# Browsing by Subject "Superconductivity"

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Item Open Access Andreev conversion in the quantum Hall regime(2022) Zhao, LingfeiHigh quality type-II superconducting contacts have recently been developed for a variety of 2D systems, allowing one to explore superconducting proximity in the quantum Hall (QH) regime, which is one of the routes for creating exotic topological states and excitations. Here, we experimentally explore an interface between two prototypical phases of electrons with conceptually different ground states: the integer quantum Hall insulator and the s-wave superconductor. We find clear signatures of hybridized electron and hole states similar to chiral Majorana fermions, which we refer to as chiral Andreev edge states (CAES). They propagate along the interface in the direction determined by magnetic field and their interference can turn an incoming electron into an outgoing electron or a hole, depending on the phase accumulated by the CAES along their paths. However, the observed signals are small in comparison to theoretical predictions which calls for a better understanding of the limitations imposed by the physics of real materials. We then perform a systematic study of Andreev conversion in the QH regime. We find that the probability of Andreev conversion of electrons to holes follows an unexpected but clear trend: the dependencies on temperature and magnetic field are nearly decoupled. These trends unveil the loss and decoherence mechanisms of CAES. To complement our understanding of a QH-superconductor interface, we also study the thermal response under tens of nA current bias. We find that the superconductor is significantly overheated at low field in comparison to a similar-sized normal metal and the temperature distribution is not uniform. Our results demonstrate the existence of chiral edge states propagating along a QH-superconductor interface and interfering over a significant length. The study of the loss, decoherence and overheating of these states further paves the way for engineering topological superconductivity in exotic quantum circuits.

Item Open Access Fluctuation Effects in One-Dimensional Superconducting Nanowires(2010) Li, PengThis thesis focuses on the fluctuation in the switching current $I_s$ of superconducting Al nanowires. We discovered that the maximum current which nanowires can support is limited by a single phase slip at low temperature.

Al superconducting nanowires less than 10 nm wide were fabricated based on a MBE grown InP ridge template in an edge-on geometry. The method utilizes a special substrate featuring a high standing 8nm-wide InP ridge. A thin layer of Al was evaporated on the substrate and Al on the ridge formed nanowires.

The fluctuation effects starts to dominate in the nanowire due to reduced energy barrier. One of such effects is the phase slip. The phase slip is a topological event, during which the superconducting phase between two superconducting electrodes changes by $2\pi$. The phase slip broadens the normal-superconducting transition. Part of the nanowire becomes normal during the phase slip and forms a normal core. The normal core generates heat and causes the premature switching in superconducting nanowires.

The nanowire becomes superconducting below the critical temperature $T_c$. The superconducting-normal transition was studied in the thesis. The transition of nanowires with superconducting leads qualitatively fits the thermally activated phase slip (TAPS) theory. On the other hand, the transition of the nanowires with normal leads showed a resistive tail due to the inverse-proximity effect.

The nanowire switches from the superconducting state to the normal state as the current is increased. Ideally, the maximum current is set by a pair-breaking mechanism, by which the kinetic energy of quasi-particles exceeds the bonding energy of Cooper pairs. This is called the critical current, $I_c$. In practice, the measured maximum current, called the switching current $I_s$, cannot reach $I_c$ because of the phase slip.

$I_s$ shows stochasticity due to the phase slip. For the nanowires with superconducting leads, the average $I_s$ approximately follows but falls below $I_c$. The fluctuation in $I_s$ shows non-monotonic behavior, in contrast to other studies. The fluctuation first increases and then decreases rapidly with increasing temperature. The fluctuation behavior is consistent with a scenario where the switch is triggered by a single phase slip at low temperature while by multiple phase slips at higher temperature. Thermal activation of phase slips appears dominant at most temperatures. However, in the thinnest nanowire, the saturation of the fluctuation at low temperature indicates that the phase slips by macroscopic quantum tunneling.

The superconducting nanowires with normal leads were also studied. One of the distinctive properties of our nanowire (the critical field of 1D nanowire is 10 times larger than that of a 2D superconducting film) allowed us to study the same nanowire with different leads (superconducting or normal). Both the average $I_s$ and the fluctuation in $I_s$ differed qualitatively depending on whether the leads were superconducting or normal. The temperature dependence of the average $I_s$ followed the $I_c$ of the Josephson junction instead of the phenomenological pair-breaking $I_c$. The difference was found to depend on both the temperature (close to $T_c$ or 0) and the length (shorter or longer than the charge imbalance length). Our study also showed that nonlinear current-voltage (IV) curves were observed due to the inverse-proximity effect.

Item Open Access Graphene-based Josephson junctions: phase diffusion, effects of magnetic field, and mesoscopic properties.(2012) Borzenets, Ivan ValerievichWe report on graphene-based Superconductor-Normal metal-Superconductor Joseph- son junctions with contacts made from lead. The high transition temperature of this superconductor allows us to observe the supercurrent branch at temperatures up to 2 K. We are able to detect a small, but non-zero, resistance despite the Josephson junctions being in the superconducting state. We attribute this resistance to the phase diffusion regime, which has not been yet identified in graphene. By measuring the resistance as a function of temperature and gate voltage, we can further charac- terize the nature of electromagnetic environment and dissipation in our samples. In addition we modulate the critical current through grapehene by an external magnetic field; the resulting Fraunhofer interference pattern shows several periods of oscilla- tions. However, deviations from the perfect Fraunhofer pattern are observed, and their cause is explained by a simulation that takes into account the sample design.

Item Open Access Multiterminal Inverse AC Josephson Effect.(Nano letters, 2021-11-15) Arnault, Ethan G; Larson, Trevyn FQ; Seredinski, Andrew; Zhao, Lingfei; Idris, Sara; McConnell, Aeron; Watanabe, Kenji; Taniguchi, Takashi; Borzenets, Ivan; Amet, François; Finkelstein, GlebWhen a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect─the phase of the junction locks to the drive frequency. As a result, the*I*-*V*curves of the junction acquire "Shapiro steps" of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multiterminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest that multiterminal Josephson junctions are a playground to study highly connected nonlinear networks with novel topologies.Item Open Access Out of Equilibrium Superconducting States in Graphene Multiterminal Josephson Junctions(2022) Arnault, Ethan GreggMultiterminal Josephson junctions have attracted attention, driven by the promise that they may host synthetic topological phase of matter and provide insight into Floquet states. Indeed, the added complexity of the additional contacts in multiterminal Josephson junctions greatly expands its parameter space, allowing for unexpected results. This work sheds light onto the out of equilibrium superconducting states that can exist within a ballistic multiterminal Josephson junction. The application of a microwave excitation produces unexpected fractional Shapiro steps, which are a consequence of the multiterminal circuit network. The application of a finite voltage reveals a robust cos 2φ supercurrent along the multiplet biasing condition nV1=-mV2. This supercurrent is found to be born from the RCSJ equations and has a stability condition analogous to Kapitza’s pendulum. Finally, the injection of hot carriers poisons supercurrent contributions from the Andreev spectrum, revealing a continuum mediated supercurrent.

Item Open Access Superconducting Electron Transport in Graphene-Based Josephson Junctions(2017) Ke, ChungTingGraphene – a single atomic layer of graphite – is one of the most studied quasi two-dimensional materials (2D). Its electronic properties are particularly interesting, for example allowing one to study the physics of 2D relativistic electrons. Recently, graphene samples were coupled to superconducting leads, thus forming S-N-S (superconducting-normal-superconducting), or “Josephson” junctions. It was found that superconducting current (“supercurrent”) could flow through the normal (i.e. non-superconducting) graphene regions. The mechanism of this supercurrent is not fully explored. In this work, we study the supercurrent transport in three different regimes dependent on the electronic properties of graphene: diffusive, ballistic and quantum Hall (QH). In a diffusive device, the mean free path (scattering length) ξ_S of an electron is shorter than the length between the SC contacts, L. In the ballistic limit, the scattering length ξ_S exceeds L. These two regimes are explored without external magnetic field. On the other hand, the QH regime is induced by application of a strong magnetic field perpendicular to the plane of the sample. When the cyclotron radius rC is smaller than the junction length L/2, electron trajectories form closed orbits in the bulk of graphene and skipping orbits at the edge. Below I describe our findings in these regimes in more details.

For the diffusive case, the crucial energy scale is the Thouless energy, ETH = ħD/L^2, where D is diffusive constant. We find that the product of the critical current (maximal current through the device) and its normal resistance, I_CR_N, follows a universal linear dependence of E_TH for more than three orders of magnitude. However, the I_CR_N product is found to be much smaller than the theoretically predicted value of ~10E_TH/e.

To explore the ballistic regime, we worked with graphene encapsulated in hexagonal-Boron Nitride (h-BN), which greatly improves the transport properties of graphene. Here, we study the ballistic Josephson junctions in the short and long junction limits, determined by comparing the length of the junction with the induced superconducting coherence length. For the long junction limit, the temperature dependence of supercurrent is controlled by the energy level spacing as extracted from the Fabry-Perot (FP) oscillations. On the other hand, in the short junction limit, the superconducting gap will be the characteristic energy. Furthermore, we also study the supercurrent distribution in the graphene Josephson junctions by measuring the interference pattern in a small magnetic field. A unique periodicity modification around the Dirac point (DP) is observed.

Lastly, we demonstrate the first observation of supercurrent in the QH regime. Since in high magnetic fields the electron trajectories develop into cyclotron orbits, the bulk of the graphene is gapped by the so-called Landau quantization, and the only transport channels are chiral edge states on the borders of graphene. We study the magnetic interference of the supercurrent and demonstrate that the supercurrent indeed flows along the edges of the graphene region. Using different junction geometries, we examine possible mechanisms for this supercurrent. Our results may pave the way to realizing Majorana fermion or parafermion states predicted to be formed in certain hybrid QH-SC devices.

To conclude, we have explored supercurrent transport in multiple different regimes in the graphene Josephson junctions.

Item Open Access Transport Mechanisms of Quantum Hall Supercurrents in Graphene Josephson Junctions(2018) Wei, Ming-TsoThe existence of supercurrent in the quantum Hall regime with periodic magnetic interference patterns, first observed by Amet et al. in 2016, has created new opportunities to access topological superconductivity through quantum Hall edge states. However, a puzzle is found in the measured h/2e periodicity, as it violates the theoretical predicted h/e periodicity of the supercurrents carried by chiral quantum Hall edge states. Thus the observed supercurrents have not yet been robustly confirmed.

In this dissertation, we study the transport mechanisms of supercurrents in the quantum Hall regime in graphene Josephson junctions. First, a device with individually gated vacuum edges extended beyond the contacts is studied to determine whether the measured supercurrents are consistent with the theoretical prediction that both edges participate in transport. Next, a device with a third normal contact on one vacuum edge is used to study how supercurrents are influenced by an injected normal current. Finally, a device with a T-shaped asymmetric contact and a flat contact separated by a 90nm short channel is fabricated to examine the coupling of the chiral electron-hole hybrid modes. Despite that fact that theoretical explanation of the h/2e periodicity are still outstanding, these studies have extended our understanding of supercurrents in the quantum Hall regime. This may lay the foundation of realizing Majorana fermions and parafermions with symmetry-breaking edge states in quantum Hall/superconductor hybrid devices.

Item Open Access Zero Crossing Steps and Anomalous Shapiro Maps in Graphene Josephson Junctions.(Nano letters, 2020-10) Larson, Trevyn FQ; Zhao, Lingfei; Arnault, Ethan G; Wei, Ming-Tso; Seredinski, Andrew; Li, Henming; Watanabe, Kenji; Taniguchi, Takashi; Amet, François; Finkelstein, GlebThe AC Josephson effect manifests itself in the form of "Shapiro steps" of quantized voltage in Josephson junctions subject to radiofrequency (RF) radiation. This effect presents an early example of a driven-dissipative quantum phenomenon and is presently utilized in primary voltage standards. Shapiro steps have also become one of the standard tools to probe junctions made in a variety of novel materials. Here we study Shapiro steps in a widely tunable graphene-based Josephson junction in which the high-frequency dynamics is determined by the on-chip environment. We investigate the variety of patterns that can be obtained in this well-understood system depending on the carrier density, temperature, RF frequency, and magnetic field. Although the patterns of Shapiro steps can change drastically when just one parameter is varied, the overall trends can be understood and the behaviors straightforwardly simulated, showing some key differences from the conventional RCSJ model. The resulting understanding may help interpret similar measurements in more complex materials.