We present a theory of quantum-coherent transport through a lateral p-n-p structure in graphene, which fully accounts for the interference of forward and backward scattering on the p-n interfaces. The backreflection amplitude changes sign at zero incidence angle because of the Klein phenomenon, adding a phase $π$ to the interference fringes. The contributions of the two p-n interfaces to the phase of the interference cancel with each other at zero magnetic field, but become imbalanced at a finite field. The resulting half a period shift in the Fabry-Perot fringe pattern, induced by a relatively weak magnetic field, can provide a clear signature of Klein scattering in graphene. This effect is shown to be robust in the presence of spatially inhomogeneous potential of moderate strength.
We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, $Δ_1$ and $Δ_2$. We consider two main situations, $Δ_1=0,Δ_2\neq0$ and $Δ_1=-Δ_2$. They are different in a fundamental aspect: only the latter feature kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we…
We report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interferences, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively. It allows to confirm the existence of two nearly degenerate orbitals. At resonance, the transmission of the nanotube approaches unity, and the nanotube becomes noiseless, as observed in quantum point contacts. In this weak backscattering regime, the dependence of the noise on the ba…
The quantum transport formalism based on tight-binding models is known to be powerful in dealing with a wide range of open physical systems subject to external driving forces but is, at the same time, limited by the memory requirement's increasing with the number of atomic sites in the scattering region. Here we demonstrate how to achieve an accurate simulation of quantum transport feasible for experimentally sized bulk graphene heterojunctions at a strongly reduced computational cost. Without free tuning parameters, we show excellent agreement with a recent experiment on Klein backscattering …
We observe conductivity oscillations with aperiodic spacing to only one side of the tunneling current in a dual-gated graphene field effect transistor with an n-p-n type potential barrier. The spacing and width of these oscillatoins were found to be inconsistent with pure Farbry-Perot-type interferences, but are in quantitative agreement with theoretical predictions that attribute them to resonant tunneling through quasi-bound impurity states. This observation may be understood as another signature of Klein tunneling in graphene heterojunctions and is of importance for future development and m…
We fabricate a graphene p-n-p heterojunction and exploit the coherence of weakly-confined Dirac quasiparticles to resolve the underlying scattering potential using low temperature scanning gate microscopy. The tip-induced perturbation to the heterojunction modifies the condition for resonant scattering, enabling us to detect localized Fabry-Perot cavities from the focal point of halos in scanning gate images. In addition to halos over the bulk we also observe ones spatially registered to the physical edge of the graphene. Guided by quantum transport simulations we attribute these to modified r…
We study the role of Coulomb interaction in an electronic Fabry-Perot interferometer (FPI) realized with chiral edge states in the integer quantum Hall regime in the limit of weak backscattering. Assuming that a compressible Coulomb island in a bulk region of the FPI is formed, we develop a capacitance model which explains the plethora of experimental data on the flux and gate periodicity of conductance oscillations. It is also shown that a suppression of finite-bias visibility stems from a combination of weak Coulomb blockade and a nonequilibrium dephasing by the quantum shot noise.
Quantum-mechanical calculations of electron magneto-transport in ideal graphene nanoribbons are presented. In noninteracting theory, it is predicted that an ideal ribbon that is attached to wide leads should reveal Fabry-Perot conductance oscillations in magnetic field. In the theory with Coulomb interaction taken into account, the oscillation pattern should rather be determined by the Aharonov-Bohm interference effect. Both of these theories predict the formation of quasi-bound states, albeit of different structures, inside the ribbon because of strong electron scattering on the interfaces be…
The realization of p-n junctions in graphene, combined with the gapless and chiral nature of its massless Dirac fermions has led to the observation of many intriguing phenomena such as quantum Hall effect in bipolar regime, Klein tunneling, and Fabry-Pérot interferences all of which involve electronic transport across p-n junctions. Ballistic snake states propagating along the p-n junctions have been predicted to induce conductance oscillations, manifesting their twisting nature. However, transport studies along p-n junctions have so far only been performed in low mobility devices. Here, we re…
We investigate Fabry-Perot interference in an ultraclean carbon nanotube resonator. The conductance shows a clear superstructure superimposed onto conventional Fabry-Perot oscillations. A sliding average over the fast oscillations reveals a characteristic slow modulation of the conductance as a function of the gate voltage. We identify the origin of this secondary interference in intervalley and intravalley backscattering processes which involve wave vectors of different magnitude, reflecting the trigonal warping of the Dirac cones. As a consequence, the analysis of the secondary interference …
In mesoscopic electronic systems, the Fabry-Pérot (FP) oscillation is observed in various 1D devices. As for higher dimensions, numerous transverse channels usually lead to dephasing that quenches the overall oscillation of the conductance. Up to now, the FP oscillation in 2D electronic systems is only reported in graphene-based devices, and very recently, the \emph{pn} junctions of inverted InAs/GaSb double quantum well [Phys. Rev. X 10, 031007 (2020)]. In the latter, the band shape of a sombrero hat plays an essential role, which introduces a novel mechanism of electron-hole hybridization fo…
We present a detailed theoretical investigation of transport through a single-walled carbon nanotube (SWNT) in good contact to metal leads where weak backscattering at the interfaces between SWNT and source and drain reservoirs gives rise to electronic Fabry-Perot (FP) oscillations in conductance and shot noise. We include the electron-electron interaction and the finite length of the SWNT within the inhomogeneous Tomonaga-Luttinger liquid (TLL) model and treat the non-equilibrium effects due to an applied bias voltage within the Keldysh approach. In low-frequency transport properties, the TLL…
The superior intrinsic properties of graphene have been a key research focus for the past few years. However, external components, such as metallic contacts, serve not only as essential probing elements, but also give rise to an effective electron cavity, which can form the basis for new quantum devices. In previous studies, quantum interference effects were demonstrated in graphene heterojunctions formed by a top gate. Here phase coherent transport behavior is demonstrated in a simple two terminal graphene structure with clearly-resolved Fabry-Perot oscillations in sub-100 nm devices. By aggr…
We study the two-terminal transport properties of a metallic single-walled carbon nanotube with good contacts to electrodes, which have recently been shown [W. Liang et al, Nature 441, 665-669 (2001)] to conduct ballistically with weak backscattering occurring mainly at the two contacts. The measured conductance, as a function of bias and gate voltages, shows an oscillating pattern of quantum interference. We show how such patterns can be understood and calculated, taking into account Luttinger liquid effects resulting from strong Coulomb interactions in the nanotube. We treat back-scattering …
We analyze interference phenomena in the quantum-Hall analog of the Fabry-Perot interferometer, exploring the roles of the Aharonov-Bohm effect, Coulomb interactions, and fractional statistics on the oscillations of the resistance as one varies the magnetic field B and/or the voltage V_G applied to a side gate. Coulomb interactions couple the interfering edge mode to localized quasiparticle states in the bulk, whose occupation is quantized in integer values. For the integer quantum Hall effect, if the bulk-edge coupling is absent, the resistance exhibits an Aharonov-Bohm (AB) periodicity, wher…
Interference and tunneling are two signature quantum effects that are often perceived as the yin and yang of quantum mechanics: particle simultaneously propagating along several distinct classical paths versus particle penetrating through a classically inaccessible region via a single least-action path. Here we demonstrate that the Dirac quasiparticles in graphene provide a dramatic departure from this paradigm. We show that Zener tunneling in gapped bilayer graphene (BLG), which governs transport through p-n heterojunctions, exhibits common-path interference that takes place under the tunnel …
This work performs a numerical study of electron transport through the fundamental logic gate in valleytronics - a valley valve consisting of two or increasing number of valley filters. Various typical effects on the transport are investigated, such as those due to interface scattering, long- and short- range impurity scattering, edge roughness, strain, inter-filter spacing, or increasing number of valley filters. For illustration, we consider the class of specific valves built from graphene quantum wire valley filters in single layer or bilayer graphene, with the filters subject to separate c…
This article provides a pedagogical review on Klein tunneling in graphene, i.e. the peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two simple situations in detail: a massless Dirac electron incident either on a potential step or on a potential barrier and use elementary quantum wave mechanics to obtain the transmission probability. We emphasize the connection to related phenomena in optics, such as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot resonances, negative refraction index materials (the so called meta-materials), …
