Valley Splitting Research Articles

Large and controllable spin-valley splitting in two-dimensional WS2/h−VN heterostructure

Inspired by the profound physical connotations and potential application prospects of the valleytronics, we design a two-dimensional (2D) WS2/h-VN magnetic van der Waals (vdW) heterostructure and study the control of valley degree of freedom through the first-principles calculations. A considerable spin splitting of 627 meV is obtained at the K valley, accompanied with a strong suppression of that at the K' valley. An intrinsic large valley splitting of 376 meV is generated in the valence band, which corresponds to an effective Zeeman magnetic field of 2703 T. Besides of the valence band, the conduction band of WS2 possesses a remarkable spin splitting also, and valley labelled dark exciton states are present at the K' valley. The strengths of spin and valley splitting relied on the interfacial orbital hybridization are further tuned continually by the in-plane strain and interlayer spacing. Maximum spin and valley splitting of 654 and 412 meV are finally achieved, respectively, and the effective Zeeman magnetic field can be enhanced to 2989T with a -3 % strain. Time-reversal symmetry breaking and the sizable Berry curvature in the heterostructure lead to a prominent anomalous Hall conductivity at the K and K' valleys. Based on these finding, a prototype filter device for both the valley and spin is proposed.

Few-electrode design for silicon MOS quantum dots

Silicon metal-oxide-semiconductor (MOS) spin qubits have become a promising platform for quantum information processing, with recent demonstrations of high-fidelity single and two-qubit gates. To move beyond a few qubits, however, more scalable designs that reduce the fabrication complexity and electrode density are needed. Here, we introduce a two-metal-layer MOS quantum dot device in which tunnel barriers are naturally formed by gaps between electrodes and controlled by adjacent accumulation gates. The accumulation gates define the electron reservoirs and provide tunability of the tunnel rate of nearly 8.5 decades V−1, determined by a combination of charge sensor electron counting measurements and by direct transport. The valley splitting in the few-electron regime is probed by magneto-spectroscopy up to a field of 6 T, providing an estimate for the ground-state gap of 290 μeV. We show preliminary characterization of a double quantum dot, demonstrating that this design can be extended to linear dot arrays that should be useful in applications like electron shuttling. These results motivate further innovations in MOS quantum dot design that can improve the scalability prospects for spin qubits.

Materials selection rules for optimum power factor in two-dimensional thermoelectrics

Two-dimensional (2D) materials have emerged as the ideal candidates for many applications, including nanoelectronics, low-power devices, and sensors. Several 2D materials have been shown to possess large Seebeck coefficients, thus making them suitable for thermoelectric (TE) energy conversion. Whether even higher TE power factors can be discovered among the ≈2000 possible 2D materials (Mounet et al 2018 Nat. Nanotechnol. 13 246–52) is an open question. This study aims at formulating selection rules to guide the search for superior 2D TE materials without the need for expensive atomistic simulations. We show that a 2D material having a combination of low effective mass, higher separation in the height of the step-like density of states, and valley splitting, which is the energy difference between the bottom of conduction band and the satellite valley, equal to 5 kBT will lead to a higher TE power factor. Further, we find that inelastic scattering with optical phonons plays a significant role: if inelastic scattering is the dominant mechanism and the energy of the optical phonon equals 5 kBT, then the TE power factor is maximized. Starting from a model for carrier transport in MoS2 and progressively introducing the aforementioned features results in a two-orders-of-magnitude improvement in the power factor. Compared to the existing selection rules or material descriptors, features identified in this study provide the ability to comprehensively evaluate TE capability of a material and helps in identifying future TE materials suitable for applications in waste-heat scavenging, thermal sensors, and nanoelectronics cooling.

SOI MOS Technology for Spin Qubits

We fabricated Si Quantum Dot (QD) devices using relatively minor adaptations of a standard SOI CMOS process flow. We demonstrated that the spin of confined charges could be controlled via a local electrical-field excitation, owing in the caseof electrons to a geometrically-enabled tuning of the valley splitting and inter-valley spin-orbit coupling. We discuss improvement paths such as extending the spin coherence time by using epi-layers of nuclear-spin-free 28Si (99.992%) as a device template, and developing novel 3D architectures compatible with topological quantum error correction schemes.

Giant valley splitting in monolayer WS2 by magnetic proximity effect

Lifting the valley degeneracy of monolayer transition metal dichalcogenides (TMDs) would allow versatile control of the valley degree of freedom. We report a giant valley exciton splitting of 16 meV/T for monolayer WS2, using the proximity effect from an EuS substrate, which is enhanced by nearly two orders of magnitude from that obtained by an external magnetic field. More interestingly, a sign reversal of the valley splitting is observed as compared to that of WSe2 on EuS. Using first principles calculations, we investigate the complex behavior of exchange interactions between TMDs and EuS. The sign reversal is attributed to competing ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions for Eu- and S- terminated EuS surface sites. They act differently on the conduction and valence bands of WS2 compared to WSe2. Tuning the sign and magnitude of the valley exciton splitting offers opportunities for control of valley pseudospin for quantum information processing.

Magnetic brightening, large valley Zeeman splitting, and dynamics of long-lived A and B dark excitonic states in monolayer WS2

We theoretically investigate the magnetic brightening, valley Zeeman splitting, and valley dynamics of long-lived A and B dark excitons (A-DEs and B-DEs) in monolayer ${\mathrm{WS}}_{2}$, subjected to tilted magnetic fields. Biexciton states and indirect intervalley excitons, with the latter composed of a hole in the $K$ valley and an electron in the $\mathrm{\ensuremath{\Lambda}}$ valley, are also taken into account. We reveal that both in-plane and out-of-plane field components greatly affect the magnetic brightening process due to correlations among different excitonic quasiparticles but in distinct roles. Specifically, the in-plane component primarily enables the dark-state brightening, while the perpendicular one not only modifies the bright-dark splitting inside a given valley, but also lifts the valley degeneracy of either bright or dark excitonic states. Moreover, in the presence of a tilted magnetic field with a nonzero in-plane component, we observe that both A-DEs and B-DEs can be brightened, with the latter requiring a much stronger field for a certain intensity of light emission. Remarkably, we find that the valley splitting of A-DEs is around twice as large as that of A bright excitons but vanishes for B-DEs, as a result of the combined effect of the spin and orbital magnetic moments on the energy shifts of the two valleys. In addition, as the tilt angle of the field with respect to the normal direction of ${\mathrm{WS}}_{2}$ sheet increases from ${0}^{\ensuremath{\circ}}$ to ${180}^{\ensuremath{\circ}}$, the bright-dark splittings for A and B excitons exhibit an opposite behavior, but both feature an ``X''-like pattern when the field is oriented in-plane. Finally, it is observed that the temperature greatly affects the light emission of bright and brightened dark states, while the corresponding temperature dependence is distinct for A and B excitons.

Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy.

Circular-polarization-resolved magneto-infrared studies of multilayer epitaxial graphene (MEG) are performed using tunable quantum cascade lasers in high magnetic fields up to 17.5 T. Landau level (LL) transitions in the monolayer and bilayer graphene inclusions of MEG are resolved, and considerable electron-hole asymmetry is observed in the extracted electronic band structure. For monolayer graphene, a four-fold splitting of the n = 0 to n = 1 LL transition is evidenced and attributed to the lifting of the valley and spin degeneracy of the zeroth LL and the broken electron-hole symmetry. The magnetic field dependence of the splitting further reveals its possible mechanisms. The best fit to experimental data yields effective g-factors, gVS* = 6.7 and gZS* = 4.8, for the valley and Zeeman splittings, respectively.

Scanning tunneling microscope study of quantum Hall isospin ferromagnetic states in the zero Landau level in a graphene monolayer

A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the relativistic zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor v = 0 of charge-neutral graphene, have been extensively explored in experiment. To date, identification of these high-field broken-symmetry states has mostly relied on macroscopic transport techniques. Here, we study splitting of the zero LL of graphene at partial filling and demonstrate a direct approach by imaging the QHIFM states at atomic scale with a scanning tunneling microscope. At half filling of the zero LL (v = 0), the system is in a spin unpolarized state and we observe a linear magnetic-field-scaling of valley splitting. Simultaneously, the spin degeneracy in the two valleys is also lifted by the magnetic fields. When the Fermi level lies inside the spin-polarized states (at v = 1 or -1), the spin splitting is dramatically enhanced because of the strong many-body effects. At v = 0, we direct image the wavefunctions of the QHIFM states at atomic scale and observe an interaction-driven density wave featuring a Kekule distortion, which is responsible for the large gap at charge neutrality point in high magnetic fields.

Exotic impurity-induced states in single-layer h -BN: The role of sublattice structure and intervalley interactions

By using a combination of density functional theory, tight-binding, and effective mass calculations, we explore the electronic properties of donor and acceptor states of substitutional impurities in single-layer $h$-BN. We find that the impurity level structure inside the electronic gap is quite exotic, as it strongly depends on the sublattice position of the impurity and its behavior as a donor or an acceptor. For instance, when an acceptor atom replaces a nitrogen atom, the intervalley interaction induced by the impurity potential is found to be strong and the resulting level structure consists only of nondegenerate levels with strong valley and spin splitting. On the other hand, when an acceptor replaces a boron atom, the intervalley interaction is much weaker and near-valley-degenerate levels are found. Donor impurities behave in a similar fashion. The differences between these two types of level structures can be traced to the peculiar sublattice-resolved electronic structure of pristine $h$-BN, in which the valence and conduction wave functions at the $K$ and ${K}^{\ensuremath{'}}$ points are composed only of nitrogen and boron ${p}_{z}$ orbitals, respectively, and to the dependence of the intervalley interaction on them. We predict that this impurity level structure must also be present in other two-dimensional semiconductors and insulators with similar sublattice-resolved electronic states, such as other hexagonal III-V binary compounds and, consequently, offer the possibility of engineering the optical properties of these materials for potential applications in future devices.

Bandstructure Effects in the Electronic Transport of Silicon Nanowire in [100] and [110] Transport Orientations

An electronic transport study about band structure effects of silicon nanowire (Si-NW) in [100] and [110] transport orientations has been done. A dispersion calculation has also been done for a sp3d5s* hybridized atomistic model along with a Poisson solver. A ballistic model has been used for the evaluation of I-V characteristics. For [100] and [110] transport-oriented nanowires, the total gate capacitance was decreased by 30%. The carrier velocity was affected by both [100] and [110] transport-oriented nanowires. The velocities depend on degeneracy and effective mass of the dispersion. In our study, we have used 3nm thick nanowire oriented in [100] and [110] directions. The [100] oriented nanowire gives better ON-current performance as compared to [110] oriented nanowire. We have studied the valley splitting effects which can lift the degeneracies of 3nm wires. The effective mass which changes with various transport orientations and quantization, was increased with quantization for [100] while it was decreased for [110] transport orientated nanowire.

Spin-Blockade Spectroscopy of Si / Si - Ge Quantum Dots

We implement a technique for measuring the singlet-triplet energy splitting responsible for spin-to-charge conversion in semiconductor quantum dots. This method, which requires fast, single-shot charge measurement, reliably extracts an energy in the limits of both large and small splittings. We perform this technique on an undoped, accumulation-mode Si/SiGe triple-quantum dot and find that the measured splitting varies smoothly as a function of confinement gate biases. Not only does this demonstration prove the value of having an $in~situ$ excited-state measurement technique as part of a standard tune-up procedure, it also suggests that in typical Si/SiGe quantum dot devices, spin-blockade can be limited by lateral orbital excitation energy rather than valley splitting.

Controlling valley splitting and polarization of dark- and bi-excitons in monolayer WS2 by a tilted magnetic field

We developed a comprehensive theoretical framework focusing on many-body effects of exciton species in monolayer WS2, including bright and dark excitons, and intra- and inter-valley biexcitons, to investigate valley dynamics in monolayer WS2 subjected to a tilted magnetic field . In particular, the evolution of the exciton population densities and the many-body particle scatterings are considered to calculate the valley polarization () as a function of the magnetic field. We found valley splittings for the dark exciton and biexciton energy levels that are larger than those of bright excitons, of −0.23 meV T−1. For example, −0.46 meV T−1 for dark excitons and −0.69 meV T−1 for bright-dark intra-valley biexcitons. Furthermore, inter-valley bright-dark excitons have an opposite valley energy splittings of +0.23 meV T−1. For the samples pumped by linearly polarized light, exhibits distinct magnetic field dependence for different types of many-body particle states. Among them, the of the intra-valley bright-dark biexcitons increases with increasing magnetic field and reaches nearly 50% at B = 65 T. The brightened dark exciton, on the other hand, exhibits vanishing , indicating long valley relaxation time. Remarkably, the inter-valley bright-dark biexciton shows unconventional behavior with an inverted . The opposite for intra- and inter-valley bright-dark biexcitons, coupled with their large valley splitting and long valley lifetime may facilitate their coherent manipulation for quantum computing.

Quantum Transport Properties of Industrial Si28/SiO228

We investigate the structural and quantum transport properties of isotopically enriched $^{28}$Si/$^{28}$SiO$_2$ stacks deposited on 300 mm Si wafers in an industrial CMOS fab. Highly uniform films are obtained with an isotopic purity greater than 99.92\%. Hall-bar transistors with an equivalent oxide thickness of 17 nm are fabricated in an academic cleanroom. A critical density for conduction of $1.75\times10^{11}$ cm$^{-2}$ and a peak mobility of 9800 cm$^2$/Vs are measured at a temperature of 1.7 K. The $^{28}$Si/$^{28}$SiO$_2$ interface is characterized by a roughness of $\Delta=0.4$ nm and a correlation length of $\Lambda=3.4$ nm. An upper bound for valley splitting energy of 480 $\mu$eV is estimated at an effective electric field of 9.5 MV/m. These results support the use of wafer-scale $^{28}$Si/$^{28}$SiO$_2$ as a promising material platform to manufacture industrial spin qubits.

Valley optomechanics in a monolayer semiconductor

Interfacing nanomechanics with photonics and charge/spin-based electronics has transformed information technology and facilitated fundamental searches for the quantum-to-classical transition1–3. Utilizing the electron valley degree of freedom as an information carrier, valleytronics has recently emerged as a promising platform for developments in computation and communication4–7. Thus far, explorations of valleytronics have focused on optoelectronic and magnetic means8–16. Here, we realize valley–mechanical coupling in a resonator made of the monolayer semiconductor MoS2 and transduce valley information into mechanical states. The coupling is achieved by exploiting the magnetic moment of valley carriers with a magnetic field gradient. We optically populate the valleys and observe the resulting mechanical actuation using laser interferometry. We are thus able to control the valley–mechanical interaction by adjusting the pump-laser light, the magnetic field gradient and temperature. Our work paves the way for realizing valley-actuated devices and hybrid valley quantum systems. Transduction of valley information to mechanical states in a monolayer MoS2 resonator can be realized by optically pumping the valley carriers and applying an out-of-plane magnetic field gradient to induce a displacement-dependent valley splitting.

Shape effect on the valley splitting in lead selenide nanowires

We study the cross-section shape and size effects on the valley splitting in PbSe nanowires within the framework of empirical $s{p}^{3}{d}^{5}{s}^{*}$ tight-binding method. We consider idealized prismatic nanowires, grown along [110], with the cross-section shape varying from rectangular (terminated by ${001}$ and ${110}$ facets) to rhombic (terminated mostly by ${111}$ facets). The valley splitting energies have the maximal value (up to hundreds of meV) in rectangular nanowires, while in rhombic ones they are almost absent. The shape dependence is shown to be similar in nanowires with different point symmetry in a wide range of cross-section sizes.

Enhanced Valley Splitting of Transition-Metal Dichalcogenide by Vacancies in Robust Ferromagnetic Insulating Chromium Trihalides.

Recently, single-layer CrI3, a member of the chromium trihalides CrX3 (where X = Cl, Br, or I), has been exfoliated and experimentally demonstrated as an atomically thin material suitable for two-dimensional spintronics. Valley splitting due to the magnetic proximity effect has been demonstrated in a WSe2/CrI3 van der Waals heterojunction. However, the understanding of the mechanisms behind the favorable performance of CrI3 is still limited. Here, we systematically study the carrier mobility and the intrinsic point defects in CrX3 and assess their influence on valley splitting in WSe2/CrI3 by first-principles calculations. The flat-band nature induces extremely large carrier mass and ultralow carrier mobility. In addition, intrinsic point defects-localized states in the middle of the band gap-show deep transition energy levels and act as carrier recombination centers, further lowering the carrier mobility. Moreover, vacancies in CrI3 can enhance ferromagnetism and valley splitting in a WSe2/CrI3 heterojunction, proving that chromium trihalides are excellent ferromagnetic insulators for spintronic and valleytronic applications.

High-Magnetic-Field Tunneling Spectra of ABC-Stacked Trilayer Graphene on Graphite.

ABC-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the ABC-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields.

Valley aspect of lateral tunneling transport

We theoretically study the valley aspect of lateral tunneling transport in valleytronic materials, using AB-stacked (Bernal-stacked) bilayer graphene as a material example. A lateral structure with multiple well/barrier interfaces is considered. A full-zone tight-binding method is employed, allowing for the study of intervalley mixing in electron states. We study the degree of tunneling current valley contrast under the condition of a source-drain bias or barrier asymmetry. For a single-barrier structure, it is found that the intervalley mixing is negligible, and the contrast is positively correlated with the barrier width and height. For a double-barrier structure, the effect of resonant tunneling is investigated. The intervalley mixing is shown to be significantly enhanced at resonant tunneling. In addition, the resonant levels are found valley split, and a proposal is given which exploits the splitting for the generation of a sizable tunneling current valley polarization. Based on a simple model using momentum-shifted thermal distribution for obliquely incident electrons, the temperature dependence of tunneling current valley polarization is also examined. An interesting crossover from the valley-orbit interaction-dominant polarization to the warping-dominant polarization is found to occur as the temperature is increased.

Valley splitting in the van der Waals heterostructure WSe2/CrI3 : The role of atom superposition

A recent experiment shows that the ${K}^{\ensuremath{'}}K$ valley degeneracy can be lifted in monolayer ${\mathrm{WSe}}_{2}$ deposited on a layered ferromagnetic substrate of ${\mathrm{CrI}}_{3}$. In this work, we take a van der Waals heterostructure ${\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$ to model the monolayer ${\mathrm{WSe}}_{2}$ on the ${\mathrm{CrI}}_{3}$ substrate and investigate the effects underpinning the ${K}^{\ensuremath{'}}K$ valley splitting based on first-principles calculations. We demonstrate that the interfacial atom superposition plays an important role and a W-Cr superposition is essential for a relatively large valley splitting. The results indicate inevitable sample-to-sample variations in the ${K}^{\ensuremath{'}}K$ valley splitting in the ${\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$. Furthermore, we show that the ${K}^{\ensuremath{'}}K$ valley splitting can be tuned in the trilayer ${\mathrm{CrI}}_{3}/{\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$ from nearly zero to more than two times of that in the bilayer ${\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$ by manipulating the layer alignment.

Valley-dependent Lorentz force and Aharonov-Bohm phase in strained graphene p−n junction

Veselago lens focusing in graphene p-n junction is promising for realizations of new generation electron optics devices. However, the effect of the strain-induced Aharonov-Bohm interference in a p-n junction has not been discussed before. We provide an experimentally feasible setup based on the Veselago lens in which the presence of strain can result in both the valley-dependent Lorentz force and Aharonov-Bohm interference. In particular, by employing the Green's function and tight binding methods, we study the strain induced by dislocations and line defects in a p-n junction and show how the resulting Aharonov-Bohm phase and interference can be detected. Furthermore, for a different strain configuration, e.g. corresponding to corrugated graphene, we find strong signatures of valley splitting induced by the fictitious magnetic field. Our proposal can be useful for mapping elastic deformations and defects, and for studying valley dependent effects in graphene.