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 graphene.PACS numbers: 73.22. Pr, 75.70.Tj, 73.63.Fg, Introduction. Graphene and its derivatives [1][2][3][4], such as bilayer graphene (BLG) and carbon nanotubes (CNT), have attracted wide interest due to its peculiar bandstructure with low energy excitations described by Diraclike Hamiltonians. Moreover, these materials are usually placed on substrates, which allows high control of its geometry, doping, and placement of metallic gates [5][6][7][8][9]. Topological insulators were predicted for graphene [10], but later it was found that the intrinsic spin-orbit interaction (SOI) is too weak [11,12]. For BLG, first-principle calculations also show weak SOI [13,14]. In an other proposal, topologically confined bound states were predicted to occur in BLG where a gap and band inversion is enforced by gates [15]. Quite remarkably, these states are localized in the region where the voltage changes sign, are independent of the edges of the sample, and propagate along the direction of the gates, thus forming effectively a quantum wire [15][16][17]. At any fixed energy, the spectrum inside the gap is topologically equivalent to four Dirac cones, each cone consisting of a pair of states with opposite momenta.

We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect (QAHE). Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits.

Space-and time-resolved measurements of spin drift and diffusion are performed on a GaAs-hosted two-dimensional electron gas. For spins where forward drift is compensated by backward diffusion, we find a precession frequency in absence of an external magnetic field. The frequency depends linearly on the drift velocity and is explained by the cubic Dresselhaus spin-orbit interaction, for which drift leads to a spin precession angle twice that of spins that diffuse the same distance.Drift and diffusion of charge carriers in semiconductor nanostructures are the foundation of information technology. The spin of the electron is being investigated as an additional or complementary degree of freedom that can enhance the functionality of electronic devices and circuits [1][2][3]. In the presence of spin-orbit interaction (SOI), the spins of moving electrons precess about effective magnetic fields that depend on the electron momentum vector, k [4]. In a two-dimensional electron gas (2DEG), this precession has been proposed as a gatetunable switching mechanism [5,6]. Spin diffusion and spin drift have been studied using optical [7][8][9][10][11] and electrical techniques [12,13]. A local spin polarization expands diffusively into a spin mode with a spatial polarization pattern that is characteristic of the strength and symmetry of the SOI [14]. An additional drift induced by an electric field does not modify the spatial precession period in the case of linear SOI [15][16][17][18]. This is because spins that travel a certain distance and direction precess on average by the same angle, irrespective of how the travel is distributed between diffusion and drift. Therefore, no spin precession occurs for quasi-stationary electrons, i.e. for electrons where drift is compensated by diffusion.In this letter, we experimentally observe such unexpected drift-induced spin precession of stationary electron spins in the absence of an external magnetic field. Using an optical pump-probe technique, we investigate the spatiotemporal dynamics of locally excited spin polarization in an n-doped GaAs quantum well. Spin polarization probed at a fixed position is found to precess with a finite frequency, ω. This is identified as a consequence of cubic SOI, which affects spin drift and spin diffusion differently. A simple model predicts that drifting spins precess twice as much as spins that diffuse the same distance. This difference leads to a dependence ω ∝ β 3 v dr , where β 3 is the cubic SOI coefficient and v dr the drift velocity. We demonstrate quantitative agreement between model and experiment, and extract a β 3 in agreement with literature values. Monte-Carlo simulations confirm the validity of the model and pinpoint deviations that occur when the drift-induced SOI field is small compared arXiv:1602.05095v3 [cond-mat.mes-hall]

We theoretically investigate negative differential resistance (NDR) for ballistic transport in semiconducting armchair graphene nanoribbon (aGNR) superlattices (5 to 20 barriers) at low bias voltages VSD < 500 mV. We combine the graphene Dirac hamiltonian with the Landauer-Büttiker formalism to calculate the current ISD through the system. We find three distinct transport regimes in which NDR occurs: (i) a "classical" regime for wide layers, through which the transport across bandgaps is strongly suppressed, leading to alternating regions of nearly unity and zero transmission probabilities as a function of VSD due to crossing of bandgaps from different layers. (ii) a quantum regime dominated by superlattice miniband conduction, with current suppression arising from the misalignment of miniband states with increasing VSD; and (iii) a Wannier-Stark ladder regime with current peaks occurring at the crossings of Wannier-Stark rungs from distinct ladders. We observe NDR at voltage biases as low as 10 mV with a high current density, making the aGNR superlattices attractive for device applications.

The theory of spin drift and diffusion in two-dimensional electron gases is developed in terms of a random walk model incorporating Rashba, linear and cubic Dresselhaus, and intersubband spin-orbit couplings. The additional subband degree of freedom introduces new characteristics to the persistent spin helix (PSH) dynamics. As has been described before, for negligible intersubband scattering rates, the sum of the magnetization of independent subbands leads to a checkerboard pattern of crossed PSHs with long spin lifetime. For strong intersubband scattering we model the fast subband dynamics as a new random variable, yielding a dynamics set by averaged spin-orbit couplings of both subbands. In this case the crossed PSH becomes isotropic, rendering circular (Bessel) patterns with short spin lifetime. Additionally, a finite drift velocity breaks the symmetry between parallel and transverse directions, distorting and dragging the patterns. We find that the maximum spin lifetime shifts away from the PSH regime with increasing drift velocity. We present approximate analytical solutions for these cases and define their domain of validity. Effects of magnetic fields and initial package broadening are also discussed.

We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling. Second, a typical lattice discretization of the firstorder derivative k → −i∂x skips the central point and allow spurious low-energy, highly oscillating solutions known as fermion doublers. While a no-go theorem states that the doublers cannot be eliminated without artificially breaking a symmetry, here we show that the symmetry broken by the Wilson's mass approach is equivalent to the enforcement of hard-wall boundary conditions, thus making the no-go theorem irrelevant when confinement is foreseen. We illustrate our arguments by calculating the following: (i) the band structure and transport properties across thin films of the topological insulator Bi2Se3, for which we use ab-initio density functional theory calculations to justify the model; and (ii) the band structure of zigzag graphene nanoribbons. arXiv:1708.03514v2 [cond-mat.mes-hall]

Recently, orbital-textures have been found in Rashba and topological insulator (TI) surface states as a result of the spin-orbit coupling (SOC). Here, we predict a px/py orbital texture, in linear dispersive Dirac bands, arising at the K/K' points of χ-h0 borophene chiral monolayer. Combining first-principles calculations with effective hamiltonians, we show that the orbital pseudospin has its direction locked with the momentum in a similar way as TIs' spin-textures. Additionally, considering a layer pseudospin degree of freedom, this lattice allows stackings of layers with equivalent or opposite chiralities. In turn, we show a control of the orbital textures and layer localization through the designed stacking and external electric field. For instance, for the opposite chirality stacking, the electric field allows for an on/off switch of the orbital-textured Dirac cone.

Effective spin-orbit (SO) Hamiltonians for conduction electrons in wurtzite heterostructures are lacking in the literature, in contrast to zincblende structures. Here we address this issue by deriving such an effective Hamiltonian valid for quantum wells, wires, and dots with arbitrary confining potentials and external magnetic fields. We start from an 8×8 Kane model accounting for the s-p z orbital mixing important to wurtzite structures, but absent in zincblende, and apply both quasi-degenerate perturbation theory (Löwdin partitioning) and the folding down approach to derive an effective 2×2 electron Hamiltonian. Focusing on wurtzite quantum wells, we later on also perform a self-consistent Poisson-Schrödinger calculation in the Hartree approximation to determine the relevant SO couplings. We obtain the usual k-linear Rashba term arising from the structural inversion asymmetry of the wells and, differently from zincblende structures, a bulk Rashba-type term induced by the inversion asymmetry of the wurtzite lattice. Our results show this latter term to be the main contribution to the Rashba coupling in wurtzite wells. We also find linear-and cubic-in-momentum Dresselhaus contributions. Both the bulk Rashba-type term and the Dresselhaus terms originate exclusively from the admixture of s-and p z -like states in wurtzites structures. Interestingly, in these systems the linear Rashba and the Dresselhaus terms have the same symmetry and can in principle cancel each other out completely, thus making the spin a conserved quantity. We determine the intrasubband (intersubband) Rashba α ν (η) and linear Dresselhaus β ν (Γ) SO strengths of GaN/AlGaN single and double wells with one and two occupied subbands (ν = 1, 2). For the GaN/Al 0.3 Ga 0.7 N single well with one occupied subband, we obtain the total spin splitting coefficient α eff 1 = α 1 + β 1 ∼ 7.16 meV·Å, in agreement with weak antilocalization measurements. In the case of two occupied subbands, we observe that the intersubband Rashba η is much weaker than the intrasubband coupling α ν . For double wells even in the presence of strong built-in electric fields (spontaneous and piezoelectric, crucial in GaN/AlGaN wells), we find a seemingly symmetric potential configuration at which both the Rashba η and Dresselhaus Γ intersubband couplings exhibit their highest strengths. On the other hand, we observe that the intrasubband Dresselhaus coefficients β 1 and β 2 interchange their values as the gate voltage V g varies across zero; a similar behavior, though less pronounced, is seen for the Rashba couplings α 1 and α 2 . We believe our general effective Hamiltonian for electrons in wurtzite heterostructures put forward here, should stimulate additional theoretical works on wurtzite quantum wells, wires, and dots with variously defined geometries and external magnetic fields.