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Register a new userQuantum Hall edge states under periodic driving: a Floquet induced chirality switch
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Added by
Angiolo Huaman Mgter
Publication date
2020
fields
Physics
and research's language is
English
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We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multi-terminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at $pm,hbarOmega/2$ lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, where two terms cancel out exactly. More interestingly, we show that near the Dirac point changing the laser polarization (circular right or circular left) controls the Hall conductance, by allowing to switch it on or off, or even by flipping its sign, thereby reversing the chirality of the edge states. This might lead to new avenues to fully control topologically protected transport.
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Indium Arsenide (InAs) near surface quantum wells (QWs) are ideal for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance. We analyze the experimental data using the Landauer-B{u}ttiker formalism, generalized to allow for Andreev reflection processes. Our analysis is consistent with a lower-bound for the averaged Andreev conversion of about 15%. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.
Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here we shed further light on the nature of these modes by analyzing a simple type of periodic driving where the hopping along one spatial direction is modulated sinusoidally with time while the hopping along the other spatial direction is kept constant. We obtain the phase diagram for the quasienergy spectrum at flux 1/3 as the driving frequency $omega$ and the hopping anisotropy are varied. A series of topologically distinct phases with counter-propagating edge modes appear due to the harmonic driving, similar to the case of a periodically kicked system studied earlier. We analyze the time dependence of the pair of Floquet edge states localized at the same edge, and compare their Fourier components in the frequency domain. In the limit of small modulation, one of the Floquet edge mode within the pair can be viewed as the edge mode originally living in the other energy gap shifted in quasienergy by $hbar omega$, i.e., by absorption or emission of a photon of frequency $omega$. Our result suggests that counter-propagating Floquet edge modes are generic features of periodically driven integer quantum Hall systems, and not tied to any particular driving protocol. It also suggests that the Floquet edge modes would remain robust to any static perturbations that do not destroy the chiral edge modes of static quantum Hall states.
We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias voltage applied to the neighboring quantum point contact, which originates from the Luttinger liquid physics which describes the Hall fluid. General expressions are obtained using a screened Coulomb interaction. The dephasing rate is strictly proportional to the zero frequency backscattering current noise, which allows to describe exactly the weak to strong backscattering crossover using the Bethe-Ansatz solution.
Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material which becomes a quantum spin Hall insulator when the well width exceeds d_{C}=6.3 nm. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. These results provide evidence for superconductivity induced in the helical edges of the quantum spin Hall effect, a promising step toward the demonstration of one-dimensional topological superconductivity. Our results also provide a direct measurement of the widths of these edge channels, which range from 180 nm to 408 nm.
Topological superconductors represent a phase of matter with nonlocal properties which cannot smoothly change from one phase to another, providing a robustness suitable for quantum computing. Substantial progress has been made towards a qubit based on Majorana modes, non-Abelian anyons of Ising ($Z_2$) topological order whose exchange$-$braiding$-$produces topologically protected logic operations. However, because braiding Ising anyons does not offer a universal quantum gate set, Majorana qubits are computationally limited. This drawback can be overcome by introducing parafermions, a novel generalized set of non-Abelian modes ($Z_n$), an array of which supports universal topological quantum computation. The primary route to synthesize parafermions involves inducing superconductivity in the fractional quantum Hall (fqH) edge. Here we use high-quality graphene-based van der Waals devices with narrow superconducting niobium nitride (NbN) electrodes, in which superconductivity and robust fqH coexist. We find crossed Andreev reflection (CAR) across the superconductor separating two counterpropagating fqH edges which demonstrates their superconducting pairing. Our observed CAR probability of the integer edges is insensitive to magnetic field, temperature, and filling, which provides evidence for spin-orbit coupling inherited from NbN enabling the pairing of the otherwise spin-polarized edges. FqH edges notably exhibit a CAR probability higher than that of integer edges once fully developed. This fqH CAR probability remains nonzero down to our lowest accessible temperature, suggesting superconducting pairing of fractional charges. These results provide a route to realize novel topological superconducting phases with universal braiding statistics in fqH-superconductor hybrid devices based on graphene and NbN.
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