Magnetotunneling spectroscopy of chiral two-dimensional electron systems

Pratley, Luke; Zülicke, U.

doi:10.1103/physrevb.88.245412

Cited by 12 publications

(19 citation statements)

References 48 publications

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“…dotted lines mark G = 0 for the two curves.overlaps with empty states in the other, so that electrons can tunnel with energy and momentum conservation [8,9]. When V b = V 2 (inset ii) the cones intersect along a straight line and the current reaches a resonant maximum.A magnetic field, B, applied perpendicular to the graphene layers quantises the electron energy into a spectrum of unequally-spaced Landau levels (LLs) defined by E n b,t = sgn(n b,t ) 2|n b,t | v F /l B , where n b,t is the LL index in the bottom (b) and top (t) layers, and l B = /eB [18,[20][21][22][23][24][25][26][27][28][29][30]33]. By comparing our measured tunnel current with transfer Hamiltonian calculations, we demonstrate the composite spatial-spinor form of the quantised Landau states and the effect of chirality on the measured current-voltage characteristics.…”

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confidence: 99%

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

et al. 2015

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A new class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer [1]. An exemplar of such a structure is a transistor device in which relativistic Dirac Fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantises graphene's gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following a tunnelling event, is a form of Klein tunnelling for inter-layer transitions.An electron moving through the hexagonal crystal structure of graphene is not only quasi-relativistic but also exhibits chirality [2], which means that its wavefunction amplitude is intrinsically coupled to the direction of motion. This gives rise to the phenomenon of Klein tunnelling whereby an electron can pass with unity transmission through a potential barrier formed in the graphene layer [3,4]. In principle, chirality should affect the electronic properties of graphene-based devices. To investigate this effect we focus on a van der Waals heterostructure in which Dirac fermions can resonantly tunnel between two graphene electrodes separated by a hexagonal boron nitride tunnel barrier [5][6][7][8]. Recent work on this type of transistor has demonstrated that even a small misalignment of the crystalline lattices of the two graphene electrodes lowers the translation symmetry in the plane of the tunnel barrier and gives rise to an impulse which modifies the dynamics of the tunnelling electron [7][8][9][10][11][12]. By applying a quantising magnetic field perpendicular to the layers, we show that electron tunnelling is governed by the laws of conservation of energy and of in-plane momentum. In addition, we find that the effect of electron chirality on the tunnel current is enhanced by a quantising magnetic field. We a θ KbSilicon dioxide B I θ Figure 1: a Schematic of the device showing the two misaligned graphene lattices (bottom, red and top, blue) separated by a boron nitride tunnel barrier, yellow. b dashed black lines show the Brillouin zone boundary for electrons in the bottom graphene layer. Red arrows show the vector positions of the Dirac points K b ± (red circles) relative to the Γ point. Blue arrows show the positions of the Dirac points in the top layer, Kt ± (blue circles), misorientated at an angle θ to the bottom layer.also demonstrate that, following an electron tunnelling transition, the semiclassical cyclotron trajectory of the electron changes in a way that is analogous to intralayer Klein tunnelling.Our device, with bias, V b , and gate, V g , voltages applied, is shown schem...

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Resonant tunnelling between the chiral Landau states of twisted graphene lattices

et al. 2015

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“…However, the usual tunneling formalism, which does not take into account the interference between the two components of the wavefunction of the tunneling electrons, fails in the case of chiral quasiparticles. Here, we show that, the tunneling current-voltage characteristics I (Vb,B) in the presence of an in-plane magnetic field B (18), essentially depend on the pseudospin orientation and enable us to detect the valley sublattice structure determined by the relative phase between the two sublattice components of the Dirac spinor vector wavefunction of electrons in graphene.…”

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confidence: 89%

Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures

Wallbank

Ghazaryan

Misra

et al. 2016

Science

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Chirality is a fundamental property of electrons with the relativistic spectrum found in graphene and topological insulators. It plays a crucial role in relativistic phenomena, such as Klein tunneling, but it is difficult to visualize directly. Here, we report the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. We use a strong in-plane magnetic field as a tool to resolve the contributions of the chiral electronic states that have a phase difference between the two components of their vector wave function. Our experiments not only shed light on chirality, but also demonstrate a technique for preparing graphene's Dirac electrons in a particular quantum chiral state in a selected valley.

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“…The in-plane component produces a relative shift in momentum space of the Dirac cones in adjacent layers. This effect results in an unusual energy spectrum and dependence of the interlayer tunneling current on the magnetic field [6][7][8][9]12]. Magnetoresistance and tunneling spectroscopy for the in-plane magnetic field were measured in thin films of TIs [10,11], a graphite mesa [12], and a graphene double layer [13].…”

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confidence: 99%

Effects of a tilted magnetic field in a Dirac double layer

et al. 2015

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We calculate the energy spectrum of a Dirac double layer, where each layer has the Dirac electronic dispersion, in the presence of a tilted magnetic field and small interlayer tunneling. We show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic field. Using a semiclassical analysis, we show that these special tilt angles are determined by the Berry phase of the Dirac Hamiltonian. The interlayer tunneling conductance also exhibits an oscillatory dependence on the magnetic field tilt angle, known as the angular magnetoresistance oscillations (AMRO). Our results are applicable to graphene double layers and thin films of topological insulators.

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Magnetotunneling spectroscopy of chiral two-dimensional electron systems

Cited by 12 publications

References 48 publications

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures

Effects of a tilted magnetic field in a Dirac double layer

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