Bulk Inversion Symmetry Research Articles

Engineering Spin-Orbit Interactions in Silicon Qubits at the Atomic-Scale.

Spin-orbit interactions arise whenever the bulk inversion symmetry and/or structural inversion symmetry of a crystal is broken providing a bridge between a qubit's spin and orbital degree of freedom. While strong interactions can facilitate fast qubit operations by all-electrical control, they also provide a mechanism to couple charge noise thereby limiting qubit lifetimes. Previously believed to be negligible in bulk silicon, recent silicon nano-electronic devices have shown larger than bulk spin-orbit coupling strengths from Dresselhaus and Rashba couplings. Here, it is shown that with precision placement of phosphorus atoms in silicon along the [110] direction (without inversion symmetry) or [111] direction (with inversion symmetry), a wide range of Dresselhaus and Rashba coupling strength can be achieved from zero to 1113 × 10-13eV-cm. It is shown that with precision placement of phosphorus atoms, the local symmetry (C2v, D2d, and D3d) can be changed to engineer spin-orbit interactions. Since spin-orbit interactions affect both qubit operation and lifetimes, understanding their impact is essential for quantum processordesign.

Structure-Guided Approaches for Enhanced Spin-Splitting in Chiral Perovskite.

Hybrid organic-inorganic perovskites with diverse lattice structures and chemical composition provide an ideal material platform for novel functionalization, including chirality transfer. Chiral perovskites combine organic and inorganic sublattices, therefore encoding the structural asymmetry into the electronic structures and giving rise to the spin-splitting effect. From a structural chemistry perspective, the magnitude of the spin-splitting effect crucially depends on the noncovalent and electrostatic interaction within the chiral perovskite, which induces the local site and long-range bulk inversion symmetry breaking. In this regard, we systematically retrospect the structure-property relationships in chiral perovskite. Insight into the rational design of chiral perovskites based on molecular configuration, dimensionality, and chemical composition along with their effects on spin-splitting manifestation is presented. Lastly, challenges in purposeful material design and further integration into chiral perovskite-based spintronic devices are outlined. With an understanding of fundamental chemistry and physics, we believe that this Perspective will propel the application of multifunctional spintronic devices.

Spin-orbit coupled spin-polarised hole gas at the CrSe2-terminated surface of AgCrSe2

In half-metallic systems, electronic conduction is mediated by a single spin species, offering enormous potential for spintronic devices. Here, using microscopic-area angle-resolved photoemission, we show that a spin-polarised two-dimensional hole gas is naturally realised in the polar magnetic semiconductor AgCrSe2 by an intrinsic self-doping at its CrSe2-terminated surface. Through comparison with first-principles calculations, we unveil a striking role of spin-orbit coupling for the surface hole gas, unlocked by both bulk and surface inversion symmetry breaking, suggesting routes for stabilising complex magnetic textures in the surface layer of AgCrSe2.

Spin–orbit proximity effect and topological superconductivity in graphene/transition-metal dichalcogenide nanoribbons

Spin–orbit coupling (SOC) plays a determinate role in spintronics and topological physics. Previous studies indicate that the SOC in graphene nanoribbon (GNR) can be enhanced by the proximity effect from two-dimensional transition-metal dichalcogenide (2D-TMD). However, the bulk inversion symmetry of GNR/2D-TMD restricts further increase of the proximity-induced SOC in GNR. In this view, we introduce a TMD nanoribbon (TMDNR) with finite width, and propose three methods to break the bulk inversion symmetry, i.e. defects in TMDNR, spatial interlayer edge coupling, and twist between GNR and TMDNR, which can further enhance the SOC in the GNR by roughly 30 times, 20 times and 150 times, respectively, depending on the relative energy between the Dirac point of GNR and the states of TMDNR. Furthermore, the significantly enhanced SOC can drive the GNR into a topological superconducting phase. By introducing the Zeeman splitting and s-wave superconductivity in the GNR, quasi one-dimensional topological superconductivity and Majorana zero modes (MZMs) can be achieved in the GNR. At last we propose a feasible experimental method to realize and manipulate MZMs in the GNR/TMDNR system.

Observation of spatially resolved Rashba states on the surface of CH3NH3PbBr3 single crystals

Hybrid organic-inorganic perovskites (HOIPs) are prime candidates for studying Rashba effects due to the heavy metal and halogen atoms in their crystal structure coupled with predicted inversion symmetry breaking. Nevertheless, observation of the Rashba effect in cubic CH3NH3PbBr3 single crystals that possess bulk inversion symmetry is the subject of extensive debate due to the lack of conclusive experiments and theoretical explanations. Here, we provide experimental evidence that Rashba state in cubic CH3NH3PbBr3 single crystals at room temperature occurs exclusively on the crystal surface and depends on specific surface termination that results in local symmetry breaking. We demonstrate this using a suite of spatially resolved and depth-sensitive techniques, including circular photogalvanic effect, inverse spin Hall effect, and multiphoton microscopy, that are supported by first principle calculations. Our work suggests using surface Rashba states in these materials for spintronic applications.

Longitudinal and transverse electric field manipulation of hole spin-orbit qubits in one-dimensional channels

Holes confined in semiconductor nanostructures realize qubits where the quantum mechanical spin is strongly mixed with the quantum orbital angular momentum. The remarkable spin-orbit coupling allows for fast all electrical manipulation of such qubits. We study an idealization of a CMOS device where the hole is strongly confined in one direction (thin film geometry), while it is allowed to move more extensively along a one-dimensional channel. Static electric bias and $ac$ electrical driving are applied by metallic gates arranged along the channel. In quantum devices based on materials with a bulk inversion symmetry, such as silicon or germanium, there exists different possible spin-orbit coupling based mechanisms for qubit manipulation. One of them, the $g$-tensor magnetic resonance ($g$-TMR), relies on the dependence of the effective $g$-factors on the electrical confinement. In this configuration the hole is driven by an $ac$ field parallel to the static electric field and perpendicular to the channel (transverse driving). Another mechanism, which we refer to here as iso-Zeeman electric dipole spin resonance (IZ-EDSR), is due to the Rashba spin-orbit coupling that leads to an effective time-dependent magnetic field experienced by the pseudo-spin oscillating along the quantum channel (longitudinal driving). We compare these two modes of operation and we describe the conditions where the magnitudes of the Rabi frequencies are the largest. Different regimes can be attained by electrical tuning where the coupling to the $ac$ electric field is made either weak or strong...

Second-order topological non-Hermitian skin effects

Higher-order topology realizes topologically robust corner modes as a manifestation of nontriviality. We theoretically propose non-Hermitian skin effects which stem from second-order topology of chiral-symmetric Hermitian systems. It is found that the skin modes are localized at the corners. We demonstrate two types of second-order topological skin effects by two-dimensional intrinsic and extrinsic second-order topology. The intrinsic second-order topological skin effect is characterized topologically by bulk inversion symmetry as well as chiral symmetry. Meanwhile, the extrinsic second-order topological skin effect occurs from the topological correspondence between the edges and corners. We show that the non-Hermitian skin modes emerge by using a relationship between second-order and conventional first-order topology.

Interfacial Dzyaloshinskii-Moriya interaction of antiferromagnetic materials

The interface between a ferromagnet (FM) or antiferromagnet (AFM) and a heavy metal (HM) results in an antisymmetric exchange interaction known as the interfacial Dzyaloshinskii-Moriya interaction (iDMI) which favors non-collinear spin configurations. The iDMI is responsible for stabilizing noncollinear spin textures such as skyrmions in materials with bulk inversion symmetry. Interfacial DMI values have been previously determined theoretically and experimentally for FM/HM interfaces, and, in this work, values are calculated for the metallic AFM MnPt and the insulating AFM NiO. The heavy metals considered are W, Re, and Au. The effects of the AFM and HM thicknesses are determined. The iDMI values of the MnPt heterolayers are comparable to those of the common FM materials, and those of NiO are lower.

Topological evolution of correlated band structures and heavy-fermion-like behavior in a molybdenum-based metal organic framework C48S36Mo6

Owing to the fascinating properties of two dimensional transition metal dichalcogenides and the stability of ZIF-8 as the subclass of metal organic frameworks (MOFs), we propose a Mo-based MOFs material C48S36Mo6 containing organic ligands connecting to each other by Mo4+ metal ions. We reveal heavy-fermion-like electronic behaviour that results from highly localized impurity-like Mo-d electrons and tiny energy difference (<0.4 meV/atom) between antiferromagnetic and ferromagnetic state, using the generalized gradient approximation and its combination with Coulomb correlation U. Considering thermal fluctuation and weak magnetic exchange energy, C48S36Mo6 is a nonmagnetic metal at room temperature, and magnetic insulator at low temperature with a correlation-driven metal–insulator transition. Our Wannier functions analysis indicates that topological properties of energy bands around the Fermi level can be perturbed by correlation U, leading to moving of close nodal lines in three dimensional momentum space. Further introducing of spin–orbit coupling opens a small inverted energy gap of 3 meV at original nodal line due to bulk inversion symmetry. If a gate voltage of 48 meV is applied, the Fermi level will fall into the small energy gap of band inversion, and the system will realize a phase transition from Kondo metal to topological Kondo insulator.

Layer-dependent spin-orbit torques generated by the centrosymmetric transition metal dichalcogenide β−MoTe2

Single-crystal materials with sufficiently low crystal symmetry and strong spin-orbit interactions can be used to generate novel forms of spin-orbit torques on adjacent ferromagnets, such as the out-of-plane antidamping torque previously observed in WTe$_2$/ferromagnet heterostructures. Here, we present measurements of spin-orbit torques produced by the low-symmetry material $\beta$-MoTe$_2$, which unlike WTe$_2$ retains bulk inversion symmetry. We measure spin-orbit torques on $\beta$-MoTe$_2$/Permalloy heterostructures using spin-torque ferromagnetic resonance as a function of crystallographic alignment and MoTe$_2$ thickness down to the monolayer limit. We observe an out-of-plane antidamping torque with a spin torque conductivity as strong as 1/3 of that of WTe$_2$, demonstrating that the breaking of bulk inversion symmetry in the spin-generation material is not a necessary requirement for producing an out-of-plane antidamping torque. We also measure an unexpected dependence on the thickness of the $\beta$-MoTe$_2$ -- the out-of-plane antidamping torque is present in MoTe$_2$/Permalloy heterostructures when the $\beta$-MoTe$_2$ is a monolayer or trilayer thick, but goes to zero for devices with bilayer $\beta$-MoTe$_2$.

Interfacial magnetic anisotropy from a 3-dimensional Rashba substrate.

We study the magnetic anisotropy which arises at the interface between a thin film ferromagnet and a 3-d Rashba material. We use a tight-binding model to describe the bilayer, and the 3-d Rashba material characterized by the spin-orbit strength α and the direction of broken bulk inversion symmetry n̂. We find an in-plane uniaxial anisotropy in the ẑ × n̂ direction, where ẑ is the interface normal. For realistic values of α, the uniaxial anisotropy is of a similar order of magnitude as the bulk magnetocrystalline anisotropy. Evaluating the uniaxial anisotropy for a simplified model in 1-d shows that for small band filling, the in-plane easy axis anisotropy scales as α4 and results from a twisted exchange interaction between the spins in the 3-d Rashba material and the ferromagnet. For a ferroelectric 3-d Rashba material, n̂ can be controlled with an electric field, and we propose that the interfacial magnetic anisotropy could provide a mechanism for electrical control of the magnetic orientation.

Skyrmions in chiral magnets with Rashba and Dresselhaus spin-orbit coupling

Skyrmions are topological spin textures of interest for fundamental science and applications. Previous theoretical studies have focused on systems with broken bulk inversion symmetry, where skyrmions are stabilized by easy-axis anisotropy. We investigate here systems that break surface inversion symmetry, in addition to possible broken bulk inversion. This leads to two distinct Dzyaloshinskii-Moriya (DM) terms with strengths $D_\perp$, arising from Rashba spin-orbit coupling (SOC), and $D_\parallel$ from Dresselhaus SOC. We show that skyrmions become progressively more stable with increasing $D_\perp/D_\parallel$, extending into the regime of easy-plane anisotropy. We find that the spin texture and topological charge density of skyrmions develops nontrivial spatial structure, with quantized topological charge in a unit cell given by a Chern number. Our results give a design principle for tuning Rashba SOC and magnetic anisotropy to stabilize skyrmions in thin films, surfaces, interfaces and bulk magnetic materials that break mirror symmetry.

Precise measurement of weak strain by second-harmonic generation from silicon (111) surface

The weak strain induced by uniaxial strain device is calibrated by strain-induced second-harmonic generation (SISHG) from silicon (111) surface. Dependences of the strain-induced second-harmonic intensity on sample azimuth angle show that the strain leads to increase of SH intensity. The high consistency of the SH-measured strain and the applied strain indicates that weak strain can be accurately calibrated by SISHG. The small applied strain does not greatly affect the 3 m symmetry of silicon (111) surface, but enhances the SH intensity evidently. The bulk inversion symmetry of crystal silicon vanished under applying of uniaxial strain and this also has demonstrated by first-principles simulation. Furthermore, the theoretical relative variation of Si–Si bond length agrees exactly with the applied strain along [111] direction.

Optical coherent current control at surfaces: Theory of injection current

We present a study of optical coherent control of injection currents at surfaces of cubic semiconductors, predicting that this new optical effect will serve as a surface-sensitive probe of fundamentally and technologically important crystals with both bulk inversion symmetry (such as cubic diamond $\overline{6}m2$ or $\overline{6}$) and noncentrosymmetric systems (such as zinc-blende symmetry $\overline{4}\overline{3}m$). In crystals with any of these symmetries, this effect vanishes in the bulk, but it is allowed in surface regions due to the breaking of the bulk symmetry there. We present the results of ab initio calculations for injected currents at prototypical clean and Sb-covered GaAs(110)($1\ifmmode\times\else\texttimes\fi{}1$) and clean Si(111)($2\ifmmode\times\else\texttimes\fi{}1$) surfaces, which have well-understood and experimentally reproducible reconstructions. The effects are shown to be essentially sensitive to surface structure, and the injected currents can be interpreted in terms of the surface electronic structure. Calculated magnitudes indicate that the currents should be easily observable, and the calculated spectra of all of the surfaces demonstrate interesting behavior as a function of the energy of the incident light. Finally, layer-by-layer analysis provide detailed access to the surface properties through explicit separation of the contributions coming from different layers.

Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

A previous work [Shen, Ma, Xie, and Zhang, Phys. Rev. Lett. 92, 256603 (2004)] on two-dimensional quantum wells with Rashba type spin-orbit interaction under a strong perpendicular magnetic field is generalized to include the Dresselhaus coupling. The Rashba coupling and the Dresselhaus coupling interplay with the Zeeman effect in opposing ways. The former tends to produce a resonant spin Hall effect at certain magnetic fields while the latter suppresses it. Due to the resonant spin Hall effect, the spin Hall current is highly nonohmic at low temperatures. The condition for the resonant spin Hall conductance in the presence of both Rashba and Dresselhaus couplings is derived using a perturbation method. In the presence of disorder, we argue that the resonant spin Hall conductance occurs when the two Zeeman split extended states near the Fermi level become degenerate due to the Rashba coupling, and that the quantized charge Hall conductance changes by $2{e}^{2}∕h$ instead of ${e}^{2}∕h$ as the magnetic field changes through the resonant field.

Surface solitons due to second order cascaded nonlinearity

In this paper we show theoretically that cascaded surface solitons can exist on the surface of a medium with the bulk inversion symmetry center. Although in the bulk of such media the second order nonlinearity vanishes, χ (2)=0, the optical quadratic nonlinearity appears due to the contribution of spatial derivatives of the fields to the nonlinear response. This nonlinearity is localized at the surface and leads to the cascaded χ (2) surface solitons.

Second-harmonic generation at the interface between Si(100) and thin SiO2 layers

In materials that have bulk inversion symmetry, optical second harmonic generation (SHG) is sensitive to regions where the inversion symmetry is broken, i.e., a surface or interface. We measure SHG from the interface between Si(100) and thin layers of SiO2. Measurements on a series vicinal samples (0°–5° off axis) show that one- and threefold symmetries in the SHG signal increase with increasing off-axis angle. Comparison to x-ray scattering measurements of the interface roughness, for a set of on-axis samples, demonstrates the sensitivity of SHG to interface roughness.

Nonlinear magneto-optical response of s- and d-wave superconductors.

The nonlinear magneto-optical response of $s$- and $d$-wave superconductors is discussed. We carry out the symmetry analysis of the nonlinear magneto-optical susceptibility in the superconducting state. Due to the surface sensitivity of the nonlinear optical response for systems with bulk inversion symmetry, we perform a group theoretical classification of the superconducting order parameter close to a surface. For the first time, the mixing of singlet and triplet pairing states induced by spin-orbit coupling is systematically taken into account. We show that the interference of singlet and triplet pairing states leads to an observable contribution of the nonlinear magneto-optical Kerr effect. This effect is not only sensitive to the anisotropy of the gap function but also to the symmetry itself. In view of the current discussion of the order parameter symmetry of High-T$_c$ superconductors, results for a tetragonal system with bulk singlet pairing for various pairing symmetries are discussed.

Electric field induced second harmonic generation spectroscopy on a metal-oxide-silicon structure

Spectroscopic electric-field-induced second harmonic generation on a Si(111)–SiO2–Cr metal-oxide-silicon structure shows a bias-independent ‘‘interface’’ resonance at 3.25 eV and a ‘‘bulk’’ resonance at 3.43 eV which is strongly bias dependent. The symmetry forbidden bulk dipole contribution becomes observable, and even dominating, due to the bias-induced band-bending that breaks the bulk inversion symmetry. The origin of these resonances is discussed, as well as the prospects for using second harmonic generation as a probe of metal-oxide-silicon characteristics.