Valley Degree Of Freedom Research Articles

Spin-degenerate regimes for single quantum dots in transition metal dichalcogenide monolayers

Strong spin-orbit coupling in transition metal dichalcogenide (TMDC) monolayers results in spin resolvable band structures about the $K$ and $K'$ valleys such that the eigenbasis of a 2D quantum dot (QD) in a TMDC monolayer in zero field is described by the Kramers pairs $|0\rangle_-=|K'\uparrow\rangle$, $|1\rangle_-=|K\downarrow\rangle$ and $|0\rangle_+=|K\uparrow\rangle$, $|1\rangle_+=|K'\downarrow\rangle$. The strong spin-orbit coupling limits the usefulness of single TMDC QDs as spin qubits. Possible regimes of spin-degenerate states, overcoming the spin-orbit coupling in monolayer TMDC QDs are investigated in both zero field, where the spin and valley degrees of freedom become fourfold degenerate, and twofold degeneracy in some magnetic field, localised to a given valley. Such regimes are shown to be achievable in MoS$_{2}$, where the spin orbit coupling is sufficiently low and of the right sign such that the spin resolved conduction bands intersect at points about the $K$ and $K'$ valleys and as such may be exploited by selecting suitable critical dot radii.

Valley-polarized exciton–polaritons in a monolayer semiconductor

Single layers of transition metal dichalcogenides are two-dimensional direct bandgap semiconductors with degenerate, but inequivalent, `valleys' in the electronic structure that can be selectively excited by polarized light. Coherent superpositions of light and matter, exciton-polaritons, have been observed when these materials are strongly coupled to photons, but these hybrid quasiparticles do not harness the valley-sensitive excitations of monolayer transition metal dichalcogenides. Here, we demonstrate evidence for valley polarized exciton-polaritons in monolayers of MoS$_2$ embedded in a dielectric microcavity. Unlike traditional microcavity exciton-polaritons, these light-matter quasiparticles emit polarized light with spectral Rabi splitting. The interplay of cavity-modified exciton dynamics and intervalley relaxation in the high-cooperativity regime causes valley polarized exciton-polaritons to persist to room temperature, distinct from the vanishing polarization in bare monolayers. Achieving polarization-sensitive polaritonic devices operating at room temperature presents a pathway for manipulating novel valley degrees of freedom in coherent states of light and matter.

Microwave Spectroscopy of a Carbon Nanotube Charge Qubit

Carbon nanotube quantum dots allow accurate control of electron charge, spin and valley degrees of freedom in a material which is atomically perfect and can be grown isotopically pure. These properties underlie the unique potential of carbon nanotubes for quantum information processing, but developing nanotube charge, spin, or spin-valley qubits requires efficient readout techniques as well as understanding and extending quantum coherence in these devices. Here, we report on microwave spectroscopy of a carbon nanotube charge qubit in which quantum information is encoded in the spatial position of an electron. We combine radio-frequency reflectometry measurements of the quantum capacitance of the device with microwave manipulation to drive transitions between the qubit states. This approach simplifies charge-state readout and allows us to operate the device at an optimal point where the qubit is first-order insensitive to charge noise. From these measurements, we are able to quantify the degree of charge noise experienced by the qubit and obtain an inhomogeneous charge coherence of 5 ns. We use a chopped microwave signal whose duty-cycle period is varied to measure the decay of the qubit states, yielding a charge relaxation time of 48 ns.

Valley polarized relaxation and upconversion luminescence from Tamm-plasmon trion–polaritons with a MoSe2 monolayer

Transition metal dichalcogenides represent an ideal testbed to study excitonic effects, spin-related phenomena and fundamental light-matter coupling in nanoscopic condensed matter systems. In particular, the valley degree of freedom, which is unique to such direct band gap monolayers with broken inversion symmetry, adds fundamental interest in these materials. Here, we implement a Tamm-plasmon structure with an embedded MoSe2 monolayer and study the formation of polaritonic quasi-particles. Strong coupling conditions between the Tamm-mode and the trion resonance of MoSe2 are established, yielding bright luminescence from the polaritonic ground state under non-resonant optical excitation. We demonstrate, that tailoring the electrodynamic environment of the monolayer results in a significantly increased valley polarization. This enhancement can be related to change in recombination dynamics shown in time-resolved photoluminescence measurements. We furthermore observe strong upconversion luminescence from resonantly excited polariton states in the lower polariton branch. This upconverted polariton luminescence is shown to preserve the valley polarization of the trion–polariton, which paves the way towards combining spin-valley physics and exciton scattering experiments.

Robustly protected carrier spin relaxation in electrostatically doped transition-metal dichalcogenides

Transition-metal dichalcogenides are unique semiconductors because of their exclusive coupling between the spin and the valley degrees of freedom. The spin flip simultaneously requires a large amount of the crystal momentum variation; hence most of the carrier scattering is expected to be the spin-conserving intravalley scattering. Analysis of the quantum interference effects on the magnetoconductivity in ${\mathrm{WSe}}_{2},{\mathrm{MoSe}}_{2}$, and ${\mathrm{MoS}}_{2}$ reveals that the spin-relaxation time is orders of magnitude longer than the carrier momentum scattering time, indicating that the valley-spin coupling robustly protects the spin polarization from carrier scatterings. In addition, the electron-spin-relaxation time of ${\mathrm{MoSe}}_{2}$ is found to be anomalously short compared to other members, which is likely the origin of the ultrafast valley scattering of excitons in ${\mathrm{MoSe}}_{2}$.

Bound state properties of ABC-stacked trilayer graphene quantum dots

The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts (Song et al 2016 Nano Lett. 16 6245), we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a potential exhibits a transition from one group of Landau levels to another group, which can be understood analytically through perturbation theory. Our results provide insight into the transport property of TLG QDs, with possible applications to study of spin qubits and valleytronics in TLG QDs.

Dressed photon-orbital states in a quantum dot: Intervalley spin resonance

The valley degree of freedom is intrinsic to spin qubits in Si/SiGe quantum dots. It has been viewed alternately as a hazard, especially when the lowest valley-orbit splitting is small compared to the thermal energy, or as an asset, most prominently in proposals to use the valley degree of freedom itself as a qubit. Here we present experiments in which microwave electric field driving induces transitions between both valley-orbit and spin states. We show that this system is highly nonlinear and can be understood through the use of dressed photon-orbital states, enabling a unified understanding of the six microwave resonance lines we observe. Some of these resonances are inter-valley spin transitions that arise from a non-adiabatic process in which both the valley and the spin degree of freedom are excited simultaneously. For these transitions, involving a change in valley-orbit state, we find a tenfold increase in sensitivity to electric fields and electrical noise compared to pure spin transitions, strongly reducing the phase coherence when changes in valley-orbit index are incurred. In contrast to this non-adiabatic transition, the pure spin transitions, whether arising from harmonic or subharmonic generation, are shown to be adiabatic in the orbital sector. The non-linearity of the system is most strikingly manifest in the observation of a dynamical anti-crossing between a spin-flip, inter-valley transition and a three-photon transition enabled by the strong nonlinearity we find in this seemly simple system.

Apparent breakdown of Raman selection rule at valley exciton resonances in monolayerMoS2

The valley degree of freedom in atomically thin transition metal dichalcogenides (TMDCs) has generated great interest due to the possibility of using it to store and control information in analogy to the spin degree of freedom in spintronics. A signature of the valley pseudospin is the selective coupling of valley excitons to photons with defined helicity. This selectivity can have important consequences for a variety of optical phenomena associated with the valley excitons. Here we report that Raman features that seemingly violate the Raman selection rules can become prominent at valley exciton resonances in atomically thin $\mathrm{Mo}{\mathrm{S}}_{2}$. Specifically, the Raman selection rule requires the excitation and scattering photons to have opposite circular polarizations for the in-plane $E$\ensuremath{'} mode phonon, but we observe an apparent $E$\ensuremath{'} Raman peak for excitation and scattered photons with the same circular polarization at exciton resonances. We attribute this peak to a defect-assisted process that involves phonons in the transverse optical $E$\ensuremath{'} branch slightly away from the \ensuremath{\Gamma} point, a process that can be enhanced by the selective coupling of valley pseudospin to photon helicity. Thus, the valley pseudospin, in addition to the crystal symmetry, may be important in understanding the Raman scattering spectra for excitations close to valley exciton resonances.

Enhanced spin-flip scattering by surface roughness inWS2andMoS2armchair nanoribbons

The band structures of single-layer MoS$_2$ and WS$_2$ present a coupling between spin and valley degrees of freedom that suppresses spin-flip scattering and spin dephasing. Here we show that out-of-plane deformations, such as corrugations or ripples, enhance spin-flip scattering in armchair MoS$_2$ and WS$_2$ nanoribbons. Spin transport in the presence of surface roughness is systematically investigated, employing the non-equilibrium Green's function method along with the tight-binding approximation. Both transmission and conductance have been calculated as a function of surface roughness. Our results indicate that the spin-flip rate, usually neglected in flat pristine samples, increases significantly with the surface roughness amplitude. These results are important for the design and fabrication of transition metal dichalcogenides based spintronic devices.

Controlling plasmon modes and damping in buckled two-dimensional material open systems

Full ranges of both hybrid plasmon-mode dispersions and their damping are studied systematically by our recently developed mean-field theory in open systems involving a conducting substrate and a two-dimensional (2D) material with a buckled honeycomb lattice, such as silicene, germanene, and a group IV dichalcogenide as well. In this hybrid system, the single plasmon mode for a free-standing 2D layer is split into one acoustic-like and one optical-like mode, leading to a dramatic change in the damping of plasmon modes. In comparison with gapped graphene, critical features associated with plasmon modes and damping in silicene and molybdenum disulfide are found with various spin-orbit and lattice asymmetry energy bandgaps, doping types and levels, and coupling strengths between 2D materials and the conducting substrate. The obtained damping dependence on both spin and valley degrees of freedom is expected to facilitate measuring the open-system dielectric property and the spin-orbit coupling strength of individual 2D materials. The unique linear dispersion of the acoustic-like plasmon mode introduces additional damping from the intraband particle-hole modes, which is absent for a free-standing 2D material layer, and the use of molybdenum disulfide with a large bandgap simultaneously suppresses the strong damping from the interband particle-hole modes.

Temporal and spatial valley dynamics in two-dimensional semiconductors probed via Kerr rotation

Monolayer transition metal dichalcogenides (TMDCs) offer a tantalizing platform for control of both spin and valley degrees of freedom, which may enable future optoelectronic devices with enhanced and novel functionalities. Here, we investigate the valley dynamics of two prototypical members of TMDCs, namely $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$, using time-resolved Kerr rotation (TRKR) at temperatures from 10 K to 300 K. This pump-probe technique enables sub-picosecond temporal resolution, providing insight into ultrafast valley dynamics, which is inaccessible by polarized and time-resolved photoluminescence spectroscopy. Bi-exponential decay dynamics were observed for both materials at low temperatures, and the fast decay component indicated a rapid exciton valley depolarization time $(l10\phantom{\rule{0.16em}{0ex}}\mathrm{ps})$ due to strong Coulomb exchange interactions between the $K$ valleys. However, the slow decay components (several tens of picoseconds) were attributed to different origins in the two materials, which were further elucidated by temperature-dependent TRKR measurements. Moreover, the spatial dependence of the TRKR intensity across $\mathrm{Mo}{\mathrm{S}}_{2}$ monolayer flakes indicated a weaker valley polarization near the edges, which is likely associated with quenched excitons near the grain boundaries or a disordered edge region in chemical vapor deposition--grown monolayers. These temporal and spatial TRKR measurements reveal insight into the complex dynamics of valley excitonic states, which will be critical for valleytronic applications of monolayer TMDCs.

Valleytronics and phase transition in silicene

Magnetic and transport properties of silicene in the presence of perpendicular electromagnetic fields and a ferromagnetic material are studied. It is shown that for small exchange field, the magnetic moment associated with each valley is opposite for the other and it gives a shift in band energy, by a Zeeman-like coupling term. Thus opening a new horizon for valley–orbit coupling. Magnetic proximity effect is seen to adjust the spintronics of each valley. Valley polarization is calculated using the semi classical formulation of electron dynamics. It can be modified and measured due to its contribution in Hall conductivity. Quantum phase transitions are observed in silicene, providing a tool to control the topological state experimentally. The strong dependence of the physical properties on valley degree of freedom is an important step towards valleytronics.

Valley splitting in the transition-metal dichalcogenide monolayer via atom adsorption.

In this letter we study the valley degeneracy splitting of the transition-metal dichalcogenide monolayer by first-principles calculations. The local magnetic moments are introduced into the system when the transition-metal atoms are adsorbed on the monolayer surface. The Zeeman effect arising from the local magnetic moment at transition-metal atom sites lifts the valley degeneracy. Anomalous charge, spin and valley Hall effects can be accessed due to valley splitting when we can only excite carriers of one valley. The valley splitting depends on the direction of magnetization and thus can be tuned continuously by an external magnetic field. This tunable valley splitting offers a practical avenue for exploring device paradigms based on the spin and valley degrees of freedom.

Generation and Evolution of Spin-, Valley-, and Layer-Polarized Excited Carriers in Inversion-Symmetric WSe_{2}.

We report the spin-selective optical excitation of carriers in inversion-symmetric bulk samples of the transition metal dichalcogenide (TMDC) WSe_{2}. Employing time- and angle-resolved photoelectron spectroscopy (trARPES) and complementary time-dependent density functional theory (TDDFT), we observe spin-, valley-, and layer-polarized excited state populations upon excitation with circularly polarized pump pulses, followed by ultrafast (<100 fs) scattering of carriers towards the global minimum of the conduction band. TDDFT reveals the character of the conduction band, into which electrons are initially excited, to be two-dimensional and localized within individual layers, whereas at the minimum of the conduction band, states have a three-dimensional character, facilitating interlayer charge transfer. These results establish the optical control of coupled spin-, valley-, and layer-polarized states in centrosymmetric materials with locally broken symmetries and suggest the suitability of TMDC multilayer and heterostructure materials for valleytronic and spintronic device concepts.

Concepts of ferrovalley material and anomalous valley Hall effect.

Valleytronics rooted in the valley degree of freedom is of both theoretical and technological importance as it offers additional opportunities for information storage, as well as electronic, magnetic and optical switches. In analogy to ferroelectric materials with spontaneous charge polarization, or ferromagnetic materials with spontaneous spin polarization, here we introduce a new member of ferroic family, that is, a ferrovalley material with spontaneous valley polarization. Combining a two-band k·p model with first-principles calculations, we show that 2H-VSe2 monolayer, where the spin–orbit coupling coexists with the intrinsic exchange interaction of transition-metal d electrons, is such a room-temperature ferrovalley material. We further predict that such system could demonstrate many distinctive properties, for example, chirality-dependent optical band gap and, more interestingly, anomalous valley Hall effect. On account of the latter, functional devices based on ferrovalley materials, such as valley-based nonvolatile random access memory and valley filter, are contemplated for valleytronic applications.

Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers.

The direct gap interband transitions in transition metal dichalcogenide monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the K^{+} or K^{-} valley in momentum space are induced. Linearly polarized laser excitation prepares a coherent superposition of valley states. Here, we demonstrate the control of the exciton valley coherence in monolayer WSe_{2} by tuning the applied magnetic field perpendicular to the monolayer plane. We show rotation of this coherent superposition of valley states by angles as large as 30° in applied fields up to 9T. This exciton valley coherence control on the ps time scale could be an important step towards complete control of qubits based on the valley degree of freedom.

Stark control

By exploiting the optical Stark effect, the valley degree of freedom in monolayer transition metal dichalcogenides can be selectively manipulated and detected using all-optical methods.

Valley Polarization by Spin Injection in a Light-Emitting van der Waals Heterojunction.

The band structure of transition metal dichalcogenides (TMDCs) with valence band edges at different locations in the momentum space could be harnessed to build devices that operate relying on the valley degree of freedom. To realize such valleytronic devices, it is necessary to control and manipulate the charge density in these valleys, resulting in valley polarization. While this has been demonstrated using optical excitation, generation of valley polarization in electronic devices without optical excitation remains difficult. Here, we demonstrate spin injection from a ferromagnetic electrode into a heterojunction based on monolayers of WSe2 and MoS2 and lateral transport of spin-polarized holes within the WSe2 layer. The resulting valley polarization leads to circularly polarized light emission that can be tuned using an external magnetic field. This demonstration of spin injection and magnetoelectronic control over valley polarization provides a new opportunity for realizing combined spin and valleytronic devices based on spin-valley locking in semiconducting TMDCs.

Spin-polarized valley Hall effect in ultrathin silicon nanomembrane via interlayer antiferromagnetic coupling

Fundamental understanding of two-dimensional materials has spurred a surge in the search for topological quantum phase associated with the valley degree of freedom (VDOF). We discuss a spin-polarized version to the VDOF in which spin degeneracy is broken by the antiferromagnetic exchange coupling (LAFM) between opposite layers of the quasi-two-dimensional silicon nanomembrane (SiNM). Based on first principles calculations, we found that the LAFM state in SiNM can lead to metal–insulator transition (MIT). The broken degeneracy of spin degree of freedom in this insulating state of ultrathin SiNM may differ for different valleys, so that the SiNM can be exploited to produce the spatially separated spin and valley currents. We propose that the tunable spin-polarized valley photocurrents can be generated in an experimentally feasible ellipsometry setup. Our work shows promise for the development of spintronic and valleytronic devices compatible with current silicon industry.

Spin- and valley-polarized transport in a monolayer ofMoS2

We investigate dc and ac transport in a monolayer of ${\mathrm{MoS}}_{2}$ in the presence of an effective mass asymmetry, a momentum-dependent term, and an out-of plane or in-plane Zeeman term. Analytical results are presented for both dc and ac conductivities in the framework of linear response theory. We show that the spin-Hall conductivity exhibits a strong dependence on the strength of the spin-orbit interaction while both spin- and valley-Hall conductivities show a very weak dependence on the temperature. The sum of the well separated spin-up and spin-down components of the diffusive dc longitudinal conductivity is linear in the electron concentration though the Fermi level is a nonmonotonic function of it. Further, we evaluate the power absorption spectrum and assess its dependence on the spin and valley degrees of freedom as well as on the scattering which is essential at low frequencies.