Session W02: Topological Superconductivity in Heterostructures

Chiral supercurrent in quantum Hall Josephson junctions

Hybridizing superconductivity with the quantum Hall (QH) effects has major potential for designing novel circuits capable of inducing and manipulating non-Abelian states. In this talk I will present our recent results on quantum Hall Josephson junctions based on graphene nanoribbons. I will show that with suitably designed junctions, a robust supercurrent can develop on the quantum Hall plateau of normal state resistance h/2e² and withstand up to 8 teslas. The particular feature of those junctions is a chiral supercurrent with an unusual 2Φ₀=h/e flux periodicity, indicating that the Andreev bound states propagate in a chiral fashion via the quantum Hall edge channels and form a loop along the sample periphery. The key parameters that limit the supercurrent in the quantum Hall regime and their consequences for more exotic quantum Hall states will also be discussed.   

Absorption peaks in topological phase transition of planar Josephson junctions

Planar Josephson junctions provide an attractive platform to experimentally realize topological superconductivity [1,2]. We consider a planar Josephson junction inductively coupled to a microwave circuit QED system and investigate the effects of topological transitions on the microwave absorption spectra. The microwave field induces ac phase fluctuations across the junction, which drive transitions between the Andreev levels in the microwave range [3,4]. The planar Josephson junction is in topological class D and thus can support Majorana states at the ends of the junction [5,6]. Tight-binding simulations of the system show sudden change in the absorption characteristics of the system as a system parameter is changed to induce topological transitions.

Funding Acknowledgment:

U.S. ONR Grants No. N000141712793 and MURI No. N000142212764.   

Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures

Parafermion zero modes can arise in hybrid structures composed of $ u=1/m$ fractional quantum Hall edges proximitized with an s-wave superconductor. Here we consider parafermion and Cooper pair tunneling, and backscattering in a junction formed in such hybrid structures. We find that the $4pi m$ periodicity due to parafermion-only tunneling reduces, in the presence of backscattering, to $4pi$-periodic at zero temperature and $2pi$-periodic at finite temperature unless the fermion parity is fixed. Nevertheless, a clear signature of parafermion tunneling remains in the shape of the current-phase relation.   

‘Pseudo Majorana’ Modes in Clean Planar Josephson Junctions

The unambiguous detection of Majorana bound states is essential for the study of such exotic states. In the presence of disorder, even theoretically, it is challenging to identify reliably the topological phase of the superconducting system and the presence of Majorana states. For quasi one-dimensional superconducting nanowires it has been proposed that the separation length of low energy modes can be used to assess the nature of such modes: low energy modes with a separation length comparable to the length of the nanowire can be identified as Majorana bound states. In this talk I will present results for planar Josephson junctions, a promising platform to realize Majorana bound states. We focus on the clean limit and find that very low energy modes, with large separation length, can be present even when the Josephson junction is known to be in a topologically trivial phase. I will then discuss the mechanism that can lead to the formation of such “pseudo-Majorana” states.   

Disorder and Microwave Signatures of Topological Transitions in Planar Josephson Junctions

We analytically and numerically investigate the effect of disorder on topological transitions in planar Josephson junctions as the Zeeman field, spin-orbit coupling strength and chemical potential is varied [1-3]. We find that the topological properties of these systems depend sensitively on the disorder and demonstrate reentrant behavior of topological phases [4]. We also consider microwave detection of topological transitions in planar Josephson junctions where the Josephson junction is inductively coupled to microwave circuit QED detector and observe the effect of the transitions in the microwave signature of planar Josephson junctions.

[1] M. C. Dartiailh, W. Mayer, J. Yuan, K. S. Wickramasinghe, A. Matos-Abiague, I. Žutić, and J. Shabani, Phys. Rev. Lett. 126, 036802 (2021).

[2] F. Pientka, A. Keselman, E. Berg, A. Yacoby, A. Stern, and B. I. Halperin, Phys. Rev. X 7, 021032 (2017).

[3] T. Zhou, M. C. Dartiailh, K. Sardashti, J. E. Han, A. Matos-Abiague, J. Shabani, and I. Žutić, Nat Commun 13, 1 (2022).

[4] B. Pekerten, A. Teker, Ö. Bozat, M. Wimmer, and İ. Adagideli, Physical Review B 95, (2017).   

Can Majorana and parafermion zero modes engineered in quantum Hall edges survive edge reconstruction?

Majorana and parafermion zero modes can be trapped at domain walls of quantum hall edges proximitised by

superconductors and ferromagnets. Softening of the edge potential of the ν=1 quantum Hall edge  allows for a narrow  ν=1/3

strip to be deposited near the edge by reconstruction. Subsequent edge renormalisation due to inter-edge interactions and 

disorder induced tunneling leads to a new edge structure, which naively allows for both Majorana and parafermion zero modes.

However,  constraints imposed by the total charge and spin of the bulk quantum Hall systems show that the ground state manifold

of the reconstructed system has a four-fold degeneracy  with two even parity and two odd parity sectors, thus leading 

to a Z₂ Χ Z₂ symmetry.  When the ferromagnet between

the superconductors is removed, the many-body spectrum shows a 4π Josephson effect with the states in each Z₂ being

energetically decoupled. Signatures of the new states appear when the edge velocities of the reconstructed edges are different.   

Topological Superconductivity in Chiral Carbon Nanotubes: Superconducting Diode Effects

Topological superconductivity (TSC) has been intensively investigated over the past decades, but difficulties in pinning down TSC phases has called for novel experiments. To this end, the superconducting diode effect (SDE) has attracted interest in recent years as a way to shed light on TSC but also to enable a number of applications. In this talk, we will present analytic and numerical results on the SDE in chiral carbon nanotubes (CNTs). We find that chiral nanotubes in Josephson junctions can exhibit large diode efficiencies far exceeding those of superconducting chiral nanotubes when an external magnetic field is applied along the nanotube. Furthermore, our numerical simulations show that the Josephson diode polarity can be tuned by electrostatically gating CNTs in a Josephson junction. Lastly, we will discuss the diode effect as a superconducting CNT is tuned into a TSC phase and the role of chirality in this case.   

Characterizing disorder in surface InAs heterostructures

Two-dimensional superconductor-semiconductor hybrid heterostructures have been utilized in a range of quantum devices, from voltage tunable gatemon qubits to realization of topological phases. In recent years, it has become increasingly clear that the presence of disorder in these structures can result in spurious results in experiments involving them. We aim to study the effect of disorder by correlating transport properties with observing the critical density at which the system undergoes an apparent metal to insulator transition. We discuss strategies for improved material growth and sample nanofabrication.   

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene

Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayer WSe2 revealed robust, ultraclean superconductivity coexisting with sizable induced spin-orbit coupling. Here, we propose BLG/WSe2 as a platform to engineer gate-defined planar topological Josephson junctions, where the normal and superconducting regions descend from a common material. More precisely, we show that if superconductivity in BLG/WSe2 is gapped and emerges from a parent state with intervalley coherence, then Majorana zero-energy modes can form in the barrier region upon applying weak in-plane magnetic fields. Our results spotlight a potential pathway for “internally engineered” topological superconductivity that minimizes detrimental disorder and orbital-magnetic-field effects.   

Unconventional superconducting phenomena in topological Dirac semimetal α-Sn thin films

 α-Sn, which has a diamond crystal structure, has recently attracted attention as a rich topological material platform. When grown on an InSb (001) substrate, α-Sn is transformed to a topological Dirac semimetal (TDS) with high-mobility and nontrivial surface and bulk band components [1]. Incorporation of superconductivity into the TDS α-Sn is expected to open a way to topological superconductivity that can host Majorana fermions [2].

 We study magnetotransport properties of a 5 nm-thick α-Sn thin film grown on an undoped InSb (001) substrate, which shows a superconducting transition at T_C = 4.2K after being kept in ambient conditions for 20 months. The superconducting α-Sn layer exhibits large in-plane critical magnetic fields (H_C) exceeding the Pauli limit, and H_C changes by 1.5 times when the magnetic field is applied at an angle of 45° and 135° with respect to the current. Furthermore, the critical current changes upon reversing the current direction under an in-plane magnetic field. This superconducting diode effect reaches 2% and changes sign with varying the magnetic field. These results thus highlight rich topological physics in superconducting α-Sn.

[1] L. D. Anh et al, Adv. Mater. 33, 2104645 (2021). [2] S. Kobayashi, & M. Sato, Phys. Rev. Lett. 115, 187001 (2015).   

Impact of disorder on the topological superconductivity realized in planar semiconductor-superconductor structures: Comparison between Majorana nanowires and Josephson junctions

 

Pristine semiconductor-superconductor (SM-SC) hybrid nanowires and Josephson junctions have been intensely studied in recent years as promising platforms for realizing topological superconductivity and Majorana zero modes (MZMs). Disorder effects have been widely identified as the major roadblock for realizing stable MZMs in hybrid nanowires. However, there are no systematic studies of disorder effects in planar Josephson junctions at the same modeling level. We perform a detailed numerical analysis of the low-energy physics of Josephson junction structures based on an effective microscopic model that incorporates two types of disorder, charge impurities inside the semiconductor and surface roughness on the superconducting film. We consider different parameter regimes, including weak and strong effective SM-SC coupling, low and high chemical potential values, and weak and strong disorder strength. The results are benchmarked using disordered hybrid nanowires realized in planar SM-SC structures similar to those involved in the fabrication of Josephson junctions and having similar model parameters and disorder strengths.  We find that the topological superconducting phase hosted by a Josephson junction structure is, generally, more robust against disorder than the topological superconductivity realized in a hybrid nanowire with similar parameters. On the other hand, operating the Josephson junction in a regime characterized by large chemical potential values leads to huge finite-size effects that can destroy the stability of MZMs.   

Optimizing Josephson junction geometry for an enhanced induced gap

Planar Josephson junction based on two-dimensional electron gas (2DEG) particularly InAs is a promising platform for the study of topological superconductivity and Majorana zero modes (MBSs). While tremendous progress has been made in the search for topological superconductivity and MBSs in this system, there is an increasing concern within the community regarding the nature of the low-energy modes responsible for the experimental observations. Disorder and a small topological gap could effectively create a competition with trivial Andreev bound state physics mimicking some of the MBS signatures. To improve the performance of our Josephson junctions, we follow proposals that suggest zigzag-shaped junctions and Josephson junctions with spatially modulated width could have enhanced topological gaps [1, 2]. We fabricate planar Josephson junctions with various geometries using our epitaxial aluminum on semiconducting indium arsenide quantum wells. Our studies of induced gaps in these junctions suggest enhanced induced gaps at finite fields. We will discuss the implications and future device architectures.    

[1] T. Laeven, B. Nijholt, M. Wimmer, and A. R. Akhmerov, Enhanced Proximity Effect in Zigzag-Shaped Majorana Josephson Junctions, Phys. Rev. Lett. 125, 086802 (2020).

[2] P. P. Paudel, T. Cole, B. D. Woods, and T. D. Stanescu, Enhanced topological superconductivity in spatially modulated planar Josephson junctions, Phys. Rev. B 104, 155428 (2021).