Observation of perfect Andreev reflection due to Klein paradox in a topological superconducting state
Seunghun Lee, Valentin Stanev, Xiaohang Zhang, Drew Stasak, Jack Flowers, Joshua S. Higgins, Sheng Dai, Thomas Blum, Xiaoqing Pan, Victor M. Yakovenko, Johnpier… 展开作者
Seunghun Lee, Valentin Stanev, Xiaohang Zhang, Drew Stasak, Jack Flowers, Joshua S. Higgins, Sheng Dai, Thomas Blum, Xiaoqing Pan, Victor M. Yakovenko, Johnpierre Paglione, Richard L. Greene, Victor Galitski, Ichiro Takeuchi
In 1928, P. Dirac proposed a new wave equation to describe relativistic electrons. Shortly afterwards, O. Klein solved a simple potential step problem for the Dirac equation and stumbled upon an apparent paradox - the potential becomes transparent when the height is larger than the electron energy. For massless particles, backscattering is completely forbidden in Klein tunneling, leading to perfect transmission through any potential barrier. Recent advent of condensed matter systems with Dirac-like excitations, such as graphene and topological insulators (TIs), has opened the possibility of observing the Klein tunneling experimentally. In the surface states of TIs, fermions are bound by spin-momentum locking, and are thus immune to backscattering due to time-reversal symmetry. Here we report the observation of perfect Andreev reflection in point contact spectroscopy - a clear signature of Klein tunneling and a manifestation of the underlying relativistic physics of a proximity-induced superconducting state in a topological Kondo insulator.
Coupling of Klein-Andreev Resonant States in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$-graphene-Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ Devices
College of Nanoscale Science and Engineering, SUNY Polytechnic Institute（纽约州立大学波利技术学院纳米科学与工程）；College of Nanotechnology, Science, and Engineering, University at Albany, SUNY（纽约州立大学奥尔巴尼分校纳米技术科学与工程学院）；Department of Applied Physics, Aalto University（阿尔托大学应用物理系）；Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory（布鲁克海文国家实验室凝聚态物理与材料科学部）；Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文学系）
We investigate the Schrödinger (non-relativistic) and the Dirac (``relativistic") billiards in the universal regime. The study is based on a non-ideal quantum resonant scattering numerical simulation. We show universal results that reveal anomalous behavior on the conductance, on the shot-noise power and on the respective eigenvalues distributions. In particular, we demonstrate the Klein's paradox in the graphene and tunable suppression/amplification transitions on the typical observables of the quantum dots.
Reflection and transmission of electrons scattered by a rectangular potential step in the presence of an external magnetic field parallel to the electron beam is described with the use of the Dirac equation. It is shown that in addition to the known effects present in the so called Klein paradox, the presence of magnetic field gives rise to electron components with reversed spin in the reflected and transmitted beams. The spin-flip scattering processes are caused by the spin-orbit interaction activated by electric field of the potential step and transverse momentum components of electron motio…
Efficient manipulation of magnons for information processing is a central topic in spintronics and magnonics. An outstanding challenge for long-distance spin transport with minimal dissipation is to overcome the relaxation of magnons and to amplify the spin current they carry. Here, we propose to amplify magnon currents based on the realization of the bosonic Klein paradox in magnetic nanostructures. This paradox involves the magnon's antiparticle, the antimagnon, of which the existence is usually precluded by magnetic instabilities as it is an excitation at negative energy. We show that, by a…
After having derived boundary conditions for dressed-state electrons in a dice lattice, we investigate the electron tunneling through a square electrostatic potential barrier in both dice lattices and graphene under a linearly-polarized off-resonance and high-frequency dressing field, and demonstrate the anomalous Klein paradox for a nonzero incident angle, resulted from the misalignment of optically-controllable elliptical dispersion for Dirac-cone dressed states and the direction of incoming kinetic particles in our system. This finite incident angle is found depending on the type of light p…
It is supposed the existence of a curved graphene sheet with the geometry of a Bour surface $B_{n}$, such as the catenoid (or helicoid), $B_{0}$, and the classical Enneper surface, $B_{2}$, among others. In particular, in this work, the propagation of the electronic degrees of freedom on these surfaces is studied based on the Dirac equation. As a consequence of the polar geometry of $B_{n}$, it is found that the geometry of the surface causes the Dirac fermions to move as if they would be subjected to an external potential coupled to a spin-orbit term. The geometry-induced potential is interpr…
In the "ballistic" regime, the transport across a normal metal (N)/superconductor (S) point-contact is dominated by a quantum process called Andreev reflection. Andreev reflection causes an enhancement of the conductance below the superconducting energy gap, and the ratio of the low-bias and the high-bias conductance cannot be greater than 2 when the superconductor is conventional in nature. In this regime, the features associated with Andreev reflection also provide energy and momentum-resolved spectroscopic information about the superconducting phase. Here we theoretically consider various t…
We investigate the band structure of ABCA-tetralayer graphene (ABCA-TTLG) subjected to an external potential $V$ applied between top and bottom layers. Using the tight-binding model, including the nearest $t$ and next-nearest-neighbor $t'$ hopping, low-energy model and two-band approximation model we study the band structure variation along the lines $Γ-M-K-Γ$ in the first Brillouin zone, electronic band gap near Dirac point $K$ and transmission properties, respectively. Our results reveal that ABCA-TTLG exhibits markedly different properties as functions of $t'$ and $V$. We show that the hopp…
Unlike the more common local conductance spectroscopy, nonlocal conductance can differentiate between nontopological zero-energy modes localized around inhomogeneities, and true Majorana edge modes in the topological phase. In particular, negative nonlocal conductance is dominated by the crossed Andreev reflection. In graphene, the Andreev reflection and the inter-band Klein tunneling couple electron-like and hole-like states through the action of either a superconducting (SC) pair potential or an electrostatic potential. We are here probing quantum phenomena in modified graphitic samples. Fou…
The Andreev conductance across 2d normal metal (N)/superconductor (SC) junctions with relativistic Dirac spectrum is investigated theoretically in the Blonder-Tinkham-Klapwijk formalism. It is shown that for relativistic materials, due to the Klein tunneling instead of impurity potentials, the local strain in the junction is the key factor that determines the transparency of the junction. The local strain is shown to generate an effective Dirac $δ$-gauge field. A remarkable suppression of the conductance are observed as the strength of the gauge field increases. The behaviors of the conductanc…
Quantization Mapping on Dirac Dynamics via Voltage-Driven Charge Density in Monolayer Graphene: A Klein Paradox and Entropy-Ruled Wavevector Mechanics Study
KPR Institute of Engineering and Technology（KPR工程技术学院）
Klein tunneling and conductance for Dirac fermions in ABC-stacked trilayer graphene (ABC-TLG) through symmetric and asymmetric double potential barriers are investigated using the two and six-band continuum model. Numerical results for our system show that the transport is sensitive to the height, the width and the distance between the two barriers. Klein paradox at normal incidence and resonant features at non-normal incidence in the transmission result from resonant electron states in the wells or hole states in the barriers and strongly influence the ballistic conductance of the structures.
The Klein paradox, first introduced in relation to chiral tunneling, is also manifested in the study of bound-states in single-layer graphene with a 1D square-well potential. We derive analytic (and numerical) solutions for bound-state wavefunctions, in the absence and in the presence of an external transverse magnetic field, and calculate the corresponding dipole transition rates, which can be probed by photon absorption experiments. The role of parity and time-reversal symmetries is briefly discussed. Our results are also relevant for the physics of bound states of light in periodic optical …
We investigate the behavior of spin polarized currents in two-dimensional topological insulators (TI). Stationary solutions inside a HgTe/CdTe quantum well (QW) were obtained by Bernevig-Hughes-Zhang (BHZ) model modified by a electric and magnetic barrier inside a non-completely insulating bulk. An attenuated quantum spin Hall (QSH) effect occurs in the gaped region with an apparent Klein-like paradox. Even more interesting, for strong potential regime, the interaction between the quasiparticles and the barriers allows spin inversion of this electronic states in a distinct channel conduction. …
The Klein paradox consists in the perfect tunneling of relativistic particles through high potential barriers. As a curious feature of particle physics, it is responsible for the exceptional conductive properties of graphene. It was recently studied in the context of atomic condensates and topological photonics and phononics. While in theory the perfect tunneling holds only for normal incidence, so far the angular dependence of the Klein tunneling and its strong variation with the barrier height were not measured experimentally. In this work, we capitalize on the versatility of atomic vapor ce…
Superconductivity can be induced in a normal material via the leakage of superconducting pairs of charge carriers from an adjacent superconductor. This so-called proximity effect is markedly influenced by graphene unique electronic structure, both in fundamental and technologically relevant ways. These include an unconventional form of the leakage mechanism the Andreev reflection and the potential of supercurrent modulation through electrical gating. Despite the interest of high-temperature superconductors in that context, realizations have been exclusively based on low-temperature ones. Here …
We study the transmission probability of Dirac fermions in graphene scattered by a triangular double barrier potential in the presence of an external magnetic field. Our system made of two triangular potential barrier regions separated by a well region characterized by an energy gap. Solving our Dirac-like equation and matching the solutions at the boundaries allowed us to express our transmission and reflection coefficients in terms of transfer matrix. We show in particular that the transmission exhibits oscillation resonances that are manifestations of the Klein tunneling effect. The triangu…
Massless Dirac fermions in graphene provide unprecedented opportunities to realize the Klein paradox, which is one of the most exotic and striking properties of relativistic particles. In the seminal theoretical work [Katsnelson et al., Nat. Phys. 2 620 (2006)], it was predicted that the massless Dirac fermions can pass through one-dimensional (1D) potential barriers unimpededly at normal incidence. Such a result seems to preclude confinement of the massless Dirac fermions in graphene by using 1D potential barriers. Here, we demonstrate, both experimentally and theoretically, that massless Dir…
Transport properties of massive Dirac particles are investigated through an oscillating barrier. The Floquet quasienergies related to the time-dependent potential appear both in transmission and reflection as sidebands around the incoming electron's energy. We take all relevant sidebands into account and present time averaged transmission and reflection probabilities in a wide energy range. Most qualitative features of scattering on a static barrier -- like Klein paradox -- are still visible, but the transmission probability in the evanescent regime observably increases due to the oscillation …
Pseudospin, an additional degree of freedom inherent in graphene, plays a key role in understanding many fundamental phenomena such as the anomalous quantum Hall effect, electron chirality and Klein paradox. Unlike the electron spin, the pseudospin was traditionally considered as an unmeasurable quantity, immune to Stern-Gerlach-type experiments. Recently, however, it has been suggested that graphene pseudospin is a real angular momentum that might manifest itself as an observable quantity, but so far direct tests of such a momentum remained unfruitful. Here, by selective excitation of two sub…
Based on the transmission coefficient of tunneling electrons, we have presented tunneling current and conductivity across a square-potential barrier for both graphene and $α$-$\mathcal{T}_3$ lattices under a linearly-polarized off-resonant dressing field. The presence of such a dressing field introduces an anisotropy factor in the energy dispersion of tunneling electrons so that the cross section of a Dirac-cone appears as elliptical. Consequently, the field-polarization controlled major axis of the ellipse will be misaligned with the normal direction of a barrier layer in the tunneling system…
We study transport properties of a phosphorene monolayer in the presence of single and multiple potential barriers of height $U_0$ and width $d$, using both continuum and microscopic lattice models, and show that the nature of electron transport along its armchair edge ($x$ direction) is qualitatively different from its counterpart in both conventional two-dimensional electron gas with Schrödinger-like quasiparticles and graphene or surfaces of topological insulators hosting massless Dirac quasiparticles. We show that the transport, mediated by massive Dirac electrons, allows one to achieve co…
