Quantized Conductance Plateaus Research Articles

Differential current noise as an identifier of Andreev bound states that induce nearly quantized conductance plateaus

Differential current noise as an identifier of Andreev bound states that induce nearly quantized conductance plateaus

Topological properties in an Aubry–André–Harper model with p-wave superconducting pairing

Abstract We study the topological properties of the one-dimensional p-wave Aubry–André–Harper (AAH) model with periodic incommensurate potential and transition coupling. The calculation results show that due to co-influence of the incommensurate potential and modulation phase, three topological phases arise in different parameter regions: a topologically trivial phase, Su–Schrieffer–Heeger (SSH)-like topological phase, and Kitaev-like topological superconducting phase with Majorana zero modes. By evaluating the Andreev reflection conductance, we see that in the Kitaev-like phase, the quantized conductance plateau comes into being at the zero-bias limit, due to the occurrence of resonant Andreev reflection. In addition, when the disorder effect is incorporated, the SSH-like topology is modified sensitively and the degenerate topological states split, whereas the Kitaev-like topological phase is robust to weak disorder. Finally, we find that disorder can induce topological phase transition, i.e. from the topologically trivial phase to the topological phase. Based on these results, we believe that our findings have significance for studying the topological phase transition in a one-dimensional topological superconducting system. Also, it provides a feasible scheme for clarifying different topological phases.

Transport through quantum anomalous Hall bilayers with lattice mismatch

We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in two layers), the inter-layer coupling results in resonant traversing between forward propagating waves in two layers. In the case of generic ratios, there is a quantized conductance plateau originated from two Chern numbers associated with two layers. However, the phase boundary of this quantization plateau consists of a fractal transitional region (instead of a clear transition line) of interpenetrating edge states (with quantized conductance) and bulk states (with unquantized conductance). We attribute these bulk states as mismatch induced in-gap bulk states. Different from in-gap localized states induced by random disorder, these in-gap bulk states are extended in the limit of vanishing random disorder. However, the detailed fine structure of this transitional region is sensitive to disorder, lattice structure, sample size, and even the configuration of leads connecting to it, due to the bulk and topologically trivial nature of these in-gap bulk states.

Chern insulator in a hyperbolic lattice

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and the research interest in the non-Euclidean generalization of topological phenomena, we investigate the Chern insulator phases in a hyperbolic $\{8,3\}$ lattice, which is made from regular octagons ($8$-gons) such that the coordination number of each lattice site is $3$. Based on the conformal projection of the hyperbolic lattice into the Euclidean plane, i.e., the Poincar\'{e} disk model, by calculating the Bott index ($B$) and the two-terminal conductance, we reveal two Chern insulator phases (with $B=1$ and $B=-1$, respectively) accompanied with quantized conductance plateaus in the hyperbolic $\{8,3\}$ lattice. The numerical calculation results of the nonequilibrium local current distribution further confirm that the quantized conductance plateau originates from the chiral edge states and the two Chern insulator phases exhibit opposite chirality. Moreover, we explore the effect of disorder on topological phases in the hyperbolic lattice. It is demonstrated that the chiral edge states of Chern insulators are robust against weak disorder in the hyperbolic lattice. More fascinating is the discovery of disorder-induced topological non-trivial phases exhibiting chiral edge states in the hyperbolic lattice, realizing a non-Euclidean analog of topological Anderson insulator. Our work provides a route for the exploration of topological non-trivial states in hyperbolic geometric systems.

Quantized and unquantized zero-bias tunneling conductance peaks in Majorana nanowires: Conductance below and above 2e2/h

Majorana zero modes can appear at the wire ends of a 1D topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states and low-energy Andreev bound states arising from smooth potential variations, and disorder-induced subgap bound states. Our focus is on the conductance peak value (i.e., equal to, greater than, or less than $2e^2/h$), as well as the robustness (plateau- or spike-like) against the tuning parameters (e.g., the magnetic field and tunneling gate voltage) for zero-bias peaks arising from the different mechanisms. We find that for Majoranas and quasi-Majoranas, the zero-bias peak values are no more than $2e^2/h$, and a quantized conductance plateau forms generically as a function of parameters. By contrast, for conductance peaks due to low-energy Andreev bound states or disorder-induced bound states, the peak values may exceed $2e^2/h$, and a conductance plateau is rarely observed unless through careful postselection and fine-tuning. Our findings should shed light on the interpretation of experimental measurements on the tunneling spectroscopy of normal-superconductor junctions of hybrid Majorana nanowires.

Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal

The quest for the topological phases of matter in an aperiodic system has been greatly developed recently. Here we investigate the effects of disorder on topological phases of a two-dimensional Ammann-Beenker tiling quasicrystalline lattice. For comparison purposes, we also consider the case of a periodic snub-square crystalline lattice, which has the same primitive tiles as the Ammann-Beenker tiling quasicrystalline lattice. By calculating the spin Bott index and the two-terminal conductance, we confirm that the topological phases with disorder share the similar properties in the two systems which possess different symmetry and periodicity. It is shown that the quantum spin Hall states are robust against weak disorder in both the quasicrystalline lattice and the crystalline lattice. More interesting is that topological Anderson insulator phases induced by disorder appear in the two systems. Furthermore, the quantized conductance plateau contributed by the topological Anderson insulator phase is verified by the distribution of local currents.

Quantum transport in Chern insulators on Möbius strips

Chern insulators (CIs) or quantum anomalous Hall (QAH) states have drawn more attention, with emergence of quantized Hall conductance but in absence of Landau levels. Here, we study the Haldane-type CI/QAH states on Möbius strips and focus on the quantum transport properties. The Möbius strips can be constructed from the twisted honeycomb-lattice strips with domain walls. Topological properties of the Möbius CI/QAH states can be identified by the local density of states, the real-space Chern numbers and the transport properties. Nearly perfect quantized conductance plateaus are observed in the numerical quantum-transport simulations. In addition, we found that adding magnetic flux in domain walls can induce alternating edge states. At last, we discussed in details the different lead connection schemes, and found that we can use multiple domain walls to obtain various higher quantized conductance plateaus.

Transport properties and typical electron orbits in 2DEG under a local gradient magnetic field

Local current information in nanodevices is very helpful for good understanding the fundamental physical phenomena. In this work, the electron motion in 2DEG under a local gradient magnetic field is studied by the recursive non-equilibrium green's function method. The considered structure is a sandwiched configuration, lead-device-lead. For clearly observing the electron trajectories, we use the wide and narrow leads to contact the device respectively. The results show that in wide lead case, the quantized conductance plateaus with oscillations are found. These oscillations might be related to the resonant transmission in longitudinal electronic states. We also observe several typical snake electron orbits when the corresponding incident energy locates at the odd conductance plateaus, because there is exactly one opened transport channel around the horizontal middle line of device. When we shrink the width of leads and let electrons inject only from the lower half of device, the conductance suppression is very significant due to the energy level broadening in center device. In this case, we can find clear S-shape and 8-shape electron orbits at a very wide range of energy. These results can help us to understand the basic physics in 2D electron systems and may guide the design of future photoelectric device.

Emergent Z2 topological invariant and robust helical edge states in two-dimensional topological metals

In this work, we study the disorder effect on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall (QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent $Z_2$ topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in {various transport experiments on QSH materials} that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.

Electromigration-induced directional steps towards the formation of single atomic Ag contacts.

Even though there have been many experimental attempts and theoretical approaches to understand the process of electromigration (EM), it has not been quantitatively understood for ultrathin structures and at grain boundaries. Nevertheless, we showed recently that it can be used reliably for the formation of single atomic point contacts after careful pre-structuring of the initial Ag nanostructures. The process of formation of nanocontacts by EM down to a single-atom point contact was investigated for ultrathin (5 nm) Ag structures at 100 K by measuring the conductance as a function of the time during EM. In this paper, we compare the process of thinning by EM of structures with constrictions below the average grain size of Ag layers (15 nm) with that of structures with much larger initial constrictions of around 150 nm having multiple grains at the centre constriction prior to the formation of a point contact. Even though clear morphological differences exist between both types of structures, quantized conductance plateaus showing the formation of single point contacts have been observed for both. Here we put emphasis on the thinning process by EM, just before a point contact is formed. To understand this thinning process, the semi-classical regime before the contact reaches the quantum regime was analyzed in detail. For this purpose, we used experimental conductance histograms in the range between 2G0 and 15G0 and their corresponding Fourier transforms (FTs). The FT analysis of the conductance histograms exhibits a clear preference for thinning along the [100] direction. Using well-established models, both atom-by-atom steps and ranges of stability, presumably caused by electronic shell effects, can be discriminated. Although the directional motion of atoms during EM leads to specific properties such as the instabilities mentioned, similarities to mechanically opened contacts with respect to cross-sectional stability were found.

Conductance quantization and shot noise of a double-layer quantum point contact

The conductance quantization and shot noise below the first conductance plateau $G_0 = 2e^2/h$ are measured in a quantum point contact fabricated in a GaAs/AlGaAs tunnel-coupled double quantum well. From the conductance measurement, we observe a clear quantized conductance plateau at $0.5G_0$ and a small minimum in the transconductance at $0.7 G_0$. Spectroscopic transconductance measurement reveals three maxima inside the first diamond, thus suggesting three minima in the dispersion relation for electric subbands. Shot noise measurement shows that the Fano factor behavior is consistent with this observation. We propose a model that relates these features to a wavenumber directional split subband due to a strong Rashba spin--orbit interaction that is induced by the center barrier potential gradient of the double-layer sample.

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor.

Majorana zero modes (MZMs) are spatially localized, zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold promise for topological quantum computing. Owing to the particle-antiparticle equivalence, MZMs exhibit quantized conductance at low temperature. By using variable-tunnel-coupled scanning tunneling spectroscopy, we studied tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e 2/h quantum conductance (where e is the electron charge and h is Planck's constant). By contrast, no plateaus were observed on either finite energy vortex bound states or in the continuum of electronic states outside the superconducting gap. This behavior of the zero-mode conductance supports the existence of MZMs in FeTe0.55Se0.45.

Topological Anderson insulator phase in a quasicrystal lattice

Motivated by the recent experimental realization of the topological Anderson insulator and research interest on the topological quasicrystal lattices, we investigate the effects of disorder on topological properties of a two-dimensional Penrose-type quasicrystal lattice that supports the quantum spin Hall insulator (QSHI) and normal insulator (NI) phases in the clean limit. It is shown that the helical edge state of the QSHI phase is robust against weak disorder. Most saliently, it is found that disorder can induce a phase transition from NI to QSHI phase in the quasicrystal system. The numerical results based on a two-terminal device show that a quantized conductance plateau can arise inside the energy gap of NI phase for moderate Anderson disorder strength. Further, it is confirmed that the local current distributions of the disorder-induced quantized conductance plateau are located on the two edges of sample. Finally, we identify this disorder-induced phase as topological Anderson insulator phase by computing the disorder-averaged spin Bott index.

Quantum interference of Josephson current in topological Anderson insulator junctions

We investigate the critical supercurrent in Josephson junctions consisting of topological Anderson insulators (TAIs) via the Matsubara Green’s function formalism. Our numerical results show that the disorder-induced edge states display distinct differences in dominating normal and supercurrent transport in the TAI phase. Unlike the hallmark of the TAI phase which exhibits a quantized conductance plateau, the critical supercurrent over the disorder strength exhibits a peak structure where the maximum value is reached at the weak-disorder boundary of the TAI phase. Although the magnitude of the averaged critical supercurrent is suppressed with increasing disorder strength, periodic oscillations of the supercurrent on an external magnetic flux survive in the TAI phase. These findings indicate that the supercurrent quantum interference effect can be an effective probe in detecting the emergence of disorder-induced edge state in TAIs.

Photomodulated edge states and multiterminal transport in silicenelike nanoribbons

We study the band structures and time-averaged transport properties of the Floquet systems irradiated by variously polarized monochromatic light theoretically based on the Floquet-Green's function method. It reveals that the circularly polarized light can generate the anisotropic chiral edge modes and the polarization of light further manipulates these modes by altering their spatial distributions and spin orientations. Benefitting from external electric and exchange fields, the valley polarizations and band gaps can be induced to implement a variety of exotic photo-dressed topological phases. Furthermore, the circularly polarized light modifies the spin-resolved dc conductance remarkably, giving rise to a highly spin-polarized transport in the bulk band-gap regime. The short-range disorder manifests itself by forming a conductance arc symmetrically with respect to zero energy as well as a half-integer quantized conductance plateau in the two-terminal Floquet devices. The transverse dc conductance in T-shape devices is sensitive to the polarization of light; namely, the left-circularly polarized light minimizes the transverse conductance while the right-handed one greatly enhances it by inverting the moving directions of the edge modes. The strong correlation between the spin and light polarizations offers us a feasible tool to either realize devices in spintronic or detect the polarization of monochromatic light by simple transport measurements.

Crossover from Coulomb blockade to ballistic transport in InAs nanowire devices

We report on the observation of a crossover from the single electron Coulomb blockade regime to the ballistic transport in individual InAs semiconducting nanowire devices. The InAs nanowires studied here were grown by molecular-beam epitaxy (MBE), which provides a clean system to study the intrinsic electrons transport in a quasi-one-dimensional system. Quantized conductance plateaus are observed for an InAs nanowire-based device by changing the Fermi level with a global back gate at low temperature, suggesting the ballistic transport of electrons. Further lowering the temperature, we observe the Coulomb blockade phenomenon with the formation of the quantum dot between the two normal metal contacts. By increasing the electron density, the characteristic Fabry–Pérot oscillations are observed, which further provides evidence for the ballistic nature of transport in the InAs nanowire device. Our observations indicate that high-quality InAs nanowires grown by MBE behave as clean quantum wires at low temperatures, which enables us to investigate novel phenomena in the quasi-one-dimensional system.

Quantized zero-bias conductance plateau in semiconductor-superconductor heterostructures without topological Majorana zero modes

We show that partially separated Andreev bound states (ps-ABSs), comprised of pairs of overlapping Majorana bound states (MBSs) emerging in quantum dot-semiconductor-superconductor heterostructures, produce robust zero bias conductance plateaus in end-of-wire charge tunneling experiments. These plateaus remain quantized at $2e^2/h$ over large ranges of experimental control parameters. In light of recent experiments reporting the observation of robust $2e^2/h$-quantized conductance plateaus in local charge tunneling experiments, we perform extensive numerical calculations to explicitly show that such quantized conductance plateaus, which are obtained by varying control parameters such as the tunnel barrier height, the super gate potential, and the applied magnetic field, can arise as a result of the existence of ps-ABSs. Because ps-ABSs can form rather generically in the topologically trivial regime, even in the absence of disorder, our results suggest that the observation of a robust quantized conductance plateau does not represent sufficient evidence to demonstrate the existence of non-Abelian topologically-protected Majorana zero modes localized at the opposite ends of a wire.

Noise signatures for determining chiral Majorana fermion modes

The conductance measurement of a half quantized plateau in a quantum anomalous Hall insulator-superconductor structure is reported by a recent experiment [Q. L. He \textit{et al.}, Science 357, 294-299 (2017)], which suggests the existence of the chiral Majorana fermion modes. However, such half quantized conductance plateau may also originates from a disorder-induced metallic phase. To identify the exact mechanism, we study the transport properties of such a system in the presence of strong disorders. Our results show that the local current density distributions of these two mechanisms are different. In particular, the current noises measurement can be used to distinguish them without any further fabrication of current experimental setup.

Quantized Majorana conductance.

Majorana zero-modes-a type of localized quasiparticle-hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e2/h, with a recent observation of a peak height close to 2e2/h. Here we report a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.

Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures

A weak superconducting proximity effect in the vicinity of the topological transition of a quantum anomalous Hall system has been proposed as a venue to realize a topological superconductor (TSC) with chiral Majorana edge modes (CMEMs). A recent experiment [Science 357, 294 (2017)] claimed to have observed such CMEMs in the form of a half-integer quantized conductance plateau in the two-terminal transport measurement of a quantum anomalous Hall-superconductor junction. Although the presence of a superconducting proximity effect generically splits the quantum Hall transition into two phase transitions with a gapped TSC in between, in this Rapid Communication we propose that a nearly flat conductance plateau, similar to that expected from CMEMs, can also arise from the percolation of quantum Hall edges well before the onset of the TSC or at temperatures much above the TSC gap. Our Rapid Communication, therefore, suggests that, in order to confirm the TSC, it is necessary to supplement the observation of the half-quantized conductance plateau with a hard superconducting gap (which is unlikely for a disordered system) from the conductance measurements or the heat transport measurement of the transport gap. Alternatively, the half-quantized thermal conductance would also serve as a smoking-gun signature of the TSC.