Fermi Line Research Articles

Theoretical occurrence of quantized chemistry of conduction mechanism in layered perovskite for the application of Resistive Random Access Memory devices

AbstractThe Density Functional Theory (DFT) calculations interpreted the electronic and optical alteration of Ruddlesden–Popper layered perovskite (Sr3Zr2O7) with substitutional doping of Ti‐, Hf‐, and Ti+Hf‐ atoms in place of Zr‐atoms by generating the oxygen vacancies (Vos) defect. Formation energy and phonon calculations confirmed that the studied composites are dynamically stable, and the lattice parameters of the considered RP perovskite with and without vacancy defects did not change by introducing a small concentration of doped elements. The doped Sr3Zr2O7 composites show band gap tuning in the presence and absence of Vos, which was 3.31 eV in pristine form, and localized states near the Fermi line due to dopant and Vos, which confirmed the quantized conductance in all composites and may be beneficial for overcoming uniformity issues in nonvolatile memory devices. Isosurface charge density calculations also verified this result by depicting the physical mechanism of charge accumulation and depletion in the layers of RP perovskite in the vicinity of defects, resulting in residual conducting filaments guiding its growth and leading it to a low resistance state. The photosensitive response of this layered perovskite also confirmed its use for memory storage applications. The valuable outcomes of this study predicted that Sr3Zr2O7+Ti+Hf is the most stable and, hence, the best composite for nonvolatile RRAM device applications.

Anomalous Diamagnetic Torque Signals in Topological Nodal-Line Semimetal NaAlSi

In topological materials, peculiar surface states protected by crystal symmetries have attracted great interest because of the possibility of unprecedented correlation with superconductivity. A topological nodal-line semimetal with a layered structure, NaAlSi shows moderately anisotropic bulk superconductivity with Tc ≅ 7.0 K. The magnetic torque curves as a function of the field angle in the superconducting state are found to show two distinct diamagnetic signals; a large broad signal arising from bulk superconductivity and a small sharp signal observed only in magnetic fields nearly parallel to the layers. The upper critical field of the bulk superconductivity follows an anisotropic 3D model with a small anisotropic factor of ∼4. A possible scenario is that the sharp signal is due to highly 2D superconductivity with a similar Tc, whose thickness is only several times of the c-axis lattice constant (0.736 nm). The band structure calculations show the presence of large Fermi lines on the (001) plane, mainly formed by the surface Si p bands. The sharp diamagnetic torque signal could arise from the (001) surface superconductivity.

Thermodynamic properties of the 2D generic helical edge states with quadrangular potential effects

We theoretically studied the generic helical edge state (GHES) with quadrangular potential in the two-dimensional (2D) HgTe/CdTe quantum well (QW) structure. We have specified the thermodynamic properties of the GHES with and without the external geometric potential. On the one hand, we first revealed the heat capacity dependence of the edge modes on the optimum temperatures. It is found that the model offers distorted Fermi lines of edge states but does not vary with the behavior of the heat capacity. In addition, we showed that the quadrangular potential term distorts the Fermi surface and contributes to particle-hole asymmetry.

Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene

We show that the e-e interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from C6 to C3, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moiré unit cell in twisted trilayer graphene.

Transition metal carbonate precursors as cathode materials for lithium ion batteries: first principles study

Lithium-ion batteries (LIBs) are frequently regarded as the best batteries ever made due to their significant energy density, low lithium reduction potential, and small size. LIBs are structurally comprised of functional parts of cathodes, anodes, separator, and electrolyte. Cathode materials are among the best possibilities of achieving the remarkable energy densities for LIBs due to their capacitance value exceeding 250 mAh/g. This study investigates the structural, electronic, mechanical and thermodynamic properties of two candidate materials: Ni0.2Mn0.5Co0.2CO3 and Ni0.2Mn0.5Co0.2O2 by means of DFT-based computational simulations. In particular, structural parameters, density of states, elastic constants and phonon dispersion curves were calculated to mimic their stability. From our results we found that the density of states reveal no energy band gap at the Fermi line for both materials, which indicate metallic characteristic. We also note that from the phonon dispersions, Ni0.2Mn0.5Co0.2CO3 shows no negative vibrations along the high Brillouin zone as compared to Ni0.2Mn0.5Co0.2O2 which displayed negative vibration. This implies that Ni0.2Mn0.5Co0.2CO3 is vibrationally stable while Ni0.2Mn0.5Co0.2O2 is unstable.

Nonsymmorphic band sticking in a topological superconductor

Single-crystal x-ray diffraction recently identified the space group of the weakly correlated yet exotic time reversal symmetry (TRS) breaking superconductor $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ to be nonsymmorphic $Cmcm$. This symmetry causes band sticking on a zone face pierced by four Fermi surfaces, leading to two nodal Fermi lines and a nodal Fermi loop on that zone face ${k}_{z}=\frac{\ensuremath{\pi}}{c}$. These line singularities are examples of perfectly flat (in energy and in geometry) nodal structures that lie precisely at a single energy, with that energy being the Fermi level ${E}_{F}$, even under variation of the carrier density. Projections onto surfaces perpendicular to that zone face produce collapsed drumhead state regions of zero area on the edges of the surface Brillouin zone. Although small by most measures, spin-orbit coupling splits the line and loop degeneracies on the Fermi surfaces (FSs) in the normal state except at two symmetry-related Dirac points, which topologically are locally dispersionless in one direction (zero velocity and infinite mass) while linear in the other two directions. The band sticking and distinctive Fermi surface placed Dirac points are most impactful in establishing $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ as a topological superconductor in the bulk, with the degenerate FSs providing a natural platform for the superconducting order-parameter symmetry necessary for describing this TRS breaking superconductor. Unlike most other crystal symmetries, spin-orbit coupling leaves intact a nodal line piercing the FS, resulting in Dirac points situated at ${E}_{F}$ lying along nodal lines. Additionally, the degeneracy exactly at the Fermi energy is central in placing $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ precisely at a Lifshitz FS instability, independent of band filling and protected by $Cmcm$ symmetry. The eight-band low-energy Bogoliubov--de Gennes quasiparticle spectrum is presented along one dispersive direction for varying strengths of TRS breaking. We include a discussion of energetics of gauge symmetry and magnetic order resulting from TRS breaking, incorporating information from experimental data. These results suggest a scenario where TRS breaking rather than gauge-symmetry breaking (superconductivity) might be the driving order parameter.

Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry

Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundaries. In conventional three-dimensional topological superconductors, Majorana in-gap states appear in the form of spin-1/2 fermions with a quasirelativistic dispersion relation. Here, we show that unconventional Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states are classified into three different categories: a spin-$s$ Majorana fermion with $(2s+1)$-fold degeneracy $(s\ensuremath{\ge}3/2)$, a Majorana Fermi line carrying two distinct topological charges, and a quartet of spin-1/2 Majorana fermions related by fourfold rotational symmetry. The spectral properties of the first two types, which go beyond conventional spin-1/2 fermions, are unique to topological superconductors and have no counterparts in topological insulators. We show that unconventional Majorana surface states can be obtained in the superconducting phase of doped ${Z}_{2}$ topological insulators or Dirac semimetals with rotational symmetry.

DFT-based Engineering of Dirac Surface States in Topological-insulator Multilayers

A highly insulating bulk state and a tunable Dirac cone surface state are required for future spintronics device applications of spin-polarized surface states in three-dimensional topological insulators. Here, a slab model with heterostructural Bi2Se3-related quintuple layers is employed to conduct first-principles simulations. The computational results show that the Dirac-point energy can be optimally tuned by the selection of an appropriate pair of materials, so that the work function of the surface quintuple layer is slightly different from that of the inner quintuple layers. The ideal surface state is obtained in a Bi2Te3/(Bi2Te2Se)4/Bi2Te3 slab, in which the Fermi lines show a significant warping effect and both in-plane and out-of-plane components of spin polarization emerge.

Coexistence of type-I and type-II nodal lines in monolayer TiBF

Topological nodal line semimetals with protected 1-D Fermi lines have continuously attracted great interest. In this study, based on first-principles calculations, we demonstrate that type-I and type-II nodal lines can coexist in the dynamically stable monolayer TiBF. Both types of nodal lines are protected by mirror symmetry in the absence of spin-orbital coupling. Besides, we find that the closed nodal lines can be effectively tuned by applying biaxial tensile strain. Interestingly, with a moderate compressive biaxial strain, a novel metal-semimetal-semiconductor phase transition can be induced, during which a 2-D double Weyl fermion emerges. The 2-D double Weyl fermion features a single Fermi point, where the conduction and the valence bands contact quadratically. We construct an effective Hamiltonian to characterize the 2-D double Weyl fermion. Additionally, we show that TiBX (X = Cl, Br, I) monolayers possess similar properties. Our findings show that the monolayer TiBF is a fascinating platform to investigate unique topological phases and that it demonstrates a great potential for nanoscale device applications.

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene.

Parallel ("nested") regions of a Fermi surface (FS) drive instabilities of the electron fluid, for example, the spin density wave in elemental chromium. In one-dimensional materials, the FS is trivially fully nested (a single nesting vector connects two "Fermi dots"), while in higher dimensions only a fraction of the FS consists of parallel sheets. We demonstrate that the tiny angle regime of twist bilayer graphene (TBLG) possesses a phase, accessible by interlayer bias, in which the FS consists entirely of nestable "Fermi lines", the first example of a completely nested FS in a two-dimensional (2D) material. This nested phase is found both in the ideal as well as relaxed structure of the twist bilayer. We demonstrate excellent agreement with recent STM images of topological states in this material and elucidate the connection between these and the underlying Fermiology. We show that the geometry of the Fermi lines network is controllable by the strength of the applied interlayer bias, and thus TBLG offers unprecedented access to the physics of FS nesting in 2D materials.

Phase diagram of a two-dimensional dirty tilted Dirac semimetal

We investigate the effects of quenched disorder on a non-interacting tilted Dirac semimetal in two dimensions. Depending on the magnitude of the tilting parameter, the system can have either Fermi points (type-I) or Fermi lines (type-II). In general, there are three different types of disorders for Dirac fermions in two dimensions, namely, the random scalar potential, the random vector potentials along and perpendicular to the tilting direction, and the random mass. We study the effects of weak disorder in terms of the renormalization group, which is performed by integrating out the modes with large energies, instead of large momenta. Since the parametrization of the low-energy degrees of freedom depends on the structure of the Fermi surface, the resulting one-loop renormalization-group equations depend on the type of tilted Dirac fermions. Whenever the disorder is a marginal perturbation, we examine its role on low-energy physics by a mean-field approximation of the replica field theory or the first-order Born approximation. Based on our analysis, we suggest the phase diagrams of a two-dimensional tilted Dirac fermion in the presence of different types of disorder.

Layer-dependent intrinsic anomalous Hall effect in Fe3GeTe2

We study the intrinsic anomalous Hall effect (AHE) in both two-dimensional and bulk ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ (FGT) van der Waals crystals, where long-range ferromagnetic order has been observed in FGT with thickness down to monolayer. We demonstrate that the FGT with number of layers ($n$) equal to 2 exhibits the strongest AHE, and the trend of the calculated anomalous Hall conductivity (AHC) per layer with $n$ is roughly consistent with the experimental observations. Such layer dependence of AHE is in sharp contrast to the similar values of magnetic moments for FGT with different thickness. The distribution of Berry curvature and configurations of Fermi lines in the reciprocal space indicate that the interlayer hybridization in bilayer FGT induces great modification of the energy dispersions around the Fermi level, leading to much more occurrence of avoided crossings of Fermi lines near the Brillouin zone boundaries. Despite the much lower value of the AHC in the pristine monolayer FGT, it can be significantly enhanced by electron doping. Our study thus provides an in-depth understanding of the evolution of the AHE and electronic structure of FGT from bulk to monolayer.

FermiSurfer: Fermi-surface viewer providing multiple representation schemes

FermiSurfer is a newly developed Fermi-surface viewer designed to facilitate the understanding of the physical properties of metals. It can display the Fermi surfaces of a material, color plots of arbitrary k-dependent quantities, the Fermi surface at arbitrary cross sections (Fermi lines), cross- or parallel-eye three-dimensional stereogram views, nodal lines, extremal orbits, and highlight the occupied or empty side of the Fermi surface. In addition, various first-principles software packages can produce input for FermiSurfer. This paper explains how to use FermiSurfer and demonstrates its usefulness by investigating the origin of the anisotropic superconductivity of YNi2B2C. Program summaryProgram Title: FermiSurferProgram Files doi:http://dx.doi.org/10.17632/36992zhpvk.1Licensing provisions: MITProgramming language: CNature of problem: The anisotropy of quantities on Fermi surfaces (the character of orbitals, etc.) strongly affects electronic properties, such as superconductivity or thermoelectricity, in metals. Observing the anisotropy, however, remains difficult. Thus, a graphical tool that can elucidate how quantities vary over complicated Fermi surfaces is highly desirable.Solution method: FermiSurfer uses the tetrahedron method to compute Fermi surfaces. The French-curve interpolation is used to display smooth Fermi surfaces.Additional comments including restrictions and unusual features : The parallel- and cross-eye stereograms are available to enhance the visibility of complicated Fermi surfaces. This program works on any operating system, such as Linux, UNIX, macOS, and Windows, in which OpenGL library is installed.

Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene.

We show that the recently observed superconductivity in twisted bilayer graphene (TBG) can be explained as a consequence of the Kohn-Luttinger (KL) instability which leads to an effective attraction between electrons with originally repulsive interaction. Usually, the KL instability takes place at extremely low energy scales, but in TBG, a doubling and subsequent strong coupling of the van Hove singularities (vHS) in the electronic spectrum occurs as the magic angle is approached, leading to extended saddle points in the highest valence band with almost perfect nesting between states belonging to different valleys. The highly anisotropic screening induces an effective attraction in a p-wave channel with odd parity under the exchange of the two disjoined patches of the Fermi line. We also predict the appearance of a spin-density wave instability, adjacent to the superconducting phase, and the opening of a gap in the electronic spectrum from the condensation of spins with wave vector corresponding to the nesting vector close to the vHS.

Type-I and type-II nodal lines coexistence in the antiferromagnetic monolayer CrAs2

Topological nodal line semimetals, hosting one-dimensional Fermi lines with symmetry protection, has become a hot topic in topological quantum matter. Due to the breaking of time reversal symmetry in magnetic system, nodal lines require protection by additional symmetries. Here, we report the discovery of antiferromagnetic type-I and type-II nodal lines coexist in the monolayer CrAs$_{2}$ based on a systematic first-principles calculation. Remarkably, the type-I nodal line in CrAs$_{2}$ form a concentric loop centered around the $\Gamma$ point is filling-enforced by nonsymmorphic analogue symmetry and robust against spin-orbital coupling. The type-II nodal lines, a kind of open nodal lines appear around the Fermi level, are protected by the mirror symmetry in the absence of spin-orbital coupling. The antiferromagnetic monolayer CrAs$_{2}$ proposed here may provide a platform for the correlation between magnetism and exotic topological phases.

The type II Weyl semimetals at low temperatures: Chiral anomaly, elastic deformations, zero sound

We consider the properties of the type II Weyl semimetals at low temperatures basing on the particular tight-binding model. In the presence of electric field directed along the line connecting the Weyl points of opposite chirality the occupied states flow along this axis giving rise to the creation of electron–hole pairs. The electrons belong to a vicinity of one of the two type II Weyl points while the holes belong to the vicinity of the other. This process may be considered as the manifestation of the chiral anomaly that exists without any external magnetic field. It may be observed experimentally through the measurement of conductivity. Next, we consider the modification of the theory in the presence of elastic deformations. In the domain of the considered model, where it describes the type I Weyl semimetals the elastic deformations lead to the appearance of emergent gravity. In the domain of the type II Weyl semimetals the form of the Fermi surface is changed due to the elastic deformations, and its fluctuations represent the special modes of the zero sound. We find that there is one to one correspondence between them and the sound waves of the elasticity theory. Next, we discuss the influence of the elastic deformations on the conductivity. The particularly interesting case is when our model describes the intermediate state between the type I and the type II Weyl semimetal. Then without the elastic deformations there are the Fermi lines instead of the Fermi points/Fermi surface, while the DC conductivity vanishes. However, even small elastic deformations may lead to the appearance of large conductivity.

Weyl nodes in periodic structures of superconductors and spin-active materials.

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), in this paper we show that certain periodic structures of S and M can behave effectively as superconductors with pairs of point nodes, near which the low-energy excitations are Weyl fermions. A simple model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero-energy surface states in the form of open Fermi lines (Fermi arcs). As a second example, a lattice model with alternating layers of S and magnetic Z2 topological insulators is solved. The calculated spectrum confirms previous predictions of Weyl nodes based on the tunnelling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.This article is part of the theme issue 'Andreev bound states'.

Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar\cite{Shankar}, by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

Topological Nodal Line Semimetal in Non-Centrosymmetric PbTaS**Supported by the National Natural Science Foundation of China under Grant No 11504366, and the National Basic Research Program of China under Grant Nos 2015CB921503 and 2016YFE0110000.

Topological semimetals are a new type of matter with one-dimensional Fermi lines or zero-dimensional Weyl or Dirac points in momentum space. Here using first-principles calculations, we find that the non-centrosymmetric PbTaS is a topological nodal line semimetal. In the absence of spin-orbit coupling (SOC), one band inversion happens around a high symmetrical point, which leads to forming a nodal line. The nodal line is robust and protected against gap opening by mirror reflection symmetry even with the inclusion of strong SOC. In addition, it also hosts exotic drumhead surface states either inside or outside the projected nodal ring depending on surface termination. The robust bulk nodal lines and drumhead-like surface states with SOC in PbTaS make it a potential candidate material for exploring the freakish properties of the topological nodal line fermions in condensed matter systems.

Fermi points and the Nambu sum rule in the polar phase of 3He

We discuss the polar phase of $^3$He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin - orbit interaction this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate, that the spin - orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu - Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.