Valley Degree Of Freedom Research Articles

Robust effective Zeeman energy in monolayer MoS2 quantum dots

We report a theoretical investigation on the energy spectrum and the effective Zeeman energy (EZE) in monolayer MoS2 circular quantum dots, subjected to an out-of-plane magnetic field. Interestingly, we observe the emergence of energy-locked modes, depending on the competition between the dot confinement and the applied magnetic field, for either the highest K-valley valence band or the lowest -valley conduction band. Moreover, an unusual dot-size-independent EZE behavior of the highest valence and the lowest conduction bands is found. Although the EZEs are insensitive to the variation of quantum confinement, both of them grow linearly with the magnetic field, similar to that in the monolayer MoS2 material. The EZEs along with their ‘robustness’ against dot confinements open opportunities of a universal magnetic control over the valley degree of freedom, for quantum dots of all sizes.

Magneto-optical transport properties of monolayerWSe2

The recent experimental realization of a high quality WSe$% _{2} $ leads to the possibility of magneto-optical measurements and the manipulation of the spin and valley degrees of freedom. We study the influence of the very strong spin-orbit coupling and of the anisotropic lifting of the valley pseudospin degeneracy on its magnetotransport properties. The energy spectrum of WSe$_{2} $ is derived and discussed in the presence of a perpendicular magnetic field $B$. Correspondingly we evaluate the magneto-optical Hall conductivity and the optical longitudinal conductivity as functions of the frequency, magnetic field, and Fermi energy. They are strongly influenced by the field $B$ and the strong spin splitting. The former exhibits valley polarization and the latter beatings of oscillations. The magneto-optical responses can be tuned in two different regimes: the mictrowave-to-terahertz regime and the visible-frequency one. The absorption peaks involving the $n=0$ LL appear in between these two regimes and show a magnetic control of the spin and valley splittings. We also evaluate the power absorption spectrum.

Making sense of transport in WSe2

Physics Among materials that have a structure similar to that of graphene, but without a band gap, transition-metal dichalcogenides—such as MoS2 and WSe2—are the most prominent examples. Much of what we know about their electronic properties has come from optical measurements; the more traditional transport experiments have proven trickier. Fallahazad et al. studied the behavior of electrons in monolayers and bilayers of WSe2 subjected to an external magnetic field. As they tuned the field, the researchers observed characteristic oscillations in the transport properties. Analyses of these oscillations suggested that the electrons' spin and valley degrees of freedom were tightly coupled at lower fields, and only uncoupled at the highest applied fields of about 30 T. Phys. Rev. Lett. 116 , 086601 (2016).

Electrical generation and control of the valley carriers in a monolayer transition metal dichalcogenide.

Electrically controlling the flow of charge carriers is the foundation of modern electronics. By accessing the extra spin degree of freedom (DOF) in electronics, spintronics allows for information processes such as magnetoresistive random-access memory. Recently, atomic membranes of transition metal dichalcogenides (TMDCs) were found to support unequal and distinguishable carrier distribution in different crystal momentum valleys. This valley polarization of carriers enables a new DOF for information processing. A variety of valleytronic devices such as valley filters and valves have been proposed, and optical valley excitation has been observed. However, to realize its potential in electronics it is necessary to electrically control the valley DOF, which has so far remained a significant challenge. Here, we experimentally demonstrate the electrical generation and control of valley polarization. This is achieved through spin injection via a diluted ferromagnetic semiconductor and measured through the helicity of the electroluminescence due to the spin-valley locking in TMDC monolayers. We also report a new scheme of electronic devices that combine both the spin and valley DOFs. Such direct electrical generation and control of valley carriers opens up new dimensions in utilizing both the spin and valley DOFs for next-generation electronics and computing.

(Invited) Spin-Valley Coupling in Monolayer Transition Metal Dichalcogenides

The monolayers of group VI transition metal dichalcogenides feature a valence band spin splitting with opposite sign in the two valleys located at corners of 1st Brillouin zone. This spin-valley coupling, particularly pronounced in tungsten dichalcogenides, can benefit potential spintronics and valleytronics with the important consequences of spin-valley interplay and the suppression of spin and valley relaxations. In this talk we discuss the spin-valley coupling in monolayers and multilayers WS2. We explored the interplay of spin and valley degrees of freedom with photocurrent experiments. We experimentally demonstrate that this giant spin-valley coupling, together with the valley dependent physical properties, may lead to rich possibilities for manipulating spin and valley degrees of freedom in these atomically thin 2D materials.

High circular polarization in electroluminescence from MoSe2

The coupling between the valley degree of freedom and the optical helicity is one of the unique phenomena in transition metal dichalcogenides. The significant valley polarization evaluated from circularly polarized photoluminescence (PL) has been reported in many transition metal dichalcogenides, except in MoSe2. This compound is an anomalous material showing ultra-fast relaxation of the valley polarized states, which causes negligible polarization in the PL. Meanwhile, circularly polarized electroluminescence (EL) has been recently reported in a WSe2 light-emitting transistor, providing another method for using the valley degree of freedom. Here, we report the EL properties of MoSe2, demonstrating electrical switching of the optical helicity. Importantly, we observed high circular polarization reaching 66%. The results imply that the dominant mechanism of circularly polarized EL is robust against intervalley scattering, in marked contrast to the PL.

Robust room temperature valley polarization in monolayer and bilayer WS2.

We report robust room temperature valley polarization in chemical-vapor-deposition (CVD) grown monolayer and bilayer WS2via polarization-resolved photoluminescence measurements using excitation below the bandgap. We show that excitation with energy slightly below the bandgap of the multi-valleyed transition metal chalcogenides can effectively suppress the random redistribution of excited electrons and, thereby, greatly enhance the efficiency of valley polarization at room temperature. Compared to mechanically exfoliated WS2, our CVD grown WS2 films also show enhancement in the coupling of spin, layer and valley degree of freedom and, therefore, provide improved valley polarization. At room temperature, using below-bandgap excitation and CVD grown monolayer and bilayer WS2, we have reached a record-high valley polarization of 35% and 80%, respectively, exceeding the previously reported values of 10% and 65% for mechanically exfoliated WS2 layers using resonant excitation. This observation provides a new direction to enhance valley control at room temperature.

Excitation gap of fractal quantum hall states in graphene

In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter’s butterfly. In this work, we develop a Hartree–Fock theory to deal with the electron-electron interaction in the Hofstadter’s butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.

Spectroscopic Signatures of AA' and AB Stacking of Chemical Vapor Deposited Bilayer MoS2.

Prominent resonance Raman and photoluminescence spectroscopic differences between AA' and AB stacked bilayer molybdenum disulfide (MoS2) grown by chemical vapor deposition are reported. Bilayer MoS2 islands consisting of the two stacking orders were obtained under identical growth conditions. Resonance Raman and photoluminescence spectra of AA' and AB stacked bilayer MoS2 were obtained on Au nanopyramid surfaces under strong plasmon resonance. Both resonance Raman and photoluminescence spectra show distinct features indicating clear differences in interlayer interaction between these two phases. The implication of these findings on device applications based on spin and valley degrees of freedom will be discussed.

Ising pairing in superconducting NbSe2 atomic layers

Two-dimensional transition metal dichalcogenides with strong spin-orbit interactions and valley-dependent Berry curvature effects have attracted tremendous recent interests. Although novel single-particle and excitonic phenomena related to spin-valley coupling have been extensively studied, effects of spin-momentum locking on collective quantum phenomena remain unexplored. Here we report an observation of superconducting monolayer NbSe$_2$ with an in-plane upper critical field over six times of the Pauli paramagnetic limit by magneto-transport measurements. The effect can be understood in terms of the competing Zeeman effect and large intrinsic spin-orbit interactions in non-centrosymmetric NbSe$_2$ monolayers, where the electronic spin is locked to the out-of-plane direction. Our results provide a strong evidence of unconventional Ising pairing protected by spin-momentum locking and open up a new avenue for studies of non-centrosymmetric superconductivity with unique spin and valley degrees of freedom in the exact two-dimensional limit.

Charge Number Dependence of the Dephasing Rates of a Graphene Double Quantum Dot in a Circuit QED Architecture

We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this fourfold periodicity in dephasing rates is an open problem, our observations hint at the fourfold degeneracy expected in graphene from its spin and valley degrees of freedom.

Spin- and valley-coupled electronic states in monolayer WSe2 on bilayer graphene

We have fabricated a high-quality monolayer WSe2 film on bilayer graphene by epitaxial growth and revealed the electronic states by spin- and angle-resolved photoemission spectroscopy. We observed a direct energy gap at the Brillouin-zone corner in contrast to the indirect nature of gap in bulk WSe2, which is attributed to the lack of interlayer interaction and the breaking of space-inversion symmetry in monolayer film. A giant spin splitting of ∼0.5 eV, which is the largest among known monolayer transition-metal dichalcogenides, is observed in the energy band around the zone corner. The present results suggest a high potential applicability of WSe2 to develop advanced devices based with the coupling of spin- and valley-degrees of freedom.

Valley entanglement of excitons in monolayers of transition-metal dichalcogenides

We show that excitons and free carriers in K and K' valleys of transition metal dichalcogenide monolayers can be entangled with respect to their valley degree of freedom by absorbing linearly polarized single photons. This effect does not require any interaction between K and K' excitons in contrast to conventional mechanisms of entanglement that are mediated by coupling between quantum systems (e.g.~entanglement of photons in nonlinear optical interactions). The valley entanglement of excitons and free carriers can be verified by measuring the polarization of their photoluminescence or fluctuations of the photocurrent under an applied in-plane DC bias.

Long-lived nanosecond spin relaxation and spin coherence of electrons in monolayer MoS2 and WS2

A range of semiconductors can host both spin and valley polarizations. Optical experiments on single layers of transition metal dichalcogenides now show that inter-valley scattering can accelerate spin relaxation. The recently discovered monolayer transition metal dichalcogenides (TMDCs) provide a fertile playground to explore new coupled spin–valley physics1,2,3. Although robust spin and valley degrees of freedom are inferred from polarized photoluminescence (PL) experiments4,5,6,7,8, PL timescales are necessarily constrained by short-lived (3–100 ps) electron–hole recombination9,10. Direct probes of spin/valley polarization dynamics of resident carriers in electron (or hole)-doped TMDCs, which may persist long after recombination ceases, are at an early stage11,12,13. Here we directly measure the coupled spin–valley dynamics in electron-doped MoS2 and WS2 monolayers using optical Kerr spectroscopy, and reveal very long electron spin lifetimes, exceeding 3 ns at 5 K (two to three orders of magnitude longer than typical exciton recombination times). In contrast with conventional III–V or II–VI semiconductors, spin relaxation accelerates rapidly in small transverse magnetic fields. Supported by a model of coupled spin–valley dynamics, these results indicate a novel mechanism of itinerant electron spin dephasing in the rapidly fluctuating internal spin–orbit field in TMDCs, driven by fast inter-valley scattering. Additionally, a long-lived spin coherence is observed at lower energies, commensurate with localized states. These studies provide insight into the physics underpinning spin and valley dynamics of resident electrons in atomically thin TMDCs.

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.

Chiral properties of topological-state loops

The angular momentum quantization of chiral gapless modes confined to a circularly shaped interface between two different topological phases is investigated. By examining several different setups, we show analytically that the angular momentum of the topological modes exhibits a highly chiral behavior, and can be coupled to spin and/or valley degrees of freedom, reflecting the nature of the interface states. A simple general one-dimensional model, valid for arbitrarily shaped loops, is shown to predict the corresponding energies and the magnetic moments. These loops can be viewed as building blocks for artificial magnets with tunable and highly diverse properties.

ChemInform Abstract: Electronic Structures and Theoretical Modelling of Two‐Dimensional Group‐VIB Transition Metal Dichalcogenides

AbstractReview: 215 refs.

Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States.

We report transport measurements on a quantum dot in a partly suspended carbon nanotube. Electrostatic tuning allows us to modify and even switch "on" and "off" the coupling to the quantized stretching vibration across several charge states. The magnetic-field dependence indicates that only the two-electron spin-triplet excited state couples to the mechanical motion, indicating mechanical coupling to both the valley degree of freedom and the exchange interaction, in contrast to standard models.

Spontaneous layer polarization and conducting domain walls in the quantum Hall regime of bilayer graphene

Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor $\nu=2$, domain walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

Collective modes in a Dirac insulator with short range interactions

We study a Haldane model with nearest neighbor interactions. We find one-dimensional like collective modes arising due to the interplay of pseudo-spin and valley degrees of freedom. In the large band gap or moderate interaction limit, these excitations are low energy modes lying in the band gap. The dispersion relations are qualitatively different in trivial insulator phase and Chern insulator phase, thus can be used to identify the topology of the Haldane model with the bulk property. We also discuss how to detect these modes in cold atom systems. An abelian gauge theory will emerge when a physical current-current interaction is introduced to the Haldane model or the Kane-Mele model.