motivated by recent experimental studies on superconductivity found in nickelate-based materials, we study the temperature dependence of the spin correlation and the superconducting pairing interaction within an effective two-band Hubbard model by the quantum Monte Carlo method. Based on parameters extracted from first-principles calculations, our intensive numerical results reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over other pairings at low temperature, which is mainly determined by the Ni 3$d$ orbital. It is also found that the effective pairing interaction is enhanced as the on-site interaction increases, demonstrating that the superconductivity is driven by strong electron-electron correlation. Even though the $(\pi,\pi)$ antiferromagnetic correlation could be enhanced by electronic interaction, there is no evidence for long-range antiferromagnetic order exhibited in nickelate-based superconductors. Moreover, our results offer possible evidence that the pure electron correlation may not account for the charge density wave state observed in nickelates.

Screening in a two-band model for superconducting infinite-layer nickelate

Starting from an effective two-dimensional two-band model for infinite layered nickelates, consisting of bands obtained from $d$ and $s$--like orbitals, we investigate to which extend it can be mapped onto a single-band Hubbard model. We identify screening of the more itinerant $s$-like band as an important driver. In absence of screening one strongly-correlated band gives an antiferromagnetic ground state. For weak screening, the strong correlations push electrons out of the $s$-band so that the undoped nickelate remains a Mott insulator with half filled $d$ orbitals. This regime markedly differs from the observations in high-$T_c$ cuprates and pairing with $s$-wave symmetry would rather be expected in the superconducting state. In contrast, for strong screening, the $s$ and $d_{x^2-y^2}$ bands are both partly filled and couple only weakly, so that one approximately finds a self-doped $d$ band as well as tendencies towards $d$-wave pairing. Particularly in the regime of strong screening mapping to a one-band model gives interesting spectral weight transfers when a second $s$ band is also partly filled. We thus find that both one-band physics and a Kondo-lattice--like regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the size of the $s$-band pocket.

Uncorrelated Excitonic Properties in Multilayered Cylindrical Quantum Dot

The unbound exciton properties in multilayered cylindrical quantum dot (CQD) (core/shell/shell) have been studied theoretically, within the effective mass approximation and two-band model. The uncorrelated energy of an exciton confined in GaAs/Ga1-x1Alx1As/Ga1-x2Alx2As CQD as a function of the core and first shell radius is presented. The numerical results show that the quantum dot size and the confinement potentials depth significantly adjust the ground state uncorrelated energy of exciton. However, the exciton wave function parameters are dependent on the core and first shell radius (R1 and R2), as well as the concentration of the barrier’s materials.

Multiband superconductivity in SrFe2−xNixAs2

In this paper, we present a detailed study of the upper critical field and the energy gap structure of SrFe2−xNixAs2 single crystals with different nickel doping levels. Superconducting transitions were measured resistively in longitudinal and transverse magnetic fields up to 16T. The anisotropy of the upper critical field Hc2||ab/Hc2||c decreases monotonically to 1.4 with decreasing temperature for all measured samples. The WHH model was not able to fit measured Hc2(T) temperature dependences well, but the effective two-band model is in good agreement with the data and anisotropy behavior. Values and temperature dependences of superconducting gaps were determined directly by multiple Andreev reflection spectroscopy on symmetrical SnS junctions. Andreev reflections study revealed two superconducting gaps; our data are in line with the experimental results on most iron-based superconductors.Article highlightsWe obtained values and temperature dependencies of two distinct energy gaps in SrFe2−xNixAs2 (Sr-122) superconductor. This is important addition to multiband superconductivity studies in Sr-122 system. Upper critical field temperature dependencies in H||c and H||ab orientations are analyzed in terms of two band model.

Floquet dynamical quantum phase transitions under synchronized periodic driving

We study a generic class of fermionic two-band models under synchronized periodic driving, i.e., with the different terms in a Hamiltonian subject to periodic drives with the same frequency and phase. With all modes initially in a maximally mixed state, the synchronized drive is found to produce nonperiodic patterns of dynamical quantum phase transitions, with their appearance determined by an interplay of the band structure and the frequency of the drive. A case study of the anisotropic XY chain in a transverse magnetic field, transcribed to an effective two-band model, shows that the modes come with quantized geometric phases, allowing for the construction of an effective dynamical order parameter. Numerical studies in the limit of a strong magnetic field reveal distinct signals of precursors of dynamical quantum phase transitions also when the initial state of the XY chain is perturbed slightly away from maximal mixing, suggesting that the transitions may be accessible experimentally. A blueprint for an experiment built around laser-trapped circular Rydberg atoms is proposed.

Floquet engineering of individual band gaps in an optical lattice using a two-tone drive

The dynamic engineering of band structures for ultracold atoms in optical lattices represents an innovative approach to understand and explore the fundamental principles of topological matter. In particular, the folded Floquet spectrum determines the associated band topology via band inversion. We experimentally and theoretically study two-frequency phase modulation to asymmetrically hybridize the lowest two bands of a one-dimensional lattice. Using quasi-degenerate perturbation theory in the extended Floquet space we derive an effective two-band model that quantitatively describes our setting. The energy gaps are experimentally probed via Landau-Zener transitions between Floquet-Bloch bands using an accelerated Bose-Einstein condensate. Separate and simultaneous control over the closing and reopening of these band gaps is demonstrated. We find good agreement between experiment and theory, establishing an analytic description for resonant Floquet-Bloch engineering that includes single- and multi-photon couplings, as well as interference effects between several commensurate drives.

Strain-modified effective two-band model for calculating the conduction band structure of strain-compensated quantum cascade lasers: effect of strain and remote band on the electron effective mass and nonparabolicity parameter

We propose a strain-modified effective two-band model to calculate the conduction band (CB) structure of strain-compensated quantum cascade lasers (QCLs). The proposed model can consider the effect of strain and remote band (RB) on the band-edge energy, electron effective mass, and nonparabolicity parameter although the currently used empirical two-band model can be applicable to only the unstrained QCLs. Based on the three-band second-order k·p Hamiltonian along with the Pikus-Bir Hamiltonian, analytical formula for the electron effective mass and nonparabolicity parameter are derived at the zone center, where the effects of strain and RB interaction are included. Then, the three-band first-order k·p Hamiltonian is reduced to the strain-modified effective two-band Hamiltonian, where the effective Kane energy, determined by the electron effective mass and nonparabolicity parameter, is used to include the nonparabolicity of the CB. By numerically solving the proposed strain-modified effective two-band model based on the finite difference method, we calculate the CB structure of several strain-compensated or unstrained QCLs in the mid-IR and terahertz range and predict their lasing wavelengths, which are well matched with the measured values in the literatures.

Superconductivity in spin- 3/2 systems: Symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces

The possible symmetries of the superconducting pair amplitude is a consequence of the fermionic nature of the Cooper pairs. For spin-$1/2$ systems this leads to the $\mathcal{SPOT}=-1$ classification of superconductivity, where $\mathcal{S}$, $\mathcal{P}$, $\mathcal{O}$, and $\mathcal{T}$ refer to the exchange operators for spin, parity, orbital, and time between the paired electrons. However, this classification no longer holds for higher spin fermions, where each electron also possesses a finite orbital angular momentum strongly coupled with the spin degree of freedom, giving instead a conserved total angular moment. For such systems, we here instead introduce the $\mathcal{JPT}=-1$ classification, where $\mathcal{J}$ is the exchange operator for the $z$-component of the total angular momentum quantum numbers. We then specifically focus on spin-$3/2$ fermion systems and several superconducting cubic half-Heusler compounds that have recently been proposed to be spin-$3/2$ superconductors. By using a generic Hamiltonian suitable for these compounds we calculate the superconducting pair amplitudes and find finite pair amplitudes for all possible symmetries obeying the $\mathcal{JPT}=-1$ classification, including all possible odd-frequency (odd-$\omega$) combinations. Moreover, one of the very interesting properties of spin-$3/2$ superconductors is the possibility of them hosting a Bogoliubov Fermi surface (BFS), where the superconducting energy gap is closed across a finite area. We show that a spin-$3/2$ superconductor with a pair potential satisfying an odd-gap time-reversal product and being non-commuting with the normal-state Hamiltonian hosts both a BFS and has finite odd-$\omega$ pair amplitudes. We then reduce the full spin-$3/2$ Hamiltonian to an effective two-band model and show that odd-$\omega$ pairing is inevitably present in superconductors with a BFS and vice versa.

Character of Doped Holes in Nd1−xSrxNiO2

We investigate charge distribution in the recently discovered high-Tc superconductors, layered nickelates. With increasing value of charge-transfer energy, we observe the expected crossover from the cuprate to the local triplet regime upon hole doping. We find that the d−p Coulomb interaction Udp makes Zhang-Rice singlets less favorable, while the amplitude of local triplets at Ni ions is enhanced. By investigating the effective two-band model with orbitals of x2−y2 and s symmetries we show that antiferromagnetic interactions dominate for electron doping. The screened interactions for the s band suggest the importance of rare-earth atoms in superconducting nickelates.

Nonlinear optical response of twisted bilayer graphene

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.

Orbital gyrotropic magnetoelectric effect and its strain engineering in monolayer NbX2

Electrical control of the orbital degrees of freedom is an important area of research in the emerging field of "orbitronics." Orbital {\it gyrotropic} magneto-electric effect (OGME) is the generation of an orbital magnetization in a nonmagnetic metal by an applied electric field. Here, we show that strain induces a large GME in the monolayer Nb$X_2$ ($X =$ S, Se) normal to the plane, primarily driven by the orbital moments of the Bloch bands as opposed to the conventional spin magnetization, without any need for spin-orbit coupling. The key physics is captured within an effective two-band valley-orbital model and it is shown to be driven by three key ingredients: the intrinsic valley orbital moment, broken $C_{3z}$ symmetry, and strain-induced Fermi surface changes. The effect can be furthermore switched by changing the strain condition, with potential for future device applications.

Ab initio k · p theory of spin-momentum locking: Application to topological surface states

Based on ab initio relativistic ${\mathbf k}\cdot{\mathbf p}$ theory, we derive an effective two-band model for surface states of three-dimensional topological insulators up to seventh order in $\mathbf{k}$. It provides a comprehensive description of the surface spin structure characterized by a non-orthogonality between momentum and spin. We show that the oscillation of the non-orthogonality with the polar angle of $\mathbf{k}$ with a $\pi/3$ periodicity can be seen as due to effective six-fold symmetric spin-orbit magnetic fields with a quintuple and septuple winding of the field vectors per single rotation of $\mathbf{k}$. Owing to the dominant effect of the classical Rashba field, there remains a single-winding helical spin structure but with a periodic few-degree deviation from the orthogonal locking between momentum and spin.

Distinguishing the gapped and Weyl semimetal scenario in ZrTe5 : Insights from an effective two-band model

Here we study the static and dynamic transport properties of a low energy two-band model proposed previously in E. Martino et al. [PRL 122, 217402 (2019), arXiv:1905.00280], with an anisotropic in-plane linear momentum dependence, and a parabolic out-of-plane dispersion. The model is extended to include a negative band gap, which leads to the emergence of a Weyl semimetal (WSM) state, as opposed to the gapped semimetal (GSM) state when the band gap is positive. We calculate and compare the zero and finite frequency transport properties of the GSM and WSM cases. The $dc$ properties that are calculated for the GSM and WSM cases are Drude spectral weight, mobility and resistivity. We determine their dependence on the Fermi energy and crystal direction. The in- and out-of-plane optical conductivities are calculated in the limit of the vanishing interband relaxation rate for both semimetals. The main common features are an $\omega^{1/2}$ in-plane and $\omega^{3/2}$ out-of-plane frequency dependence of the optical conductivity. We seek particular features related to the charge transport that could unambiguously point to one ground state over the other, based on the comparison with the experiment. Differences between the WSM and GSM are in principle possible only at extremely low carrier concentrations, and at low temperatures.

First-principles design of a Dirac semimetal: An NP monolayer

We report a two-dimensional (2D) Dirac semimetal in an orthorhombic $\mathit{Pmma}$ structure, an NP monolayer, based on first-principles calculations. The NP monolayer is found to be stable according to phonon dispersion and molecular dynamical simulations. It exhibits a pair of anisotropic Dirac cones exactly at the Fermi level, located along high symmetry lines in the Brillouin zone, and shows highly anisotropic in-plane stiffness. First-principles calculations show that Dirac cones are locally stable under strains along the $x$ or $y$ direction and electric fields perpendicular to the monolayer. The Dirac nodes are protected from gap opening by the mirror-reflection symmetry in the $x$ direction. We construct an effective two-band tight-binding model to characterize the Dirac states. Our result provides a promising 2D material for special electronics applications.

Upper Critical Field of a Two-Band SrFe2 − xNixAs2 Superconductor

The upper critical field of an iron-based SrFe2 − xNixAs2 superconductor single crystal is measured for the first time in longitudinal and transverse magnetic fields up to 16 T in the basal ab plane and to it along the c axis. The Hc2(0) values are 18 and 25 T for H ∥ c and H ∥ ab, respectively. The anisotropy of the upper critical field γ(T) = Hc2 / Hc2 decreases monotonically to 1.4 with decreasing temperature. The temperature dependence of Hc2 is not described fully by the Werthamer–Helfand–Hohenberg model taking into account the influence of orbital and spin paramagnetic effects. However, an effective two-band model reproduces well the measured temperature dependence. This indicates the two-band nature of this superconductor, where one of the bands is almost isotropic. According to the two-band model approximation, the contribution from the anisotropic band dominates near Tc, whereas the main contribution at low temperatures comes from the isotropic band with a lower diffusion coefficient.

Different behavior of upper critical field in Fe1−xSe single crystals**Project supported by the National Natural Science Foundation of China (Grant Nos. 11888101 and 11834016), the National Key Research and Development Program of China (Grant Nos. 2017YFA0303003 and 2016YFA0300300), and the Strategic Priority Research Program and Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant Nos. QYZDY-SSW-SLH001

The temperature dependences of upper critical field (Hc2) for a series of iron-deficient Fe1−xSe single crystals are obtained from the measurements of in-plane resistivity in magnetic fields up to 9 T and perpendicular to the ab plane. For the samples with lower superconducting transition temperature Tc (<7.2 K), the temperature dependence of Hc2 is appropriately described by an effective two-band model. For the samples with higher Tc (≳ 7.2 K), the temperature dependence can also be fitted by a single-band Werthamer–Helfand–Hohenberg formula, besides the two-band model. Such a Tc-dependent change in Hc2(T) behavior is discussed in connection with recent related experimental results, showing an inherent link between the changes of intrinsic superconducting and normal state properties in the FeSe system.

Topological nature of Hubbard bands in strongly correlated systems

The topological nature of the Mott-Hubbard state in strongly correlated systems is treated. These systems are described in terms of spin-charge separation, i.e. spinon-holon deconfinement in the gauge field. Analogies with the quantum Hall effect and Landau quantization are considered, the presence of the Chern-Simons term being important for proper description of the Hubbard splitting. Occurrence of topological frustrations with doping in an effective two-band model is demonstrated. The role of orbital degrees of freedom and possible occurrence of orbital currents are discussed.