Valley Mixing Research Articles

Absence of edge states in the valley Chern insulator in moiré graphene

We study the edge spectrum of twisted sheets of single layer and bilayer graphene in cases where the continuum model predicts a valley Chern insulator -- an insulating state in which the occupied moir\'e mini-bands from each valley have a net Chern number, but both valleys together have no net Chern number, as required by time reversal symmetry. In a simple picture, such a state might be expected to have chiral valley polarized counter-propagating edge states. We present results from exact diagonalization of the tight-binding model of commensurate structures in the ribbon geometry. We find that for both the single-layer and bilayer moir\'e ribbons robust edge modes are generically absent. We attribute this lack of edge modes to the fact that the edge induces valley mixing. Further, even in the bulk, a sharp distinction between the valley Chern insulator and a trivial insulator requires an exact $C_3$ symmetry.

Bipolar spin-conversion diode and quantum entanglement induced by the valley and pseudoparity mixing

Herein, we report on a zigzag graphene superconducting junction with a superconductor sandwiched in between two magnetized zigzag graphene nanoribbons, where the valley and pseudoparity mixing are shown to bring about peculiar properties. We find that the bipolar spin diode and spin-conversion diode in the ferromagnetic configuration as well as quantum entanglement in the antiferromagnetic one are exhibited. The noncollinear angle combined with the valley and pseudoparity mixing in arbitrary magnetic configurations exerts a significant influence on the transport properties. In addition, not only the bipolar spin diode and magnetic storage with high efficiencies but also the bipolar spin-conversion diode and quantum entanglement can coexist in one setup. Particularly, the bipolar spin-conversion diode can be used to directly detect and confirm the helical spin texture of the edge state in a quantum spin Hall insulator.

Exciton Fine Structure in Lead Chalcogenide Quantum Dots: Valley Mixing and Crucial Role of Intervalley Electron-Hole Exchange.

We study the exciton fine structure in quantum dots of multivalley lead chalcogenides. We demonstrate that intervalley electron-hole exchange interaction, ignored in previous studies, dramatically modifies the exciton fine structure and leads to appearance of the ultrabright valley-symmetric spin-triplet exciton state dominating interband optical absorption. Valley mixing leads to brightening of other symmetry-allowed spin-triplet states which dominate low-temperature photoluminescence.

Scanning gate microscopy mapping of edge current and branched electron flow in a transition metal dichalcogenide nanoribbon and quantum point contact

We study scanning gate microscopy conductance mapping of a zigzag ribbon exploiting tight-binding and continuum models. We show that, even though the edge modes of a pristine nanoribbon are robust to backscattering on the potential induced by the tip, the conductance mapping reveals presence of both the edge modes and the quantized spin- and valley-current carrying modes. By inspecting the electron flow from a split gate quantum point contact (QPC) we find that the mapped current flow allows to determine the nature of the quantization in the QPC as spin–orbit coupling strength affects the number of branches in which the current exits the constriction. The radial conductance oscillation fringes found in the conductance mapping reveal the presence of two possible wavevectors for the charge carriers that correspond to spin and valley opposite modes. Finally, we show that disorder induced valley mixing leads to a beating pattern in the radial fringes.

Splitting of conductance resonance through a magnetic quantum dot in graphene

We report a dual resonance feature in ballistic conductance through a quantum Hall graphene nanoribbon with a magnetic quantum dot. Such a magnetic quantum dot localizes Dirac fermions exhibiting anisotropic eigenenergy spectra with broken time-reversal symmetry. Interplay between the localized states and quantum Hall edge states is found to be two-fold, showing Breit-Wigner and Fano resonances, which is reminiscent of a double quantum dot system. By fitting the numerical results with the Fano-Breit-Wigner lineshape from the double quantum dot model, we demonstrate that the two-fold resonance is due to the valley mixing that comes from the coupling of the magnetic quantum dot with quantum Hall edge channels; an effective double quantum dot system emerges from a single magnetic quantum dot in virtue of the valley degree of freedom. It is further confirmed that the coupling is weaker for the Fano resonance and stronger for the Breit-Wigner resonace.

Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential

Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron–hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected effective Hamiltonian including interlayer effective mass, interlayer coupling and asymmetrical on-site energies due to a vertically-applied electric field. For bilayer graphene, we find two important characteristics, i.e. mixing and interference of intervalley scatterings in the presence of a scatter array, as well as a perpendicular-field induced site-energy asymmetry which deforms severely or even destroys completely the Hofstadter-type band structures due to the dependence of Bloch-wave expansion coefficients on the applied electric field.

Topological states on uneven (Pb,Sn)Se (001) surfaces

The impact of surface morphology on electronic structure of topological crystalline insulators is studied theoretically. As an example, the structure of topologically protected electronic states on a (001) (Pb,Sn)Se surface with terraces of atomic height is modeled. Within the envelope function model it is shown that valley mixing, the phenomenon responsible for the peculiar "double Dirac cone" shape of the surface state dispersion, depends crucially on the structure of the surface. By varying the width and the number of atomic layers in the terraces, a comprehensive explanation of recent experimental findings, i.e., the emergence of 1D states bound to odd-height atomic step edges as well as the collapse of "double Dirac cone" structure on a rough surface, is achieved. This approach allows us also to determine topological indices characterizing terraces and their interfaces. In the (001) surface of (Pb,Sn)Se the adjacent terraces turn out to be described by different values of the winding number topological invariant.

Impact of complex adatom-induced interactions on quantum spin Hall phases

Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in atomically thin materials and thus to unlock the much sought-after topological insulating phases in two dimensions. However, the observation of an Anderson topological transition induced by heavy adatoms has proved extremely challenging despite substantial experimental efforts. Here, we present a multi-scale approach combining advanced first-principles methods and accurate single-electron descriptions of adatom-host interactions using graphene as a prototypical system. Our study reveals a surprisingly complex structure in the interactions mediated by random adatoms, including hitherto neglected hopping processes leading to strong valley mixing. We argue that the unexpected intervalley scattering strongly impacts the ground state at low adatom coverage, which would provide a compelling explanation for the absence of a topological gap in recent experimental reports. Our conjecture is confirmed by real-space Chern number calculations and large-scale quantum transport simulations in disordered samples. This resolves an important controversy and suggests that a detectable topological gap can be achieved by engineering the spatial range of spin-orbit interactions.

Vertical distribution of aerosol optical properties in the Po Valley during the 2012 summer campaigns

Abstract. Studying the vertical distribution of aerosol particle physical and chemical properties in the troposphere is essential to understand the relative importance of local emission processes vs. long-range transport for column-integrated aerosol properties (e.g. the aerosol optical depth, AOD, affecting regional climate) as well as for the aerosol burden and its impacts on air quality at the ground. The main objective of this paper is to investigate the transport of desert dust in the middle troposphere and its intrusion into the planetary boundary layer (PBL) over the Po Valley (Italy), a region considered one of the greatest European pollution hotspots for the frequency that particulate matter (PM) limit values are exceeded. Events of mineral aerosol uplift from local (soil) sources and phenomena of hygroscopic growth at the ground are also investigated, possibly affecting the PM concentration in the region as well. During the PEGASOS 2012 field campaign, an integrated observing–modelling system was set up based on near-surface measurements (particle concentration and chemistry), vertical profiling (backscatter coefficient profiles from lidar and radiosoundings) and Lagrangian air mass transport simulations by FLEXPART model. Measurements were taken at the San Pietro Capofiume supersite (44°39′ N, 11°37′ E; 11 m a.s.l.), located in a rural area relatively close to some major urban and industrial emissive areas in the Po Valley. Mt. Cimone (44°12′ N, 10°42′ E; 2165 m a.s.l.) WMO/GAW station observations are also included in the study to characterize regional-scale variability. Results show that, in the Po Valley, aerosol is detected mainly below 2000 m a.s.l. with a prevalent occurrence of non-depolarizing particles ( > 50 % throughout the campaign) and a vertical distribution modulated by the PBL daily evolution. Two intense events of mineral dust transport from northern Africa (19–21 and 29 June to 2 July) are observed, with layers advected mainly above 2000 m, but subsequently sinking and mixing in the PBL. As a consequence, a non-negligible occurrence of mineral dust is observed close to the ground ( ∼ 7 % of occurrence during a 1-month campaign). The observations unambiguously show Saharan dust layers intruding the Po Valley mixing layer and directly affecting the aerosol concentrations near the surface. Finally, lidar observations also indicate strong variability in aerosol on shorter timescales (hourly). Firstly, these highlight events of hygroscopic growth of anthropogenic aerosol, visible as shallow layers of low depolarization near the ground. Such events are identified during early morning hours at high relative humidity (RH) conditions (RH > 80 %). The process is observed concurrently with high PM1 nitrate concentration (up to 15 µg cm−3) and hence mainly explicable by deliquescence of fine anthropogenic particles, and during mineral dust intrusion episodes, when water condensation on dust particles could instead represent the dominant contribution. Secondly, lidar images show frequent events (mean daily occurrence of ∼ 22 % during the whole campaign) of rapid uplift of mineral depolarizing particles in afternoon–evening hours up to 2000 m a.s.l. height. The origin of such particles cannot be directly related to long-range transport events, being instead likely linked to processes of soil particle resuspension from agricultural lands.

Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures

Transition metal dichalcogenides have valley degree of freedom, which features optical selection rule and spin-valley locking, making them promising for valleytronics devices and quantum computation. For either application, a long valley polarization lifetime is crucial. Previous results showed that it is around picosecond in monolayer excitons, nanosecond for local excitons and tens of nanosecond for interlayer excitons. Here we show that the dark excitons in two-dimensional heterostructures provide a microsecond valley polarization memory thanks to the magnetic field induced suppression of valley mixing. The lifetime of the dark excitons shows magnetic field and temperature dependence. The long lifetime and valley polarization lifetime of the dark exciton in two-dimensional heterostructures make them promising for long-distance exciton transport and macroscopic quantum state generations.

Intra- and inter-shell Kondo effects in carbon nanotube quantum dots

The linear response transport properties of carbon nanotube quantum dot in the strongly correlated regime are discussed. The finite-U mean field slave boson approach is used to study many-body effects. Magnetic field can rebuilt Kondo correlations, which are destroyed by the effect of spin-orbit interaction or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects of different types: spin, valley or spin-valley, also more exotic phenomena appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the effective intervalley exchange induced by short-range part of Coulomb interaction or due to the intershell mixing. In narrow gap nanotubes the full spin-orbital degeneracy might be recovered in the absence of magnetic field opening the condition for a formation of SU(4) Kondo resonance.

Erratum: Electrically driven spin qubit based on valley mixing [Phys. Rev. B 95 , 075403 (2017)

Erratum: Electrically driven spin qubit based on valley mixing [Phys. Rev. B <b>95</b> , 075403 (2017)

Valley filter and valve effect by strong electrostatic potentials in graphene

We report a theoretical study on the valley-filter and valley-valve effects in the monolayer graphene system by using electrostatic potentials, which are assumed to be electrically controllable. Based on a lattice model, we find that a single extremely strong electrostatic-potential barrier, with its strength exceeding the hopping energy of electrons, will significantly block one valley but allow the opposite valley flowing in the system, and this is dependent on the sign of the potential barrier as well as the flowing direction of electrons. In a valley-valve device composed of two independent potential barriers, the valley-valve efficiency can even amount to 100% that the electronic current is entirely prohibited or allowed by reversing the sign of one of potential barriers. The physics origin is attributed to the valley mixing effect in the strong potential barrier region. Our findings provide a simple electric way of controlling the valley transport in the monolayer graphene system.

Electron spin relaxation in a transition-metal dichalcogenide quantum dot

We study the relaxation of a single electron spin in a circular quantum dot in a transition-metal dichalcogenide monolayer defined by electrostatic gating. Transition-metal dichalcogenides provide an interesting and promising arena for quantum dot nano-structures due to the combination of a band gap, spin-valley physics and strong spin–orbit coupling. First we will discuss which bound state solutions in different B-field regimes can be used as the basis for qubits states. We find that at low B-fields combined spin-valley Kramers qubits to be suitable, while at large magnetic fields pure spin or valley qubits can be envisioned. Then we present a discussion of the relaxation of a single electron spin mediated by electron–phonon interaction via various different relaxation channels. In the low B-field regime we consider the spin-valley Kramers qubits and include impurity mediated valley mixing which will arise in disordered quantum dots. Rashba spin–orbit admixture mechanisms allow for relaxation by in-plane phonons either via the deformation potential or by piezoelectric coupling, additionally direct spin-phonon mechanisms involving out-of-plane phonons give rise to relaxation. We find that the relaxation rates scale as B6 for both in-plane phonons coupling via deformation potential and the piezoelectric effect, while relaxation due to the direct spin-phonon coupling scales independant to B-field to lowest order but depends strongly on device mechanical tension. We will also discuss the relaxation mechanisms for pure spin or valley qubits formed in the large B-field regime.

Electrically driven spin qubit based on valley mixing.

The electrical control of single spin qubits based on semiconductor quantum dots is of great interest for scalable quantum computing since electric fields provide an alternative mechanism for qubit control compared with magnetic fields and can also be easier to produce. Here we outline the mechanism for a drastic enhancement in the electrically-driven spin rotation frequency for silicon quantum dot qubits in the presence of a step at a heterointerface. The enhancement is due to the strong coupling between the ground and excited states which occurs when the electron wave function overcomes the potential barrier induced by the interface step. We theoretically calculate single qubit gate times tπ of 170 ns for a quantum dot confined at a silicon/silicon-dioxide interface. The engineering of such steps could be used to achieve fast electrical rotation and entanglement of spin qubits despite the weak spin-orbit coupling in silicon.

Reprint of : Kondo effect in a carbon nanotube with spin–orbit interaction and valley mixing: A DM-NRG study

We investigate the effects of spin–orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting Δ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments that the Kondo temperature scales inversely with the splitting Δ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis) and discuss the conditions under which Kondo revivals may be achieved.

Kondo effect in a carbon nanotube with spin–orbit interaction and valley mixing: A DM-NRG study

We investigate the effects of spin–orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting Δ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments that the Kondo temperature scales inversely with the splitting Δ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis) and discuss the conditions under which Kondo revivals may be achieved.

Polarization analysis of excitons in monolayer and bilayer transition-metal dichalcogenides

The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the optical spectra of these materials. We explain the differences between optical transitions in monolayer MoSe$_2$ and monolayer WSe$_2$, finding that indirect excitons in the latter correspond to several low-energy optical transitions that so far were attributed to excitons bound to impurities. A possible mechanism that can explain the vanishing polarization in MoSe$_2$ is discussed. Finally, we consider the effect of an out-of-plane electric field, showing that it can reduce the initial polarization of bright excitons due to a Rashba-type coupling with dark excitons.

The two classes of low-energy spectra in finite carbon nanotubes

Electrons in carbon nanotubes (CNTs) possess spin and orbital degrees of freedom. The latter is inherited from the bipartite graphene lattice with two inequivalent Dirac points. The electronic spectra obtained in several transport experiments on CNT quantum dots in parallel magnetic field often show an anticrossing of spectral lines assigned to the opposite Dirac valleys. So far this valley mixing has been attributed to the disorder, with impurity induced scattering. We show that this effect can arise also in ultraclean CNTs of the armchair class and it can be caused solely by the presence of the boundaries. In contrast, in CNTs of the zigzag class it does not occur. These two fundamentally different classes of spectra arise because of different symmetries of the low energy eigenstates of the two types of CNTs. The magnitude of the level splitting depends in a nonmonotonous way on the distance of the involved energy levels from the charge neutrality point.

Broken SU(4) symmetry in a Kondo-correlated carbon nanotube

This paper reports on the experimental and theoretical investigation of nonequilibrium Kondo effect in carbon nanotube quantum dots. At low temperature and in the absence of magnetic field, the authors observe two symmetric satellite features on either side of the zero bias peak due to the splitting of single-particle states by the spin-orbit coupling and valley mixing. Further experimental results are discussed based on the underlying symmetries of the carbon nanotube energy spectrum.