Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals.

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Realization of a two-dimensional Weyl semimetal and topological Fermi strings.

A two-dimensional (2D) Weyl semimetal, akin to a spinful variant of graphene, represents a topological matter characterized by Weyl fermion-like quasiparticles in low dimensions. The spinful linear band structure in two dimensions gives rise to distinctive topological properties, accompanied by the emergence of Fermi string edge states. We report the experimental realization of a 2D Weyl semimetal, bismuthene monolayer grown on SnS(Se) substrates. Using spin and angle-resolved photoemission and scanning tunneling spectroscopies, we directly observe spin-polarized Weyl cones, Weyl nodes, and Fermi strings, providing consistent evidence of their inherent topological characteristics. Our work opens the door for the experimental study of Weyl fermions in low-dimensional materials.

Unveiling the Role of Spin Currents on the Giant Rashba Splitting in Single-Layer WSe2.

The Rashba spin splitting in uniaxial, inversion-asymmetric materials has attracted considerable interest for spintronic applications. The most widely used theoretical framework to model such states is Kohn-Sham density functional theory (DFT) in combination with standard (semi)local exchange-correlation density functional approximations (DFAs). However, in the presence of spin-orbit coupling, DFT misses contributions due to modification of the many-body interaction by spin currents J⃗. Inclusion of the latter effects requires a spin current DFT (SCDFT) formulation, which is seldom considered. We investigate the giant Rashba splitting in single-layer WSe2, and we quantify the effect of including spin currents in DFAs of the SCDFT. Crucially, we show that SCDFT allows fully capturing the giant Rashba band splitting in single-layer WSe2, otherwise previously systematically underestimated by standard (semi)local DFAs within the DFT framework. We find the inclusion of J⃗ on the DFA increases the Rashba splitting by about 20%.

Nonconservation of the Valley Density and Its Implications for the Observation of the Valley Hall Effect.

We show that the conservation of the valley density in multivalley insulators is broken in an unexpected way by the electric field that drives the valley Hall effect. This implies that time-reversal-invariant fully gapped insulators, in which no bulk or edge state crosses the Fermi level, can support a valley Hall current in the bulk and yet show no valley density accumulation at the edges. Thus, the valley Hall effect cannot be observed in such systems. If the system is not fully gapped then valley density accumulation at the edges is possible. The accumulation has no contribution from undergap states and can be expressed as a Fermi surface average, for which we derive an explicit formula. We demonstrate the theory by calculating the valley density accumulations in an archetypical valley-Hall insulator: a gapped graphene nanoribbon. Surprisingly, we discover that a net valley density polarization is dynamically generated for certain edge terminations.

Anomalous Skew-Scattering Nonlinear Hall Effect and Chiral Photocurrents in PT-Symmetric Antiferromagnets.

Berry curvature and skew scattering play central roles in determining both the linear and nonlinear anomalous Hall effects. Yet in PT-symmetric antiferromagnetic metals, Hall effects from either intrinsic Berry curvature mediated anomalous velocity or the conventional skew-scattering process individually vanish. Here we reveal an unexpected nonlinear Hall effect that relies on both Berry curvature and skew-scattering working in cooperation. This anomalous skew-scattering nonlinear Hall effect (ASN) is PT even and dominates the low-frequency nonlinear Hall effect for PT-symmetric antiferromagnetic metals. Surprisingly, we find that in addition to its Hall response, ASN produces helicity dependent photocurrents, in contrast to other known PT-even nonlinearities in metals that are helicity blind. This characteristic enables us to isolate ASN and establishes new photocurrent tools to interrogate the antiferromagnetic order of PT-symmetric metals.

Dirac Fermion Cloning, Moiré Flat Bands, and Magic Lattice Constants in Epitaxial Monolayer Graphene.

Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals, and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. In this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moiré flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the ( 3 × 3 ) R 30 o \[(\sqrt 3 \; \times \;\sqrt 3 )R{30^o}\] supercell of graphene. The results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.

Carrier transport theory for twisted bilayer graphene in the metallic regime.

Understanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments.

Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature.

The spin Hall effect (SHE) is usually observed as a bulk effect in high-symmetry crystals with substantial spin-orbit coupling (SOC), where the symmetric spin-orbit field imposes a widely encountered trade-off between spin Hall angle (θSH) and spin diffusion length (Lsf), and spin polarization, spin current and charge current are constrained to be mutually orthogonal. Here, we report a large θSH of 0.32 accompanied by a long Lsf of 2.2 µm at room temperature in a low-symmetry few-layered semimetal MoTe2, thus identifying it as an excellent candidate for simultaneous spin generation, transport and detection. In addition, we report that longitudinal spin current with out-of-plane polarization can be generated by both transverse and vertical charge current, due to the conventional and a newly observed planar SHE, respectively. Our study suggests that manipulation of crystalline symmetries and strong SOC opens access to new charge-spin interconversion configurations and spin-orbit torques for spintronic applications.

Nonlinear Planar Hall Effect.

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Field and Current Control of the Electrical Conductivity of an Artificial 2D Honeycomb Lattice.

The conductivity of a neodymium-based artificial honeycomb lattice undergoes dramatic changes upon application of magnetic fields and currents. These changes are attributed to a redistribution of magnetic charges that are formed at the vertices of the honeycomb due to the nonvanishing net flux of magnetization from adjacent magnetic elements. It is suggested that the application of a large magnetic field or a current causes a transition from a disordered state, in which magnetic charges are distributed at random, to an ordered state, in which they are regularly arranged on the sites of two interpenetrating triangular Wigner crystals. The field and current tuning of electrical properties are highly desirable functionalities for spintronics applications. Consequently, a new spintronics research platform can be envisaged using artificial magnetic honeycomb lattices.

Observation of Out-of-Plane Spin Texture in a SrTiO_{3}(111) Two-Dimensional Electron Gas.

We explore the second order bilinear magnetoelectric resistance (BMER) effect in the d-electron-based two-dimensional electron gas (2DEG) at the SrTiO_{3}(111) surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the SrTiO_{3}(111) 2DEG is tunable and unexpectedly large.

Edge Plasmons in Two-Component Electron Liquids in the Presence of Pseudomagnetic Fields.

We study the properties of edge plasmons in two-component electron liquids in the presence of pseudomagnetic fields, which have opposite signs for the two different electronic populations and therefore preserve the time-reversal symmetry. The physical realizations of such systems are many. We discuss the case of strained graphene, solving the problem with the Wiener-Hopf technique. We show (i) that two charged counterpropagating acoustic edge modes exist at the boundary and (ii) that, in the limit of large pseudomagnetic fields, each of them involves oscillations of only one of the two electronic components. We suggest that the edge pseudomagnetoplasmons of graphene can be used to selectively address the electrons of one specific valley, a feature relevant for the emerging field of valleytronics. Our solution highlights new features missing in previous (similar) results obtained with uncontrolled approximations, namely a logarithmic divergence of the plasmon velocity, and the absence of gapped edge modes inside the bulk-plasmon gap.

Ab initio electronic structure of quasi-two-dimensional materials: A "native" Gaussian-plane wave approach.

Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is "native" to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory - density functional theory, GW approximation and Bethe-Salpeter equation - are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.

Nonlocal Anomalous Hall Effect.

The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect-the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt/YIG structures.

Violation of the Wiedemann-Franz Law in Hydrodynamic Electron Liquids.

The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultraclean conductors in the hydrodynamic regime, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor 1+τ/τ(th)(ee), where 1/τ is the momentum relaxation rate and τ(th)(ee) is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of 1/τ(th)(ee) of two-dimensional electron liquids. We show that at low temperature 1/τ(th)(ee) is 8/5 of the quasiparticle decay rate; remarkably, the same result is found in doped graphene and in conventional electron liquids in parabolic bands.

Highly confined low-loss plasmons in graphene-boron nitride heterostructures.

Graphene plasmons were predicted to possess simultaneous ultrastrong field confinement and very low damping, enabling new classes of devices for deep-subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. Although all of these great prospects require low damping, thus far strong plasmon damping has been observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this Article we exploit near-field microscopy to image propagating plasmons in high-quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine the dispersion and plasmon damping in real space. We find unprecedentedly low plasmon damping combined with strong field confinement and confirm the high uniformity of this plasmonic medium. The main damping channels are attributed to intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key to the development of graphene nanophotonic and nano-optoelectronic devices.

Corbino disk viscometer for 2D quantum electron liquids.

The shear viscosity of a variety of strongly interacting quantum fluids, ranging from ultracold atomic Fermi gases to quark-gluon plasmas, can be accurately measured. On the contrary, no experimental data exist, to the best of our knowledge, on the shear viscosity of two-dimensional quantum electron liquids hosted in a solid-state matrix. In this work we propose a Corbino disk device, which allows a determination of the viscosity of a quantum electron liquid from the dc potential difference that arises between the inner and the outer edge of the disk in response to an oscillating magnetic flux.

Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory.

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

Quantum stress focusing in descriptive chemistry.

We show that several important concepts of descriptive chemistry, such as atomic shells, bonding electron pairs, and lone electron pairs, may be described in terms of quantum stress focusing, i.e., the spontaneous formation of high-pressure regions in an electron gas. This description subsumes previous mathematical constructions, such as the Laplacian of the density and the electron localization function, and provides a new tool for visualizing chemical structure. We also show that the full stress tensor, defined as the derivative of the energy with respect to a local deformation, can be easily calculated from density functional theory.