Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions

Abstract

The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge.In this article, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically-protected gapless Andreev bound states.We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological ori-

Fractional Shapiro steps without fractional Josephson effect

“…this work we constructed a microscopic theory describing Shapiro steps in topologically trivial ballistic SNS junctions subject to external microwave radiation of arbitrary intensity. Our analysis was mainly focused on the most interesting limit of subgap voltages and temperatures revealing a number of features similar to those observed in recent experiments [8][9][10] with superconducting junctions involving topological insulators. The main such features are: i) the presence of non-vanishing "n = 0 Shapiro step", i.e.…”

“…The presence of Majorana-like bound states (1) could then be detected experimentally, e.g., by observing resonances in the form of current jumps (the so-called Shapiro steps [5][6][7] ) on the the junction I − V curve under the influence of external microwave radiation. Pronounced Shapiro steps at frequencies ω = ω J /2 were indeed detected in a number of microwave experiments performed with HgTe-and BiSb-based superconducting junctions [8][9][10] .…”

“…Such current biased regime appears to be realized in a number of recent experiments [8][9][10] . It is obvious that in this case the voltage across the junction cannot anymore be constant and should vary in time V = V (t) even in the absence of an ac signal I ac → 0.…”

“…The product of these matrices implies time convolution and curly brackets denote anticommutation. These matrices are expressed through quasiclassical propagators as QR = ǧ = ĝR ĝK 0 ĝA (9) and…”

Fragility of the Fractional Josephson Effect in Time-Reversal-Invariant Topological Superconductors

“…Our findings are relevant for experiments on both TRITOPS and nanowire-based Josephson junctions. Recent experiments investigating the Josephson effect in proximitized quantum spin Hall edges [79][80][81] observed signatures of 4π and 2π periodicity, whereas theory predicts an 8π-periodic Josephson effect [62,[66][67][68]. Subgap energy levels corresponding to the same fermion parity are predicted to have a Kramers degeneracy at integer multiples of ϕ ¼ π; thus, local mixing could induce transitions at these time-reversal-invariant points.…”