Tunneling In Graphene Research Articles

Ballistic transport and spin-dependent anomalous quantum tunneling in Rashba–Zeeman and bilayer graphene hybrid structures

In this work, we have studied the spin-dependent ballistic transport and anomalous quantum tunneling in bilayer graphene horizontally placed in between two Rashba–Zeeman (RZ) leads under external electric biasing. We investigated the transmission and conductance for the proposed system using scattering matrix formalism and the Landauer–Büttiker formula considering a double delta-like barrier under a set of experimentally viable parameters. We found that the transmission characteristics are notably different for up- and down-spin incoming electrons depending upon the strength of magnetization. Moreover, the transmission of up- and down-spin electrons is found to be magnetization orientation dependent. The maximum tunneling conductance can be achieved by tuning biasing energy and magnetization strength and choosing a material with suitable Rashba spin–orbit coupling (RSOC). This astonishing property of our system can be utilized in fabricating devices, such as spin filters. We found that the Fano factor of our system is 0.4 under strong magnetization conditions, while it reduces to 0.3 under low magnetization conditions. Moreover, we also noticed that the transmission and conductance significantly depend on the Rashba–Zeeman effect. Therefore, considering a suitable RZ material, the tunneling of the electrons can be tuned and controlled. Our result suggests that considering suitable strength and orientation of magnetization with moderate RSOC, one can obtain a different transmission probability for spin species under suitable biasing energy. These results indicate the suitability of the proposed system in fabrication of spintronic devices, such as spin filter, spin transistor, etc.

Magnetic field effect on tunneling through triple barrier in AB bilayer graphene

We investigate electron tunneling in AB bilayer graphene through a triple electrostatic barrier of heights Ui(i=2,3,4) subjected to a perpendicular magnetic field. By way of the transfer matrix method and using the continuity conditions at the different interfaces, the transmission probability is determined. Additional resonances appear for two-band tunneling at normal incidence, and their number is proportional to the value of U4 in in the case of U2<U4. However, when U2>U4, anti-Klein tunneling increases with U2. The transmission probability exhibits an interesting oscillatory behavior when U3>U2=U4 and U3<U2=U4. For fixed energy E=0.39γ1, increasing barrier widths increases the number of oscillations and decreases Klein tunneling. The interlayer bias creates a gap for U2<U3<U4 and U3>U2=U4. In the four-band tunneling case, the transmission decreases in T++, T+− and T−− channels in comparison with the single barrier case. It does, however, increase for T−+ when compared to the single barrier case. Transmission is suppressed in the gap region when an interlayer bias is introduced. This is reflected in the total conductance Gtot in the region of zero conductance. Our results are relevant for electron confinement in AB bilayer graphene and for the development of graphene-based transistors.

Probing the Inelastic Electron Tunneling via the Photocurrent in a Vertical Graphene van der Waals Heterostructure.

Inelastic electron tunneling (IET), accompanied by energy transfer between the tunneling charge carriers and other elementary excitations, is widely used to investigate the collective modes and quasiparticles in solid-state materials. In general, the inelastic contribution to the tunneling current is small compared to the elastic part and is therefore only prominent in the second derivative of the tunneling current with respect to the bias voltage. Here we demonstrate a direct observation of the IET by measuring the photoresponse in a graphene-based vertical tunnel junction device. Characteristic peaks/valleys are observed in the bias-voltage-dependent tunneling photocurrent at low temperatures, which barely shift with the gate voltage applied to graphene and diminish gradually as the temperature increases. By comparing with the second-order differential conductance spectra, we establish that these features are associated with the phonon-assisted IET. A simple model based on the photoexcited hot-carrier tunneling in graphene qualitatively explains the response. Our study points to a promising means of probing the low-energy elementary excitations utilizing the graphene-based van der Waals (vdW) heterostructures.

Realistic systems testing Klein tunneling in graphene: An ab initio calculations

We investigate the tunneling in monolayer graphene (MLG) through the potential barrier generated by the ribbons of Na, Cl and h-BN using the density functional theory (DFT) approach. Such an approach to the problem resulted in determining the shapes and parameters of the potential barriers in individual nanodevices in contrast to the tight binding (TB) approach where these parameters are assumed. In all systems we could observe the Klein tunneling features although under complex potential barrier/well profiles for some cases. The double barrier created in systems consisting of h-BN ribbons as overlayers/underlayers on graphene (h-BN/MLG/h-BN) allowed to analyze Klein tunnelling depending on the distance between two triangular barriers. The presented concept gives the possibility to measure the angular dependence of tunnelling and as such is of particular relevance to alternative/supplementary experiments to those related to observations of Klein tunnelling in graphene through potential barriers generated by applying a gate voltage.

Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene

In this paper, we have constructed a WKB approximation for graphene having a Y-shaped Kekulé lattice distortion and a special folding of the K and K′ valleys, which leads to very specific linear energy dispersions with two non-equivalent pairs of subbands. These obtained semi-classical results, which include the action, electron momentum and wave functions, are utilized to analyze the dynamics of electron tunneling through non-square potential barriers. In particular, we explore resonant scattering of an electron by a potential barrier built on Kekulé-distorted graphene. Mathematically, a group of consecutive equations for a semi-classical action have been solved by following a perturbation approach under the condition of small strain-induced coupling parameter Δ0≪1 (a good fit to its actual value Δ0∽ 0.1). Specifically, we consider a generalized model for Kek-Y graphene with two arbitrary Fermi velocities. The dependence of the electron transmission amplitude on the potential profile V(x) and band parameters of Kekulé-patterned graphene has been explored and analyzed in detail.

Carrier Dynamics for the Collective Resonant Tunneling in Quantum Dot-Based Artificial Graphene

Carrier Dynamics for the Collective Resonant Tunneling in Quantum Dot-Based Artificial Graphene

Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe2

Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the WSe$_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

Klein-Like Tunneling of Sound via Negative Index Metamaterials

Klein tunneling is a counterintuitive quantum-mechanical phenomenon, predicting perfect transmission of relativistic particles through higher-energy barriers. This phenomenon was shown to be supported at normal incidence in graphene due to pseudospin conservation. Here I show that Klein-tunneling analogy can occur in classical systems, and remarkably, does not rely on mimicking graphene's spinor wave-function structure. Instead, the mechanism requires a particular form of constitutive parameters of the penetrated medium, yielding transmission properties identical to the quantum tunneling in graphene. I demonstrate this result by simulating tunneling of sound in a two-dimensional acoustic metamaterial. More strikingly, I show that by introducing a certain form of anisotropy, the tunneling can be made unimpeded for any incidence angle, while keeping most of its original Klein dispersion properties. This phenomenon may be denoted by the omnidirectional Klein-like tunneling. The suggested tunneling mechanism and its omnidirectional variant may be useful for applications requiring lossless and direction-independent transmission of classical waves.

Subband-resolved momentum-conserved resonant tunneling in monolayer graphene/h-BN/ABA-trilayer graphene small-twist-angle tunneling device

We demonstrate twist-controlled resonant tunneling in a monolayer graphene (MLG)/hexagonal boron nitride (h-BN)/ABA-stacked trilayer graphene (TLG) van der Waals (vdW) junction, in which MLG and TLG flakes are aligned with a small twist angle θ of ∼1.05° between their crystallographic orientations through a thin h-BN barrier. Owing to the small interlayer twist, resonant tunneling attributed to the conservation of momentum and energy was observed between the single linear band of MLG and multiple subbands of TLG. We show that different subbands of TLG—bilayer-graphene-like subbands and a MLG-like subband—exhibit distinctly different resonant tunneling behaviors. Therefore, we demonstrate subband-resolved resonant tunneling. This technique provides a method to determine band parameters (Slonczewski–Weiss–McClure parameters) and probes the band dispersion of different two-dimensional materials by utilizing a MLG electrode.

Coherent-scatterer enhancement and Klein-tunneling suppression by potential barriers in gapped graphene with chirality-time-reversal symmetry

We have utilized the finite-difference approach to explore electron-tunneling properties in gapped graphene through various electrostatic-potential barriers ranging from Gaussian to a triangular envelope function in comparison with a square potential barrier. The transmission coefficient is calculated numerically for each case and applied to the corresponding tunneling conductance. It is well known that Klein tunneling in graphene will be greatly reduced in gapped graphene. Our results further demonstrate that such a decrease of transmission can be significantly enhanced for spatially-modulated potential barriers. Moreover, we investigate the effect from a bias field applied to those barrier profiles, from which we show that it enables the control of electron flow under normal incidence. Meanwhile, the suppression of Klein tunneling is found more severe for a non-square barrier and exhibits a strong dependence on bias-field polarity for all kinds of barriers. Finally, roles of a point impurity on electron transmission and conductance are analyzed with a sharp peak appearing in electron conductance as the impurity atom is placed in the middle of a square barrier. For narrow triangular and Gaussian barriers, however, the conductance peaks become significantly broadened, associated with an enhancement in tunneling conductance.

Enhanced Andreev reflection in Kekulé-Y patterned graphene

We theoretically investigate the electron-hole conversions in normal metal-superconductor junctions based on the Kekul\'e-Y (Kek-Y) patterned graphene. It is shown that, in contrast to the Klein tunneling in the pristine graphene, the perfect Andreev reflection with almost unit efficiency can be extended to a large range of incident angles in the Kek-Y patterned graphene in single-Dirac cone phase with the bias voltage in the gap. The normalized zero-bias conductance is also obtained.

Tunneling in an anisotropic cubic Dirac semi-metal

Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo)3, we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate effects from different contributions to the Hamiltonian we study the model in various limits. First, in the limit of a very thin film material where the linearly dispersive z-direction is frozen out at zero momentum and the dispersion in the x–y plane is rotationally symmetric. In this limit we find a Klein tunneling reminiscent of what is observed in single layer graphene and linearly dispersive Dirac semi-metals. Second, an increase in thickness of the material leads to the possibility of a non-zero momentum eigenvalue kz that acts as an effective mass term in the Hamiltonian. We find that these lead to a suppression of Klein tunneling. Third, the inclusion of an anisotropy parameter λ≠1 leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle θ and anisotropy parameter λ the Hamiltonian supports different numbers of modes propagating to infinity. We display this effect in form of a diagram that is similar to a phase diagram of a distant detector. Fourth, we consider coexistence of both anisotropy and non-zero kz but do not find any effect that is unique to the interplay between non-zero momentum kz and anisotropy parameter λ. Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling T−1∝θ6+O(θ8) that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where T−1∝θ2+O(θ4).

Anisotropic pseudospin tunneling in two-dimensional black phosphorus junctions

We investigate the role of pseudospin structure of few-layer black phosphorus (BP) in interband tunneling properties in lateral BP junctions. We find that interband tunneling is critically dependent on junction directions because of the anisotropic pseudospin structure of BP. When the armchair direction of BP is normal to the interface, pseudospins of incident and transmitted carriers are nearly aligned so that interband tunneling is highly effective, analogous to the Klein tunneling in graphene. However, when the zigzag direction is normal to the interface, interband tunneling is suppressed by misaligned pseudospins. We also study junctions of band-gap inverted BP where the electronic structure is characterized by two Dirac cones. In this case, intervalley tunneling is prohibited either by momentum conservation or by pseudospin mismatch while intravalley tunneling is Klein-like irrespective of the junction direction. These results provide a foundation for developing high-performance devices from BP and other pseudospin materials.

Chiral tunneling in single-layer graphene with Rashba spin-orbit coupling: Spin currents

We study forward scattering of 2D massless Dirac electrons at Fermi energy {\varepsilon} > 0 in single layer graphene through a 1D rectangular barrier of height {u_0} in the presence of uniform Rashba spin-orbit coupling (of strength {\lambda}). The role of the Klein paradox in graphene spintronics is thereby exposed. It is shown that (1) For {\varepsilon} - 2{\lambda} < {u_0}< {\varepsilon} + 2{\lambda} there is partial Klein tunneling, wherein the transmission is bounded by 1 and, quite remarkably, for small {\lambda} > {\lambda_0} {\approx} 0.1 meV, the transmission nearly vanishes when the scattering energy equals the barrier height, {\varepsilon}={u_0}. (2) Spin density and spin-current density are shown to be remarkably different than these observables predicted in bulk single layer graphene. In particular, they are sensitive to {\lambda} and {u_0}. (3) Spin current densities are space dependent, implying the occurrence of non-zero spin torque density. Such a system may serve as a graphene based spintronic device without the use of an external magnetic field or magnetic materials.

Higher-Order Topological Corner State Tunneling in Twisted Bilayer Graphene

Higher-order topological insulator is a newly discovered topological material, characterized by the topological corner states. In this work, we propose quantum oscillation that identifies the two-dimensional higher-order topological phase in twisted bilayer graphene systems. We use an instanton approach to argue that the tunneling of electrons between the topological corner states of the higher-order topological insulator generally causes the gate-tunable oscillation in the energy spectra. The oscillatory nodes signal the perfect suppression of the tunneling, which features the topological nature of the corner states. In the view of experimental realization, we propose the transport experiment that can readily observe the oscillation. Our work provides a feasible route to identify higher-order topological materials in twisted bilayer graphenes.

Wigner model for Klein tunneling in graphene

Quantum corrections to the electron-hole motion in graphene are investigated by applying the multiband Wigner approach. A diagonalization procedure regarding the pseudo-spin degree of freedom is proposed. The resulting formulation of the equation of motion reveals to be particularly close to the classical description of the particle motion. This formal analogy offers a framework in which quantum phenomena can be described with a classical language and the question of the quantum-classical correspondence can be directly investigated. Some numerical results are presented showing the ability of our quasi-diagonal Wigner model to reproduce Klein tunneling in graphene under the application of an external electric field.

Spatial confinement, magnetic localization, and their interactions on massless Dirac fermions

It is of keen interest to researchers understanding different approaches to confine massless Dirac fermions in graphene, which is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene p-n boundaries with an angle 34. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in the graphene wedge into Landau levels (LLs). The spatial confinement of the wedge affects the Landau quantization, which enables us to experimentally measure the spatial extent of the wave functions of the LLs. The magnetic fields induce a sudden and large increase in energy of the quasibound states because of a pi Berry phase jump of the massless Dirac fermions in graphene. Such a behavior is the hallmark of the Klein tunneling in graphene. Our experiment demonstrated that the angled wedge is a unique system with the critical magnetic fields for the pi Berry phase jump depending on distance from summit of the wedge.

Electronic transport and Klein tunneling in gapped AA-stacked bilayer graphene

We theoretically investigate the electronic transport and Klein tunneling in AA-stacked bilayer graphene (AA-BLG) encapsulated by dielectric materials. Using the four-band continuum model, we evaluate the transmission and reflection probabilities along with the respective conductances. We find that the interlayer mass-term difference induced by the dielectric materials opens a gap in the energy spectrum and couples the upper and lower Dirac cones in AA-BLG. This cone coupling induces an inter-cone transport that is asymmetric with respect to the normal incidence in the presence of the asymmetric mass-term. The energy spectrum of the gapped AA-BLG exhibits electron-hole asymmetry that is reflected in the associated intra- and inter-cone transport channels. We also find that even though Klein tunneling exists in gated and biased AA-BLG, it is precluded by the interlayer mass-term difference and instead Fabry-Pérot resonances appear.

Electron scattering in gapped graphene quantum dots

Due to Klein tunneling in graphene only quasi-bound states are realized in graphene quantum dots by electrostatic gating. Particles in the quasi-bound states are trapped inside the dot for a finite time and they keep bouncing back and forth till they find their way out. Here we study the effect of an induced gap on the scattering problem of Dirac electrons on a circular electrostatically confined quantum dot. Introducing an energy gap inside the quantum dot enables us to distinguish three scattering regimes instead of two in the case of gapless graphene quantum dot. We will focus on these regimes and analyze the scattering efficiency as a function of the electron energy, the dot radius and the energy gap. Moreover, we will discuss how the system parameters can affect the scattering resonances inside the dot.

Andreev tunneling and Josephson current in light irradiated graphene

We investigate the Andreev tunneling and Josephson current in graphene irradiated with high-frequency linearly polarized light. The corresponding stroboscopic dynamics can be solved using Floquet mechanism which results in an effective stationary theory to the problem exhibiting an anisotropic Dirac spectrum and modified pseudospin-momentum locking. When applied to an irradiated normal graphene - superconductor (NS) interface, such analysis reveal Andreev reflection (AR) to become an oscillatory function of the optical strength. Specifically we find that, by varying the polarization direction we can both suppress AR considerably or cause the Andreev transport to remain maximum at sub-gap excitation energies even in the presence of Fermi level mismatch. Furthermore, we study the optical effect on the Andreev bound states (ABS) within a short normal-graphene sheet, sandwiched between two s-wave superconductors. It shows redistribution of the low energy regime in the ABS spectrum, which in turn, has major effect in shaping the Josephson super-current. Subjected to efficient tuning, such current can be sufficiently altered even at the charge neutrality point. Our observations provide useful feedback in regulating the quantum transport in Dirac-like systems, achieved via controlled off-resonant optical irradiation on them.