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We study nonequilibrium Andreev resonances in a voltage-biased graphene three-terminal Josephson junction (JJ). We observe periodic oscillations of resistance with maxima at multiples of the magnetic flux quantum (noninversion regime). As we increase the bias voltage, we further observe a transition point beyond which oscillations exhibit a $\pi$ phase shift (inversion regime) with maxima of resistance occuring at multiples of half-flux quantum. At this transition point, the frequency of the oscillations is doubled. We develop a model based on the coupling of the static Andreev bound states (ABSs) to the nonequilibrium Fermi surface of graphene to explain the observed noninversion to inversion crossovers. Our model associates these crossovers to microscopic phase-sensitive Andreev reflections which couple the normal and superfluid components of the current. Our findings show that multiterminal JJs can be used to engineer unconventional energy-phase relations such as those expected in the $\pi$-shifted ABSs without relying on quartet and Floquet physics. These nonequilibrium ABSs could potentially find applications in superconducting $\pi$ qubits.

A Josephson junction, formed between two phase-biased superconductors and a normal metal, hosts a discrete spectrum of Andreev bound states (ABS). In this paper, we develop a theory for long ballistic Andreev interferometers in two-dimensional metals. We consider three frameworks in our theoretical analysis: (i) perturbation theory in the tunneling amplitudes; (ii) non-perturbative transport theory; and (iii) physically motivated approximations to visualize the conductance maps in the (flux, voltage) plane. We find a non-standard phase-sensitive Andreev reflection process in ballistic interferometers that couples the supercurrent to the non-equilibrium populations of the ABS in the normal region. Furthermore, our model shows that conductance spectroscopy follows the spectrum of the ABS in long junctions. We also discuss our results in terms of the semiclassical theory, the classical orbits being the one-dimensional Andreev tubes. Our theoretical analysis captures the results of recent experiments by the Penn State and Harvard groups., Comment: 32 pages, 16 figures, second revision, further physical discussion added

Nonreciprocal superconducting devices have attracted growing interest in recent years as they potentially enable directional charge transport for applications in superconducting quantum circuits. Specifically, the superconducting diode effect has been explored in two-terminal devices that exhibit superconducting transport in one current direction while showing dissipative transport in the opposite direction. Here, we exploit multi-terminal Josephson junctions (MTJJs) to engineer magnetic-field-free nonreciprocity in multi-port networks. We show that when treated as a two-port electrical network, a three-terminal Josephson junction (JJ) with an asymmetric graphene region exhibits reconfigurable two-port nonreciprocity. We observe nonreciprocal (reciprocal) transport between superconducting terminals with broken (preserved) spatial mirror symmetry. We explain our observations by considering a circuit-network of JJs with different critical currents.

There is growing interest in using multi-terminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate complex superconducting mechanisms such as quartet and multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of coupled two-terminal resistively and capacitively shunted junctions (RCSJs). Under appropriate bias current, the model predicts that a current flowing between two diagonal terminals in a four-terminal geometry may be represented as a sinusoidal function of a weighted sum of the superconducting phases. We show that starting from a semi-classical model with diffusive current-phase relations, the MTJJ effectively emulates a general form of the expected current-phase relation for multiplet Cooper pairings. Our study therefore suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semi-classical circuit-network effects., Comment: 9 pages, 8 figures

Three-dimensional topological insulators (TI's) in proximity with superconductors are expected to exhibit exotic phenomena such as topological superconductivity (TSC) and Majorana bound states (MBS), which may have applications in topological quantum computation. In superconductor-TI-superconductor Josephson junctions, the supercurrent versus the phase difference between the superconductors, referred to as the current-phase relation (CPR), reveals important information including the nature of the superconducting transport. Here, we study the induced superconductivity in gate-tunable Josephson junctions (JJs) made from topological insulator BiSbTeSe2 with superconducting Nb electrodes. We observe highly skewed (non-sinusoidal) CPR in these junctions. The critical current, or the magnitude of the CPR, increases with decreasing temperature down to the lowest accessible temperature (T ~ 20 mK), revealing the existence of low-energy modes in our junctions. The gate dependence shows that close to the Dirac point the CPR becomes less skewed, indicating the transport is more diffusive, most likely due to the presence of electron/hole puddles and charge inhomogeneity. Our experiments provide strong evidence that superconductivity is induced in the highly ballistic topological surface states (TSS) in our gate-tunable TI- based JJs. Furthermore, the measured CPR is in good agreement with the prediction of a model which calculates the phase dependent eigenstate energies in our system, considering the finite width of the electrodes as well as the TSS wave functions extending over the entire circumference of the TI.

We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe$_2$ nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature $T$, the increasing critical current $I_c$ exhibits a sharp upturn at a temperature $T_*$ around 20$\%$ of the junction critical temperatures for several different samples and various gate voltages. The $I_c$ vs. $T$ demonstrates a short junction behavior for $T>T_*$, but crosses over to a long junction behavior for $T