Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling

Recently, topological superconductors based on Josephson junctions in two-dimensional electron gases with strong Rashba spin-orbit coupling have been proposed as attractive alternatives to wire-based setups. Here, we elucidate how phase-controlled Josephson junctions based on quantum wells with [001] growth direction and an arbitrary combination of Rashba and Dresselhaus spin-orbit coupling can also host Majorana bound states for a wide range of parameters as long as the magnetic field is oriented appropriately. Hence, Majorana bound states based on Josephson junctions can appear in a wide class of two-dimensional electron gases. We study the effect of spin-orbit coupling, the Zeeman energies, and the superconducting phase difference to create a full topological phase diagram and find the optimal stability region to observe Majorana bound states in narrow junctions. Surprisingly, for equal Rashba and Dresselhaus spin-orbit coupling, well localized Majorana bound states can appear only for phase differences $\phi\neq\pi$ as the topological gap protecting the Majorana bound states vanishes at $\phi=\pi$. Our results show that the ratio between Rashba and Dresselhaus spin-orbit coupling or the choice of the in-plane crystallographic axis along which the superconducting phase bias is applied offer additional tunable knobs to test Majorana bound states in these systems. Finally, we discuss signatures of Majorana bound states that could be probed experimentally by tunneling conductance measurements at the edge of the junction.Comment: 21 pages, 12 figure

Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators

Anderson localization transitions are usually referred to as quantum phase transitions from delocalized states to localized states in disordered systems. Here we report an unconventional ``Anderson localization transition'' in two-dimensional quantized quadrupole insulators. Such transitions are from symmetry-protected topological corner states to disorder-induced normal Anderson localized states that can be localized in the bulk, as well as at corners and edges. We show that these localization-localization transitions (transitions between two different localized states) can happen in both Hermitian and non-Hermitian quantized quadrupole insulators and investigate their criticality by finite-size scaling analysis of the corner density. The scaling analysis suggests that the correlation length of the phase transition, on the Anderson insulator side and near critical disorder $W_c$, diverges as $\xi(W)\propto \exp[\alpha/\sqrt{|W-W_c|}]$, a typical feature of Berezinskii-Kosterlitz-Thouless transitions. A map from the quantized quadrupole model to the quantum two-dimensional $XY$ model motivates why the localization-localization transitions are Berezinskii-Kosterlitz-Thouless type.Comment: 6 pages, 3 figure

Topological Superconductivity in a Phase-Controlled Josephson Junction

Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations have non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. While signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scalable to large numbers of states. Here we present a novel experimental approach towards a two-dimensional architecture. Using a Josephson junction made of HgTe quantum well coupled to thin-film aluminum, we are able to tune between a trivial and a topological superconducting state by controlling the phase difference $\phi$ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor by measuring the tunneling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunneling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunneling conductance develops a zero-bias peak which persists over a range of $\phi$ that expands systematically with increasing magnetic fields. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and will therefore open new avenues for probing topological superconducting phases in two-dimensional systems.Comment: Supplementary contains resized figures. Original files are available upon reques

Induced Superconductivity in the Quantum Spin Hall Edge

Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states [1, 2, 3]. 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 [4, 5]. 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 [6]. 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 $d_C = 6.3 nm$ [7]. 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 nmEngineering and Applied SciencesPhysic

Electronic correlations in twisted bilayer graphene near the magic angle

Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a platform for investigating strongly correlated electrons. Here, we use scanning tunnelling microscopy to probe the local properties of highly tunable twisted bilayer graphene devices and show that the flat bands deform when aligned with the Fermi level. When the bands are half-filled, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring an enhanced splitting of the flat bands. We describe this within a microscopic model that predicts a strong tendency towards nematic ordering. Our results provide insights into symmetry-breaking correlation effects and highlight the importance of electronic interactions for all filling fractions in twisted bilayer graphene

Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle

Twisted bilayer graphene with a twist angle of around 1.1{\deg} features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of highly tunable twisted bilayer graphene devices and show that the flat bands strongly deform when aligned with the Fermi level. At half filling of the bands, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring a substantially enhanced flat band splitting that we describe within a microscopic model predicting a strong tendency towards nematic ordering. Our results provide insights into symmetry breaking correlation effects and highlight the importance of electronic interactions for all filling factors in twisted bilayer graphene.Comment: Main text 9 pages, 4 figures; Supplementary Information 25 page

Electronic correlations in twisted bilayer graphene near the magic angle

Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a platform for investigating strongly correlated electrons. Here, we use scanning tunnelling microscopy to probe the local properties of highly tunable twisted bilayer graphene devices and show that the flat bands deform when aligned with the Fermi level. When the bands are half-filled, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring an enhanced splitting of the flat bands. We describe this within a microscopic model that predicts a strong tendency towards nematic ordering. Our results provide insights into symmetry-breaking correlation effects and highlight the importance of electronic interactions for all filling fractions in twisted bilayer graphene