Low-energy Electronic Properties Research Articles

Theory for constructing effective electronic models of bilayer graphene systems

We present and discuss practical techniques for formulating effective models to describe the low-energy electronic properties of bilayer graphene systems. We show that such effective models are constructed from a collection of appropriate single-layer Bloch states of two graphene layers. In general, the obtained effective models allow the construction of a so-called moiré band structure. However, it is not the result of an irreducible representation of a translation symmetry group of the bilayer lattices except for the commensurate bilayer configurations. We also point out that the commensurate bilayer configurations are classified into three categories depending on the divisibility of the difference between two commensurate integer indices by 3. The electronic band structure of three lattice configurations, one for each category, is shown. Especially by combining with a real-space calculation, we validate the working ability of constructed effective models for generic bilayer graphene systems by showing that the effects of interlayer sliding are diminished by twisting. This result is consistent with the invariance of effective models under the interlayer sliding operation.

Electronic structures and effective models in BaPtSb and BaPtAs with ordered honeycomb structures

We investigate the low-energy electronic properties and construct the effective model Hamiltonians in the normal state for new materials BaPtSb and BaPtAs with ordered honeycomb structures. The preliminary experimental study suggested that the former compound may be a candidate of the time-reversal symmetry breaking superconductors. The low-energy electronic structures obtained from the first principles calculation mainly consist of Pt 5d and Sb/As 5p/4p orbitals, where there exist the strong hybridizations between both orbitals. We show that the main parts in the low-energy region including the Fermi surface are well described using renormalized 3 bands consisting of dominant Pt 2 bands and Sb/As 1 band. Our result provides a starting point for microscopic investigation in the superconducting states for the materials with the hexagonal structure.

Low-energy structures and electronic properties of small titanium nitride nanoclusters

Some small nanoclusters of plasmonically superior titanium nitride are generated using ab initio molecular dynamics simulation under the regime of density functional theory. The global minima structures of TiN lack symmetry in the local environment as compared to the bulk counterpart. Electronic properties, namely Bader charge, electron localization function, and density of states, help us to have a deeper understanding of these nanoclusters. In all the calculations, bulk TiN has been taken as a reference to compare the properties. It has been observed that with an increasing number of atoms in the nanoclusters, they tend to show properties similar to bulk TiN, indicating that they might as well be used as plasmonic materials.

Edge Disorder in Bottom-Up Zigzag Graphene Nanoribbons: Implications for Magnetism and Quantum Electronic Transport.

We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite" defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conductance across graphene nanoribbons is more sensitive to "bite" defects forming at the zigzag edges than at the armchair ones. Our work establishes a comprehensive understanding of the low-energy electronic properties of disordered bottom-up graphene nanoribbons.

Nature of native atomic defects in ZrTe5 and their impact on the low-energy electronic structure

Over the past decades, investigations of the anomalous low-energy electronic properties of $\mathrm{Zr}{\mathrm{Te}}_{5}$ have reached a wide array of conclusions. An open question is the growth method's impact on the stoichiometry of $\mathrm{Zr}{\mathrm{Te}}_{5}$ samples, especially given the very small density of states near its chemical potential. Here we report on high-resolution scanning tunneling microscopy and spectroscopy measurements performed on samples grown via different methods. Using density functional theory calculations, we identify the most prevalent types of atomic defects on the surface of $\mathrm{Zr}{\mathrm{Te}}_{5}$, namely, Te vacancies and intercalated Zr atoms. Finally, we precisely quantify their density and outline their role as ionized defects in the anomalous resistivity of this material.

Influence of the quasiparticle spectral weight in FeSe on spectroscopic, magnetic, and thermodynamic properties

We report on an extensive experimental and numerical study of the low-energy electronic properties of superconducting FeSe single crystals, using point-contact Andreev reflection Spectroscopy (PCAR), specific heat, and London penetration depth measurements. Taking explicitly into account Fermi surface anisotropy and recently suggested orbital-selective quasiparticle spectral weights ${Z}_{i}$ ($i={d}_{xy},{d}_{{x}^{2}\ensuremath{-}{y}^{2}},{d}_{xz},{d}_{yz},{d}_{{z}^{2}}$), our calculations quantitatively account for all our measurements as well as data from the literature, assuming that ${Z}_{yz}g{Z}_{xz}g{Z}_{xy}$. This study confirms the picture of a highly different quantum coherence of the Fe orbitals at the Fermi energy. In particular, the normal state properties (Sommerfeld coefficient and zero-temperature London penetration depth) strongly depend on the ${Z}_{i}$ values, which seem to be significantly sensitive to disorder.

Ultrafast quasiparticle dynamics in the correlated semimetal Ca3Ru2O7

The correlated polar semimetal Ca$_3$Ru$_2$O$_7$ exhibits a rich phase diagram including two magnetic transitions ($T_N$=56 K and $T_C$=48 K) with the appearance of an insulating-like pseudogap (at $T_C$). In addition, there is a crossover back to metallic behavior at $T^*$=30 K, the origin of which is still under debate. We utilized ultrafast optical pump optical probe spectroscopy to investigate quasiparticle dynamics as a function of temperature in this enigmatic quantum material. We identify two dynamical processes, both of which are influenced by the onset of the pseudogap. This includes electron-phonon relaxation and, below $T_C$, the onset of a phonon bottleneck hindering the relaxation of quasiparticles across the pseudogap. We introduce a gap-modified two-temperature model to describe the temperature dependence of electron-phonon thermalization, and use the Rothwarf-Taylor to model the phonon bottleneck. In conjunction with density functional theory, our experimental results synergistically reveal the origin of the $T$-dependent pseudogap. Further, our data and analysis indicate that $T^*$ emerges as a natural consequence of $T$-dependent gapping out of carriers, and does not correspond to a separate electronic transition. Our results highlight the value of low fluence ultrafast optics as a sensitive probe of low energy electronic structure, thermodynamic parameters, and transport properties of Ruddlesden-Popper ruthenates.

Optical conductivity, Fermi surface, and spin-orbit coupling effects in Sr2RhO4

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties of ${\mathrm{Sr}}_{2}{\mathrm{RhO}}_{4}$ in a realistic setting, and compare to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. We investigate the interplay of spin-orbit coupling, crystal field, and Coulomb interaction, including the tetragonal terms of the Coulomb tensor. We find that (i) differently than in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, the zero-frequency effective crystal-field ``enhancement'' due to Coulomb repulsion, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\varepsilon}}_{\mathrm{CF}}(\ensuremath{\omega}=0)$, is small and, depending on the parameters, even negative. (ii) In addition, the effects of (realistic) anisotropic Coulomb terms are weak. (iii) Instead, the effective zero-frequency enhancement of the spin-orbit interaction doubles the value of the corresponding local-density approximation couplings. This explains the experimental Fermi surface and supports a previous proposal based on static mean-field calculations. We find that the sign of the Coulomb-induced spin-orbit anisotropy is influenced by the octahedral rotation. Based on these conclusions, we examine recent optical conductivity experiments. (iv) We show that the spin-orbit interaction is key for understanding them; differently than in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, the ${t}_{2g}$ intraorbital contributions are small; thus, the single-band picture does not apply.

Theoretical investigation on the low-energy isomer identification, structural evolution, stability, and electronic properties of Al10–xBex (x = 1–9) nanoalloys

Numerous isomeric equilibrium structures have been identified for the Al10–xBex (x = 1–9) nanoalloy clusters by using the stochastic search procedure in combination with density functional theory calculations. The relative stability and various electronic properties of the lowest-energy Al10–xBex (x = 0–10) clusters have been systematically studied by using the B3LYP and CCSD(T) methods with the aug-cc-pVDZ basis set. The evolution of the binding energies, the second difference in energy, HOMO–LUMO gaps, vertical detachment energies, vertical ionization potentials, vertical electron affinities, and hardness with the increasing number of Be atoms in the most stable Al10–xBex (x = 0–10) clusters demonstrates that the global minimum of Al8Be2 cluster possesses a special stability. Thus, the electronic structure of the lowest-energy Al8Be2 cluster has been also detected in detail. In addition, it is found that the polarizabilities gradually decrease with increasing number of Be atoms, and the charges always transfer from Al to Be atoms in these nanoalloy clusters. We hope this work could provide helpful insight into the composition-dependent electronic properties of BeAl alloy at the nanoscale, serving as powerful guidelines for future experimental research.

Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.

Effective masses, lifetimes, and optical conductivity in Sr2RuO4 and Sr3Ru2O7 : Interplay of spin-orbit, crystal-field, and Coulomb tetragonal tensor interactions

By using the local-density approximation + dynamical mean-field theory approach, we study the low-energy electronic properties and the optical conductivity of the layered ruthenates ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. We study the interplay of spin-orbit, crystal-field, and Coulomb interactions, including the tetragonal terms of the Coulomb tensor. We show that the spin-orbit interaction is multifaced; depending on the parameter regime, filling, and temperature, it can either enhance or reduce the effective strength of correlations. We compare the results based on the two common approximations for the screened Coulomb parameters, the constrained random-phase approximation (cRPA) and the constrained local-density approximation. We show that the experimental Drude peak is better reproduced by the cRPA parameters, hinting to relatively small mass renormalizations. We find that including the spin-orbit interaction is, however, important, for a realistic description. We show that Coulomb terms with tetragonal ${D}_{4h}$ symmetry have a strong effect on the mass-enhancement anisotropy, but they do not affect sizably the total spectral function or the in-plane conductivity.

Scanning tunneling microscopy and spectroscopy of finite-size twisted bilayer graphene

Nanoscale twisted bilayer graphene (TBG) is quite instable and will change its structure to Bernal (or AB-stacking) bilayer with a much lower energy. Therefore, the lack of nanoscale TBG makes its electronic properties not accessible in experiment up to now. In this work, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 nm to 0 nm. By using scanning tunnelling microscopy, we studied carefully the structure and the electronic properties of the nanoscale TBG. Our results indicate that the low-energy electronic properties, including twist-induced van Hove singularities (VHSs) and spatial modulation of local density-of-state, are strongly affected by the translational symmetry breaking of the nanoscale TBG. Whereas, the electronic properties above the energy of the VHSs are almost not influenced by the quantum confinement even when the width of the TBG is reduced to only a single moire spot.

Structures and Electronic Properties of Ni–Al Alloy Clusters from First-Principles Calculations

Using the density functional theory calculations with the PBE exchange–correlation energy functional, we have studied the low-energy structures and electronic properties of Ni–Al alloy clusters for adsorbing or doping an aluminum atom to Nin (n = 13, 19, 23, 26, 29 and 55) clusters. The most stable structures of NinAl are viewed as adding an Al atom at the hollow triangle and rhombus site of the icosahedron (n = 13, 55) and double-icosahedron (n = 19, 23, 26 and 29) structures, respectively. For Nin−1Al, it can be seen that an Al atom gradually moves from surface (n = 13, 19, 23 and 26) to the interior site (n = 29, 55) in the most stable structures. The electronic properties of the Ni–Al alloy clusters including binding energies, magnetic properties, charge transfer and density of states have also been studied.

Origins of the structural phase transitions in MoTe2 and WTe2

Layered transition metal dichalcogenides MoTe$_2$ and WTe$_2$ share almost similar lattice constants as well as topological electronic properties except their structural phase transitions. While the former shows a first-order phase transition between monoclinic and orthorhombic structures, the latter does not. Using a recently proposed van der Waals density functional method, we investigate structural stability of the two materials and uncover that the disparate phase transitions originate from delicate differences between their interlayer bonding states near the Fermi energy. By exploiting the relation between the structural phase transitions and the low energy electronic properties, we show that a charge doping can control the transition substantially, thereby suggesting a way to stabilize or to eliminate their topological electronic energy bands.

Field-modulated low-energy electronic and optical properties of armchair silicene nanoribbons

The tight-binding model including spin–orbit coupling is used to study electronic and optical properties of armchair silicene nanoribbons (ASiNRs) in electric fields. Perpendicular electric field monotonically increases band-gap, the DOS, and absorption frequency and strength. It does not change spin-degeneracy, edge-states, and optical selection rule. However, parallel electric field strongly modulates energy dispersions resulting in oscillatory band-gaps, shift in edge-states, and destruction of spin-degeneracy. It induces more transition channels and constructs new selection rules that exhibits richer optical spectra. Modulations of electronic and optical properties of ASiNRs have strong dependence on the direction of electric field and nanoribbon's geometry.

Angular momentum and topology in semiconducting single-wall carbon nanotubes

Semiconducting single-wall carbon nanotubes are classified into two types by means of orbital angular momentum of valley state, which is useful to study their low energy electronic properties in finite-length. The classification is given by an integer $d$, which is the greatest common divisor of two integers $n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines. For the case that $d$ is equal to or greater than four, two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit nearly fourfold degeneracy and its small lift by the spin-orbit interaction. For the case that $d$ is less than or equal to two, in which two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, relationship between number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, which enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.

Weak-coupling superconductivity in a strongly correlated iron pnictide.

Iron-based superconductors have been found to exhibit an intimate interplay of orbital, spin, and lattice degrees of freedom, dramatically affecting their low-energy electronic properties, including superconductivity. Albeit the precise pairing mechanism remains unidentified, several candidate interactions have been suggested to mediate the superconducting pairing, both in the orbital and in the spin channel. Here, we employ optical spectroscopy (OS), angle-resolved photoemission spectroscopy (ARPES), ab initio band-structure, and Eliashberg calculations to show that nearly optimally doped NaFe0.978Co0.022As exhibits some of the strongest orbitally selective electronic correlations in the family of iron pnictides. Unexpectedly, we find that the mass enhancement of itinerant charge carriers in the strongly correlated band is dramatically reduced near the Γ point and attribute this effect to orbital mixing induced by pronounced spin-orbit coupling. Embracing the true band structure allows us to describe all low-energy electronic properties obtained in our experiments with remarkable consistency and demonstrate that superconductivity in this material is rather weak and mediated by spin fluctuations.

Electronic Properties of Incommensurate Atomic Layers

We present a brief theoretical overview of electronic properties of incommensurate multilayer systems, i.e., a pair of two-dimensional atomic layers stacked in an arbitrary orientation. We introduce the general theoretical scheme to describe the interlayer interaction between incommensurate crystal structures, and apply the formula to two specific examples, the twisted bilayer graphene and graphene–hBN composite bilayer. In each case, we calculate the electronic band structure and demonstrate that the low-energy electronic properties are significantly modified by the interlayer interaction, particularly when the two lattice structures are close to each other. We also study the energy spectrum and the quantum Hall effect in magnetic fields, where we see that the spectral structure exhibits a fractal nature, as known as the Hofstadter butterfly. We argue about the optical absorption properties of the twisted bilayer graphene and show that the interlayer interaction gives rise to the characteristic spectrosc...

Electronic properties of monolayer MoS2 in a modulated magnetic field

The low-energy electronic properties of molybdenum disulfide subject to the influence of a spatially-modulated magnetic field are investigated by using the Peierls tight-binding method. The band structure is found to be composed of many oscillatory parabolic subbands, which are left–right asymmetric. The electronic properties are strongly dependent on the strength and period of the modulated field. The density of states (DOS) displays many asymmetric square-root divergent peaks originating from these parabolic subbands. They can be categorized into primary and secondary peaks according to their heights. The evolution of the DOS peaks with the field strength and modulation period is explored. The energies of the DOS peaks are linearly dependent on the field strength. Furthermore, the energies of the primary peaks depend weakly on the modulation period, whereas those of the secondary ones diminish with rising period. These predictions can be validated by measuring the spectra of STS or performing magneto transmission experiments. The effects of the spin–orbit coupling on the energy spectrum and DOS are also investigated.

Interaction-induced singular Fermi surface in a high-temperature oxypnictide superconductor.

In the family of iron-based superconductors, LaFeAsO-type materials possess the simplest electronic structure due to their pronounced two-dimensionality. And yet they host superconductivity with the highest transition temperature Tc ≈ 55K. Early theoretical predictions of their electronic structure revealed multiple large circular portions of the Fermi surface with a very good geometrical overlap (nesting), believed to enhance the pairing interaction and thus superconductivity. The prevalence of such large circular features in the Fermi surface has since been associated with many other iron-based compounds and has grown to be generally accepted in the field. In this work we show that a prototypical compound of the 1111-type, SmFe0.92Co0.08AsO , is at odds with this description and possesses a distinctly different Fermi surface, which consists of two singular constructs formed by the edges of several bands, pulled to the Fermi level from the depths of the theoretically predicted band structure by strong electronic interactions. Such singularities dramatically affect the low-energy electronic properties of the material, including superconductivity. We further argue that occurrence of these singularities correlates with the maximum superconducting transition temperature attainable in each material class over the entire family of iron-based superconductors.