Floquet Majorana zero and π modes in planar Josephson junctions

Abstract

We show how Floquet Majorana fermions may be experimentally realized by periodic driving of a solid-state platform. The system comprises a planar Josephson junction made of a proximitized heterostructure containing a 2D electron gas (2DEG) with Rashba spin-orbit coupling and Zeeman field. We map the sub-gap Andreev bound states of the junction to an effective one-dimensional Kitaev model with long range hopping and pairing terms. Using this effective model, we study the response of the system to periodic driving of the chemical potential, as applied via microwaves through a top-gate. We use the bulk Floquet topological invariants to characterize the system in terms of the number of zero and π Majorana modes for experimentally realistic parameters. We present signatures of these modes on differential conductance and local density of states. A notable feature is subharmonic response to the drive when both Majorana zero and π modes are present, thus opening up the possibility of using this feature to clearly identify Majorana modes. We highlight the robustness of these features to disorder, and show that despite hybridization due to long localization lengths, the main features of the subharmonic response are still identifiable in an experimental system that is readily accessible. arXiv:1812.05191v1 [cond-mat.mes-hall]

Emergence and Manipulation of non-equilibrium Yu-Shiba-Rusinov states

“…3c and d, when plotted as a function of angle. Finally, to bridge the gap to periodically driven systems that can be described using the Floquet formalism [22][23][24], we consider the time evolution from a static impurity spin at t = 0 to an impurity spin that rotates periodically in the xz-plane with a driving frequency of ω 0 = 2π/T . We note that the periodic rotation of the impurity's spin leads to a splitting of the (static) YSR peaks in the density of states [28].…”

“…Moreover, we show that the extent to which the system is driven out-of-equilibrium is controlled by the time scale over which perturbations occur, and is directly reflected in the time and frequency dependence of N neq . Finally, our formalism bridges the gap to periodically driven magnetic structures, allowing us to visualize the emergence of Floquet YSR states [22][23][24]. Our work thus provides a theoretical framework to study the emergence of non-equilibrium phenomena on electronic time and nanoscopic length scales in complex materials.…”

Gauge‐Induced Floquet Topological States in Photonic Waveguides

“…Thanks to the flexibility of Floquet engineering, the topological properties of Floquet systems are much richer than static systems. Unconventional effects have been demonstrated by tuning the driving frequency and amplitude, such as anomalous topological Floquet edge modes, [ 30–32 ] “0” and “π” Majorana modes, [ 33,34 ] and interacting topological Floquet phases. [ 35,36 ] Importantly, the Floquet systems also enable the manipulations of artificial gauge fields (i.e., the Floquet gauge).…”

Photoinduced spin-Hall resonance in a k3 -Rashba spin-orbit coupled two-dimensional hole system

“…Such an interaction can also be used to manipulate the spin-and valley-selective transport in Dirac materials [11][12][13][14] and transition-metal dichalcogenides [15,16]. There have been extensive works on phototunable Weyl nodes [17][18][19][20][21], the 0-π transition in Josephson junctions [22,23], and Floquet engineering of Majorana modes [24][25][26][27]. Interfacial chiral modes have also been predicted in threefold topological semimetals [28], by controlling the phase of the light.…”