We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60 degree over a large energetic range in one of the valleys, and down to -60 degree in the other. In a Y-junction geometry, this can be used to create and detect valley polarization.
We study the states localized near an interface between conducting and insulating bilayer graphene (BLG) and show that they have highly unusual properties that have no analog in conventional systems. Moreover, the states belonging to the two independent valleys in the Brillouin zone of BLG show contrasting properties that allows a relatively easier experimental realization of various valley based functionalities desired in valleytronics without requiring any sophisticated techniques.
The recent proposal of using an anisotropic vacuum for generating valley coherence in transition metal dichalcogenide (TMDC) monolayers has expanded the potential of such valley degrees of freedom for applications in valleytronics. In this work, we open up a completely new regime, inaccessible with monolayer TMDCs, of spontaneously generated valley coherence in interlayer excitons in commensurate TMDC bilayer heterostructures. Using the peculiar out of plane polarization of interlayer excitons in conjunction with an in-plane anisotropic electromagnetic vacuum, we show that a much larger region…
We study spin effects of quantum wires formed in bilayer graphene by electrostatic confinement. With a proper choice of the confinement direction, we show that in the presence of magnetic field, spin-orbit interaction induced by curvature, and intervalley scattering, bound states emerge that are helical. The localization length of these helical states can be modulated by the gate voltage which enables the control of the tunnel coupling between two parallel wires. Allowing for proximity effect via an s-wave superconductor, we show that the helical modes give rise to Majorana fermions in bilayer…
Valley-selective optical selection rules and a spin-valley locking in transition-metal dichalcogenide (TMDC) monolayers are at the heart of "valleytronic physics", which exploits the valley degree of freedom and has been a major research topic in recent years. In contrast, valleytronic properties of TMDC bilayers have not been in the focus so much by now. Here, we report on the valleytronic properties and optical characterization of bilayers of WS2 as a representative TMDC material. In particular, we study the influence of the relative layer alignment in TMDC homo-bilayer samples on their pola…
A quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering d…
Intrinsic and extrinsic valley Hall effects are predicted to emerge in graphene systems with uniform or spatially-varying mass terms. Extrinsic mechanisms, mediated by the valley-dependent scattering of electrons at the Fermi surface, can be directly linked to quantum transport simulations. This is a promising route towards more complete experimental investigation of valleytronic phenomena in graphene, but a major obstacle is the difficulty in applying the sublattice-dependent potentials required. Here we show that strongly valley-dependent scattering also emerges from bilayer graphene quantum…
Probing and controlling the valley degree of freedom in graphene systems by transport measurements has been a major challenge to fully exploit the unique properties of this two-dimensional material. In this theoretical work, we show that this goal can be achieved by a quantum-wire geometry made of gapped graphene that acts as a valley filter with the following favorable features: i) all electrical gate control, ii) electrically switchable valley polarity, iii) robustness against configuration fluctuation, and iv) potential for room temperature operation. This valley filtering is accomplished b…
In the presence of a finite interlayer displacement field bilayer graphene has an energy gap that is dependent on stacking and largest for the stable AB and BA stacking arrangements. When the relative orientations between layers are twisted through a small angle to form a moir$\mathrm{\acute{e}}$ pattern, the local stacking arrangement changes slowly. We show that for non-zero displacement fields the low-energy physics of twisted bilayers is captured by a phenomenological helical network model that describes electrons localized on domain walls separating regions with approximate AB and BA stac…
Electron's tunneling through potential barrier in monolayer and bilayer graphene lattices is investigated by using full tight-binding model. Emphasis is placed on the resonance tunneling feature and inter-valley scattering probability. It is shown that normal incidence transmission probabilities for monolayer and bilayer graphene exhibit different properties. Our calculation indicates that valleytronics in graphene systems may be detected, generated and controlled by changing the structure parameters of the external electric potential.
In minimally twisted bilayer graphene, a moir{é} pattern consisting of AB and BA stacking regions separated by domain walls forms. These domain walls are predicted to support counterpropogating topologically protected helical (TPH) edge states when the AB and BA regions are gapped. We fabricate designer moir{é} crystals with wavelengths longer than 50 nm and demonstrate the emergence of TPH states on the domain wall network by scanning tunneling spectroscopy measurements. We observe a double-line profile of the TPH states on the domain walls, only occurring when the AB and BA regions are gappe…
We measure microwave photocurrent in devices made from InAs/GaInSb bilayers where both insulating bulk state and conducting edge state were observed in the inverted-band regime, consistent with the theoretical prediction for a quantum spin Hall (QSH) insulator. It has been theoretically proposed that microwave photocurrent could be a unique probe in studying the properties of QSH edge states. To distinguish possible photoresponse between bulk state and helical edge state, we prepare Hall bar and Corbino disk from the same wafer. Results show that the Corbino disk samples have a negligible phot…
Valleytronics is a pioneering technological field relying on the valley degree of freedom to achieve novel electronic functionalities. Topological valley-polarized electrons confined to domain walls in bilayer graphene were extensively studied in view of their potentials in valleytronics. Here, we study the magnonic version of domain wall excitations in 2D honeycomb ferromagnetic bilayers (FBL) with collinear order. In particular, we explore the implications of Dzyaloshinskii-Moriya interaction (DMI) and electrostatic doping (ED) on the existence and characteristics of 1D magnons confined to l…
The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $ν\in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $ν=-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing t…
We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero-modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero-mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally, and emphasize their …
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
Robustness of helical hinge states of three-dimensional weak second-order topological i sulators (WSOTIs) against disorders is studied. The pure WSOTI is obtained from a weak $\mathbb{Z}_2$ first-order topological insulator through a surface band inversion. Both bulk states and surface states in the WSOTI are gapped, and in-gap valley-momentum locked helical hinge states are topologically protected by the surface valley-Chern number. In the presence of weak disorders, helical hinge states are robust against disorders while the quantized conductance of the states is fragile due to the inter-val…
Gapped bilayer graphene can support the presence of intragap states due to kink gate potentials applied to the graphene layers. Electrons in these states display valley-momentum locking, which makes them attractive for topological valleytronics. Here, we show that kink-antikink local potentials enable modulated scattering of topological currents. We find that the kink-antikink coupling leads to anomalous steps in the junction conductance. Further, when the constriction detaches from the propagating modes, forming a loop, the conductance reveals the system energy spectrum. Remarkably, these kin…
The existence of inequivalent valleys K and K' in the momentum space of two-dimensional hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types of electronics, in analogy to the role played by electron spin. In materials with broken inversion symmetry, such as an electrically gated bilayer graphene, the momentum-space Berry curvature $Ω$ carries opposite sign in the K and K' valleys. A sign reversal of $Ω$ along an internal boundary of the sheet gives rise to counter-propagating one-dimensional conducting modes encoded with op…
A twisted graphene bilayer exhibits a triangular Moiré pattern in the local stacking, that smoothly alternates between the three basic types AA', AB' and BA'. Under an interlayer bias U, the latter two types develop a spectral gap, characterised by opposite valley Chern numbers. We show that for large enough Moiré periods and bias, these regions become depleted electronically, and topologically protected helical modes appear at their boundaries. This gives rise to a delocalised topological network of the Chalker-Coddington type, composed of valley current vortices. This network can be tailored…
We calculate the conductance of a two-dimensional bilayer with inverted electron-hole bands, to study the sensitivity of the quantum spin Hall insulator (with helical edge conduction) to the combination of electrostatic disorder and a perpendicular magnetic field. The characteristic breakdown field for helical edge conduction splits into two fields with increasing disorder, a field $B_{c}$ for the transition into a quantum Hall insulator (supporting chiral edge conduction) and a smaller field $B'_{c}$ for the transition to bulk conduction in a quasi-metallic regime. The spatial separation of t…
Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37$^\circ$. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the …
Two-dimensional semiconductors feature valleytronics phenomena due to locking of the spin and momentum valley of the electrons. However, the valley polarization is intrinsically limited in monolayer crystals by the fast intervalley electron-hole exchange. Hetero-bilayer crystals have been shown to have a longer exciton lifetime and valley depolarization time. But the reported valley polarization was low; the valley selection rules and mechanisms of valley depolarization remains controversial. Here, we report singlet and brightened triplet interlayer excitons both with over 80% valley polarizat…
A graphene bilayer shows an unusual magnetoelectric response whose magnitude is controlled by the valley-isospin density, making it possible to link magnetoelectric behavior to valleytronics. Complementary to previous studies, we consider the effect of static homogeneous electric and magnetic fields that are oriented parallel to the bilayer's plane. Starting from a tight-binding description and using quasi-degenerate perturbation theory, the low-energy Hamiltonian is derived including all relevant magnetoelectric terms whose prefactors are expressed in terms of tight-binding parameters. We con…
Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here we use magnetic focusing to probe narrow bands in graphene bilayers twisted at 2 degrees. Their minibands are found to support long-range ballistic transport limited at low temperatures by i…
Achieving a population imbalance between the two inequivalent valleys is a critical first step for any valleytronic device. A valley-polarization can be induced in biased bilayer graphene using circularly polarized light. In this paper, we present a detailed theoretical study of valley-polarization in biased bilayer graphene. We show that a nearly perfect valley-polarization can be achieved with the proper choices of external bias and pulse frequency. We find that the optimal pulse frequency $ω$ is given by $\hbarω=2a,$ where $2a$ is the potential energy difference between the graphene layers.…
Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by…
Topological insulators, along with Chern insulators and Quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the time-reversal invariant helical edge-modes in bilayer graphene/monolayer WSe$_2$-based heterostructures -- a phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising both a moiré superlattice potential and strong spin-orbit coupli…
We study theoretically interaction of a bilayer graphene with a circularly polarized ultrafast optical pulse of a single oscillation at an oblique incidence. The normal component of the pulse breaks the inversion symmetry of the system and opens up a dynamical band-gap, due to which a valley-selective population of the conduction band becomes sensitive to the angle of incident of the pulse. We show that the magnitude of the valley polarization can be controlled by the angle of incidence, the amplitude, and the angle of in-plane polarization of the chiral optical pulse. Subsequently, a sequence…
The development of valleytronics demands long-range electronic transport with preserved valley index, a degree of freedom similar to electron spin. A promising structure for this end is a topological one-dimensional (1D) channel formed in bilayer graphene (BLG) under special electrostatic conditions or specific stacking configuration, called domain wall (DW). In these 1D channels, the valley-index defines the propagation direction of the charge carriers and the chiral edge states (kink states) are robust over many kinds of disorder. However, the fabrication of DWs is challenging, requiring the…
Modulation of electronic states in two-dimensional (2D) materials can be achieved by using in-plane variations of the band gap or the average potential in lateral quantum structures. In the atomic configurations with hexagonal symmetry, this approach makes it possible to tailor the valleytronic properties for potential device applications. In this work, we present a multi-band theory to calculate the valley-dependent electron transport in graphene-based lateral quantum structures. As an example, we consider the structures with a single interface that exhibits an energy gap or potential discont…
Motivated by a recent experiment (Sanchez-Yamagishi et.al, arXiv:1602.06815) reporting evidence of helical spin-polarized edge states in layer-biased twisted bilayer graphene under a magnetic flux, we study the possibility of stabilising a Quantum Spin Hall (QSH) phase in such a system, without Zeeman or spin-orbit couplings, and with a QSH gap induced instead by electronic interactions. We analyse how magnetic flux, electric field, interlayer rotation angle, and interactions (treated at a mean field level) combine to produce a pseudo-QSH with broken time-reversal symmetry, and spin-polarized …
Topological insulators (TIs) and graphene present two unique classes of materials which are characterized by spin polarized (helical) and non-polarized Dirac-cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in TIs. Here, we report the experimental observation of the renormalized quasi-particle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 subst…
It is well-known that the ground state of homogeneous superconducting systems with spin-orbit coupling (SOC) in the presence of the Zeeman field is the so-called helical state, which is characterized by the phase modulation of the order parameter, but zero supercurrent density. In this work we investigate the realization of the helical state in a hybrid system with spatially separated superconductivity and exchange field by considering S/F bilayer on top of a 3D topological insulator. This system is characterized by strong spin-momentum locking and, consequently, provides the most favorable co…
The rich phase diagram of quantum spin-ladder systems has attracted much attention in the theoretical literature. The progress in experimental realisations of this fascinating physics however has been much slower. While materials with a ladder-like structure exist, one always has coupling between the ladders to muddy the waters. In addition, such materials exhibit limited (if any) tunability in terms of the magnetic exchange parameters, and experimental probing of the different phases is a great challenge. In this work, we show that a realisation of spin-ladder physics can occur in an engineer…
A nanoelectronic device made of twisted bilayer graphene (TBLG) is proposed to steer the direction of the current flow. The ballistic electron current, injected at one edge of the bottom layer, can be guided predominantly to one of the lateral edges of the top layer. The current is steered to the opposite lateral edge, if either the twist angle is reversed or the electrons are injected in the valence band instead of the conduction band, making it possible to control the current flow by electric gates. When both graphene layers are aligned, the current passes straight through the system without…
Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands, is a distinct feature of two-dimensional Dirac materials. Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests. Bilayer graphene (BLG) is a unique system whose intrinsic inversion sy…
Spatially indirect excitons with displaced wavefunctions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe2, by performing electric field-tunable photoluminescence measurements. Because of different out-of-pla…
Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bila…
Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley-protected is still lacking. In this study, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, …
Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polar…
We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent helical states known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional channels propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional channels. The origin of …
We consider the zero-filled quantum-Hall ferromagnetic state of bilayer graphene subject to a kink-like perpendicular electric field, which generates domain walls in the electronic state and low-energy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective field-theoretical model of these modes in terms of two weakly coupled anisotropic quantum spin-ladders, with parameters tunable through control of the electric …
We first derive the energy dispersion of bilayer MoS$_{2}$ in the presence of a perpendicular electric field $E_z$. We show that the band gap and layer splitting can be controlled by the field $E_z$. Away from the $k$ point, the intrinsic SOC splitting increases in the conduction band but is weakly affected in the valence band. We then analyze the band structure in the presence of a perpendicular magnetic field $B$ and the field $E_z$, including spin and valley Zeeman terms, and evaluate the Hall and longitudinal conductivities. We discuss the numerical results as functions of the fields $B$ a…
Berry phase plays an important role in determining many physical properties of quantum systems. However, a Berry phase altering energy spectrum of a quantum system is comparatively rare. Here, we report an unusual tunable valley polarized energy spectra induced by continuously tunable Berry phase in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about pi to 2pi by perpendicular magnetic fields. When the Berry phase equals pi or 2pi, the electron states in the two inequivalent valleys are energetically degen…
The rich and unconventional physics in layered 2D magnets can open new avenues for topological magnonics and magnon valleytronics. In particular, two-dimensional (2D) bilayer quantum magnets are gaining increasing attention due to their intriguing stacking-dependent magnetism, controllable ground states, and topological excitations induced by magnetic spin-orbit couplings (SOCs). Despite the substantial research on these materials, their topological features remain widely unexplored to date. The present study comprehensively investigates the magnon topology and magnon valley-polarization in ho…
Atomically thin transition metal dichalcogenides (TMDs) possess coupling of spin and valley degrees of freedom, making them promising for spin-valleytronics. ln monolayer TMDs, the emission helicity is locked to the valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of Zeeman effect in presence of out-of-plane magnetic field. As inversion symmetry is recovered in bilayers, the emission helicity should no longer be locked to the valleys. Here we show that Zeeman splitting, however, still persists in bilayers, as a result of an additional …
