Non-topological States Research Articles

Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice

Topological quantum interference emerges from the interplay between quantum mechanics and topology. We present evidence for two types of such interference phenomenon that can result from the quantum dynamics of initial topological states. We realize both types of topological quantum interference in a pumped non-Hermitian Su-Schrieffer-Heeger lattice that can be implemented by creation and coherent control of excitonic states of trapped neutral atoms. On quenching the system from the topological to the gapless phases and then back again, we find that interference patterns develop in the gapless phase and also after switching back to the topological phase. These patterns occur both as many-excitation interferences generated in the presence of pumping the atoms at the end sites, and as one- and two-excitation interferences seen in the absence of pumping when starting with edge excitations. Investigation of the excitation dynamics shows that these interference patterns originate from the topological nature of the initial states and are very different from quantum interferences originating from non-topological states of the lattice. Our results also reveal that unlike well-known situations where topological states are protected against local perturbations, in the non-Hermitian SSH systems resulting from driving the excited state populations, a local dissipation at each lattice site can suppress both the topological interference and the total population of the lattice.

Single-mode lasing based on PT -breaking of two-dimensional photonic higher-order topological insulator

Topological lasers are a new class of lasers that seek to exploit the special properties of topological states of light. A typical limiting factor in their performance is the existence of non-topological states with quality factors comparable to the desired topological states. We show theoretically that by distributing uniform gain and loss on two sublattices of a two-dimensional higher-order topological insulator (HOTI) lattice, single-mode lasing based on topological corner states can be sustained over a wide range of pump strengths. This behavior stems from the parity/time-reversal breaking of the topological corner states, which supplies them with more effective gain than the edge and bulk states, rather than through localized pumping of the domain corners. These results point to opportunities for exploiting non-Hermitian phenomena and designing compact high performance topological lasers.

Non-Hermitian gauged topological laser with multi protected modes

A topological laser array based on the non-Hermitian Su-Schrieffer-Heeger chain of coupled microring resonators has been presented in this manuscript. Based on the theory of the active and passive microrings in each unit cell, we have defined a PT-symmetry structure where the edge states can be protected and the imaginary gauge field cause delocalize light between the microrings. Numerical simulations based on the rate equation model and stability analysis have been performed to demonstrate the stability criteria of the presented structure. Utilizing this configuration, it has been shown that the number of protected topological supermodes can be controlled by the number of active and passive microrings in each unit cell while all the other extended supermodes are transformed into the non-topological states. Design flexibility to expand and modify the lasing stability region and topological supermode selection can be obtained based on the introduced configuration.

Full parity phase diagram of a proximitized nanowire island

We measure the charge periodicity of Coulomb blockade conductance oscillations of a hybrid InSb-Al island as a function of gate voltage and parallel magnetic field. The periodicity changes from $2e$ to $1e$ at a gate-dependent value of the magnetic field, $B^*$, decreasing from a high to a low limit upon increasing the gate voltage. In the gate voltage region between the two limits, which our numerical simulations indicate to be the most promising for locating Majorana zero modes, we observe correlated oscillations of peak spacings and heights. For positive gate voltages, the $2e$-$1e$ transition with low $B^*$ is due to the presence of non-topological states whose energy quickly disperses below the charging energy due to the orbital effect of the magnetic field. Our measurements demonstrate the importance of a careful exploration of the entire available phase space of a proximitized nanowire as a prerequisite to define future topological qubits.

Topological Transition of Superconductivity in Dirac Semimetal Nanowire Josephson Junctions.

We report the topological transition by gate control in a Cd_{3}As_{2} Dirac semimetal nanowire Josephson junction with diameter of about 64nm. In the electron branch, the quantum confinement effect enforces the surface band into a series of gapped subbands and thus nontopological states. In the hole branch, however, because the hole mean free path is smaller than the nanowire perimeter, the quantum confinement effect is inoperative and the topological property maintained. The superconductivity is enhanced by gate tuning from electron to hole conduction, manifested by a larger critical supercurrent and a larger critical magnetic field, which is attributed to the topological transition from gapped surface subbands to a gapless surface band. The gate-controlled topological transition of superconductivity should be valuable for manipulation of Majorana zero modes, providing a platform for future compatible and scalable design of topological qubits.

Detecting the Universal Fractional Entropy of Majorana Zero Modes.

A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is log2. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of 1/2log2 is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment by Hartman etal. [Nat. Phys. 14, 1083 (2018)10.1038/s41567-018-0250-5] to the case of a proximitized topological system hosting MZMs and propose a method to measure this 1/2log2 entropy change-an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non topological states.

Quantum anomalous Hall Majorana platform

We show that quasi-one-dimensional (1D) quantum wires can be written onto the surface of magnetic topological insulator (MTI) thin films by gate arrays. When the MTI is in a quantum anomalous Hall (QAH) state, MTI$/$superconductor quantum wires have especially broad stability regions for both topological and non-topological states, facilitating creation and manipulation of Majorana particles on the MTI surface.

Dynamical Buildup of a Quantized Hall Response from Nontopological States

We consider a two-dimensional system initialized in a topologically trivial state before its Hamiltonian is ramped through a phase transition into a Chern insulator regime. This scenario is motivated by current experiments with ultracold atomic gases aimed at realizing time-dependent dynamics in topological insulators. Our main findings are twofold. First, considering coherent dynamics, the nonequilibrium Hall response is found to approach a topologically quantized time-averaged value in the limit of slow but nonadiabatic parameter ramps, even though the Chern number of the state remains trivial. Second, adding dephasing, the destruction of quantum coherence is found to stabilize this Hall response, while the Chern number generically becomes undefined. We provide a geometric picture of this phenomenology in terms of the time-dependent Berry curvature.

Robustness of topological surface states against strong disorder observed inBi2Te3nanotubes

Three-dimensional topological insulators are characterized by Dirac-like conducting surface states, the existence of which has been confirmed in relatively clean metallic samples by angle-resolved photoemission spectroscopy, as well as by anomalous Aharonov-Bohm oscillations in the magnetoresistance of nanoribbons. However, a fundamental aspect of these surface states, namely, their robustness to time-reversal-invariant disorder, has remained relatively untested. In this work, we have synthesized thin nanotubes of $\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{3}$ with extremely insulating bulk at low temperatures due to disorder. Nonetheless, the magnetoresistance exhibits quantum oscillations as a function of the magnetic field along the axis of the nanotubes, with a period determined by the cross-sectional area of the outer surface. Detailed numerical simulations based on a recursive Green function method support that the resistance oscillations are arising from the topological surface states which have substantially longer localization length than that of other nontopological states. This observation demonstrates coherent transport at the surface even for highly disordered samples, thus providing a direct confirmation of the inherently topological character of surface states. The result also demonstrates a viable route for revealing the properties of topological states by suppressing the bulk conduction using disorder.

Vertical twinning of the Dirac cone at the interface between topological insulators and semiconductors.

Topological insulators are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of topological insulators have been well studied, the interface between topological insulators and semiconductors may not only be more technologically relevant, but the interaction with non-topological states may fundamentally alter the physics. Here, we present a general model to show that this type of interaction can lead to vertical twinning of the Dirac cone, whereby the hybridized non-spin-degenerate interfacial states cross twice as they span the bulk bandgap. This hybridization leads to spin-momentum locking of non-topological states with either helical (clockwise or anticlockwise) or even anti-helical (negative winding number) spin orientation depending on the parametization of the interaction. Model results are corroborated by first-principles calculations of the technologically relevant Bi2Se3 film van der Waals bound to a Se-treated GaAs substrate.

Disentangling Majorana fermions from topologically trivial low-energy states in semiconductor Majorana wires

Majorana fermions (MFs) are predicted to occur as zero-energy bound states in semiconductor nanowire-superconductor structures. However, in the presence of disorder or smooth confining potentials, these structures can also host nontopological nearly zero-energy states. Here, we demonstrate that the MFs and the nearly zero topologically trivial states have different characteristic signatures in a tunneling conductance measurement, which allows to clearly discriminate between them. We also show that low-energy nontopological states can strongly hybridize with metallic states from the leads, which generates the smooth background that characterizes the soft superconducting gap measured in tunneling experiments and produces an additional decoherence mechanism for the Majorana mode. Our results pave the way for the conclusive identification of MFs in a solid state system and provide directions for minimizing quantum decoherence in Majorana wires.