Orbital Currents Research Articles

Unconventional chiral charge order in kagome superconductor KV3Sb5.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1-4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

Pure bulk orbital and spin photocurrent in two-dimensional ferroelectric materials

We elucidate a bias-free light-induced orbital and spin current through nonlinear response theory, which generalizes the well-known bulk photovoltaic effect in centrosymmetric broken materials from charge to the spin and orbital degrees of freedom. We use two-dimensional nonmagnetic ferroelectric materials (such as GeS and its analogs) to illustrate this bulk orbital/spin photovoltaic effect, through first-principles calculations. These materials possess a vertical mirror symmetry and time-reversal symmetry but lack of inversion symmetry. We reveal that in addition to the conventional photocurrent that propagates parallel to the mirror plane (under linearly polarized light), the symmetric forbidden photocurrent perpendicular to the mirror actually contains electrons flow, which carries angular momentum information and move oppositely. This generates a pure orbital moment current with zero electric charge current. Such hidden photo-induced pure orbital current could lead to a pure spin current via spin–orbit coupling interactions. Therefore, a four-terminal device can be designed to detect and measure photo-induced charge, orbital, and spin currents simultaneously. All these currents couple with electric polarization P, hence their amplitude and direction can be manipulated through ferroelectric phase transition. Our work provides a route to generalizing nanoscale devices from their photo-induced electronics to orbitronics and spintronics.

Magneto-Optical Characterization of Trions in Symmetric InP-Based Quantum Dots for Quantum Communication Applications.

Magneto-optical parameters of trions in novel large and symmetric InP-based quantum dots, uncommon for molecular beam epitaxy-grown nanostructures, with emission in the third telecom window, are measured in Voigt and Faraday configurations of an external magnetic field. The diamagnetic coefficients are found to be in the range of 1.5–4 μeV/T2, and 8–15 μeV/T2, respectively out-of-plane and in-plane of the dots. The determined values of diamagnetic shifts are related to the anisotropy of dot sizes. Trion g-factors are measured to be relatively small, in the range of 0.3–0.7 and 0.5–1.3, in both configurations, respectively. Analysis of single carrier g-factors, based on the formalism of spin-correlated orbital currents, leads to similar values for hole and electron of ~0.25 for Voigt and ge ≈ −5; gh ≈ +6 for Faraday configuration of the magnetic field. Values of g-factors close to zero measured in Voigt configuration make the investigated dots promising for electrical tuning of the g-factor sign, required for schemes of single spin control in qubit applications.

Voltage-Controlled Magnetic Reversal in Orbital Chern Insulators.

Chern insulator ferromagnets are characterized by a quantized anomalous Hall effect and have so far been identified experimentally in magnetically doped topological insulator thin films and in bilayer graphene moiré superlattices. We classify Chern insulator ferromagnets as either spin or orbital, depending on whether the orbital magnetization results from spontaneous spin polarization combined with spin-orbit interactions, as in the magnetically doped topological insulator case, or directly from spontaneous orbital currents, as in the moiré superlattice case. We argue that, in a given magnetic state, characterized, for example, by the sign of the anomalous Hall effect, the magnetization of an orbital Chern insulator will often have opposite signs for weak n and weak p electrostatic or chemical doping. This property enables pure electrical switching of a magnetic state in the presence of a fixed magnetic field.

Suggestion for Direct Observation of Orbital Accumulation

The generation of orbital current is an intriguing research topic not only for developing energy-efficient control of spintronic devices, but also for observing new emerging phenomena, such as orbital-to-spin conversion. During the last two decades, many innovative measurement techniques have been developed for discoveries related to conversions between spin flow and natural phenomena such as light, heat, vibration, and charge flow. Observation of the orbital current also requires efforts that should result in many other state-of-the-art discoveries. However, a direct experimental way to observe the orbital current is still missing. In this article, we suggest that X-ray magnetic circular dichroism (XMCD) measurements may be a good candidate for directly observing the orbital current because it is the only way to detect orbital moment selectively. Just like spin accumulation, orbital current can also accumulate at the edge of a system, giving rise to a non-zero orbital magnetic moment. Although the orbital moment generated by orbital accumulation is expected to have a very small value, ~10‒5 μB, precise measurement with high sensitivity will allow direct observation of the orbital current.

Orbitronics: Mechanism of Orbital Current Generation and Dynamics

The orbital degree of freedom is often considered to be quenched in solids due to the potential of the crystal field. In contrast to such expectation, we showed recently that the orbital current can be electrically generated despite orbital quenching in equilibrium, leading to a phenomenon called the orbital Hall effect. In this article, we provide a pedagogical introduction to the concept of an orbital current in solids and the mechanism underlying the orbital Hall effect. We also discuss the relation between the orbital Hall effect and the spin Hall effect, as well as a way to utilize the orbital current in spin-orbitronic devices.

Registering Fish Shoals Attracted by Solitary Intensive Internal Waves

An unusual effect of attracting fish shoals by intensive internal waves was observed in the shelf zone of the Black Sea. A shoal of fish that followed a train of intense internal waves moving to the shore was detected during research using an acoustic Doppler current profiler (ADCP) in the shelf zone near the city of Gelendzhik. The wave train consisted of internal waves unusually large for the Black Sea, up to 16 m high. Orbital currents initiated by these waves intensively stirred up the sediments, which contained some nutriments attractive to the fish. The most pronounced turbulence effect was produced by two head waves of the train, which had maximum amplitudes, near which the shoals of fish were discovered. The shoals followed the internal waves for 2.5 hours, until the waves faded out upon approaching the shore.

Role of orbital hybridization in anisotropic magnetoresistance

We theoretically and numerically show that longitudinal orbital currents in ferromagnets depend on the magnetization direction, which contribute to the anisotropic magnetoresistance (AMR). This orbital contribution to AMR arises from the momentum-dependent orbital splitting, which is generally present in multi-orbital systems through the orbital anisotropy and the orbital hybridization. We highlight the latter orbital hybridization as an unrecognized origin of AMR and also as a common origin of AMR and orbital Hall effect.

Multipolar magnetism in d -orbital systems: Crystal field levels, octupolar order, and orbital loop currents

Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J\!=\!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($\mu$SR) experiments on cubic $5d^2$ osmate double perovskites Ba$_2$ZnOsO$_6$, Ba$_2$CaOsO$_6$, and Ba$_2$MgOsO$_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J\!=\!2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba$_2$YReO$_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.

Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems

Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quantities are controlled by the critical exponents $\nu$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation for impurities, we study the nuclear spin-lattice relaxation rate $1/T_1$ due to the orbital currents in disordered Weyl SMs. We find that $(T_1T)^{-1}\sim E^{2/z}$ at the QCP where $E$ is the maximum of temperature $T$ and chemical potential $\mu(T)$ relative to the Weyl point. This scaling behavior of $(T_1T)^{-1}$ is also confirmed by the self-consistent $T$-matrix approximation, where a remarkable temperature dependence of $\mu(T)$ could play an important role. We hope these results of $(T_1T)^{-1}$ will serve as an impetus for exploration of the disorder-driven quantum criticality in Weyl materials.

Propagation properties of radially polarized Pearcey-Gauss vortex beams in free space**Project supported by the National Natural Science Foundation of China (Grant Nos. 11775083 and 11374108) and the National Training Program of Innovation and Entrepreneurship for Undergraduates, China.

We investigate a family of radially polarized Pearcey–Gauss vortex beams (RPPGVBs), obtain the general propagation expressions of an RPPGVB, and study the intensity distribution, phase pattern, spin currents as well as the orbital currents when the RPPGVB propagates in free space. The focal plane and the intensity of the focal point can be adjusted by changing the position of the vortex and the scaling factors. We also investigate how the waist size influences the propagation properties.

Intrinsic orbital moment and prediction of a large orbital Hall effect in two-dimensional transition metal dichalcogenides

Carrying information using generation and detection of the orbital current, instead of the spin current, is an emerging field of research, where the orbital Hall effect (OHE) is an important ingredient. Here, we propose a new mechanism of the OHE that occurs in {\it non-}centrosymmetric materials. We show that the broken inversion symmetry in the 2D transition metal dichalcogenides (TMDCs) causes a robust orbital moment, which flow in different directions due to the opposite Berry curvatures under an applied electric field, leading to a large OHE. This is in complete contrast to the inversion-symmetric systems, where the orbital moment is induced only by the external electric field. We show that the valley-orbital locking as well as the OHE both appear even in the absence of the spin-orbit coupling. The non-zero spin-orbit coupling leads to the well-known valley-spin locking and the spin Hall effect, which we find to be weak, making the TMDCs particularly suitable for direct observation of the OHE, with potential application in {\it orbitronics}.

Orbital torque: Torque generation by orbital current injection

We propose a mechanism of torque generation by injection of an orbital current, which we call $\textit{orbital torque}$. In a magnetic bilayer consisting of a nonmagnet (NM) and a ferromagnet (FM), we consider a situation where the spin-orbit coupling (SOC) is present only in the FM. Although the SOC is absent in the NM, the orbital Hall effect can arise in the NM. When the resulting orbital Hall current is injected to the FM, the SOC of the FM converts the orbital angular momentum into spin, which exerts torque to the magnetization of the FM. Remarkably, even for small SOC strength comparable to that of $3d$ FMs, the orbital torque can be comparable to the spin torque induced by the spin Hall effect of the NM with strong SOC. This provides a way to experimentally probe the OHE and opens a new venue to achieving spin-torque devices based on light elements that exhibit gigantic orbital response. Experimental implications are discussed.

Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene

The recently predicted topological magnetoelectric effect and the response to an electric charge that mimics an induced mirror magnetic monopole are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems.

Equidensity orbitals in resultant-information description of electronic states

The equidensity orbitals (EO) are used in the resultant entropic description of molecular states which combines the probability and current contributions in the overall information content. Continuities of the modulus and phase components of electronic wavefunctions are examined, and the Harriman–Zumbach–Maschke (HZM) construction of Slater determinants yielding the prescribed electron density is explored. The conditional probability interpretation of (complex) HZM wavefunctions is formulated, the entropy/information contributions due to the state phase component are summarized, and a nonclassical origin of quantum dynamics of the resultant gradient information, related to average kinetic energy of electrons, is emphasized. The phase equilibria maximizing the resultant-entropy measures are explored, and “thermodynamic” phase minimizing the overall gradient information is determined. It generates finite orbital currents giving rise to the vanishing resultant flow of electrons in the system as a whole. Potential use of atomic and molecular EO bases in electronic structure calculations and interpretations in chemistry is discussed, and illustrative example of Gaussian probability distribution is examined in some detail.

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.

Ionic and electronic properties of the topological insulator Bi2Te2Se investigated via β -detected nuclear magnetic relaxation and resonance of Li8

We report measurements on the high temperature ionic and low temperature electronic properties of the 3D topological insulator Bi$_2$Te$_2$Se using ion-implanted $^8$Li $\beta$-detected nuclear magnetic relaxation and resonance. With implantation energies in the range 5-28 keV, the probes penetrate beyond the expected range of the topological surface state, but are still within 250 nm of the surface. At temperatures above ~150 K, spin-lattice relaxation measurements reveal isolated $^8$Li$^{+}$ diffusion with an activation energy $E_{A} = 0.185(8)$ eV and attempt frequency $\tau_{0}^{-1} = 8(3) \times 10^{11}$ s$^{-1}$ for atomic site-to-site hopping. At lower temperature, we find a linear Korringa-like relaxation mechanism with a field dependent slope and intercept, which is accompanied by an anomalous field dependence to the resonance shift. We suggest that these may be related to a strong contribution from orbital currents or the magnetic freezeout of charge carriers in this heavily compensated semiconductor, but that conventional theories are unable to account for the extent of the field dependence. Conventional NMR of the stable host nuclei may help elucidate their origin.

Orbital currents in insulating and doped antiferromagnets

We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have non-zero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with $\mathbb{Z}_2$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the N\'eel state.

Comment on “No evidence for orbital loop currents in charge-ordered YBa2Cu3O6+x from polarized neutron diffraction”

Intra-unit cell magnetic order has been observed in four different families of high-temperature superconductors from polarized neutron diffraction experiments and supported by several other techniques. That order, which does not break translation symmetry, is consistent with the predicted orbital moments generated by two microscopic loop currrents in each CuO$_2$ cell. Recently, using polarized neutron diffraction, Croft {\it et al} [Phys. Rev. B 96, 214504 (2017)] claim to find no evidence for such orbital loop currents in charge ordered ${\rm YBa_2Cu_3O_{6+x}}$. Their experiment is done with detwinned samples at least 100 times smaller than in previous experiments without counting much longer. We show by a detailed quantitative analysis of their data that contrary to their conclusion, the magnetic signal falls below their threshold of detection. None of the data reported by Croft {\it et al} challenge the universality of the intra-unit cell order in cuprates.

Reply to “Comment on ‘No evidence for orbital loop currents in charge-ordered YBa2Cu3O6+x from polarized neutron diffraction”'

The issues raised in the preceding comment of Bourges et al. [arXiv:1710.08173, Phys. Rev. B 98, 016501 (2018)] are shown to be unfounded. We highlight the complications caused by inhomogeneous beam polarization that can occur when using polarized neutron diffraction to detect small magnetic moments.