Transport in Josephson junctions is commonly described using a simplifying assumption called the Andreev approximation, which assumes that excitations are fixed at the Fermi momentum and only Andreev reflections occur at interfaces (with no normal re
flections). This approximation is appropriate for BCS-type superconductors, where the chemical potential vastly exceeds the pairing gap, but it breaks down for superconductors with low carrier density, such as topological superconductors, doped semiconductors, or superfluid quantum gases. Here, we present a generic $analytical$ framework for calculating transport in Josephson junctions that lifts up the requirement of the Andreev approximation. Using this general framework, we study in detail transport in Josephson junctions across the BCS-BEC crossover, which describes the evolution from a BCS-type superconductor with loosely-paired Cooper pairs to a BEC of tighly-paired dimers. As the interaction is tuned from the BCS to the BEC regime, we find that the overall subgap current caused by multiple Andreev reflections decreases, but nonlinearities in the current-voltage characteristic called the subharmonic gap structure become more pronounced near the intermediate unitary limit, giving rise to sharp peaks and dips in the differential conductance with even $negative$ conductance at specific voltages.
We address the challenge of realizing a Floquet-engineered Hofstadter Bose-Einstein condensate (BEC) in an ultracold atomic gas, as a general prototype for Floquet engineering. Motivated by evidence that such a BEC has been observed experimentally, w
e show, using Gross-Pitaevskii simulations, how it is dynamically realized. Our simulations support the existence of such a Hofstadter BEC through both momentum-space distributions as well as real-space phase correlations. From these simulations, we identify and characterize a multistage evolution, which includes a chaotic intermediate heating stage followed by a spontaneous reentrance to the Floquet-engineered BEC. The observed behavior is reminiscent of evolution in cosmological models, which involves a similar time progression including an intermediate turbulence en route to equilibration.
Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing. Unfortunately, analytically constructing shortcuts to adiabaticity for systems having co
mplex interactions and more than a few levels is a challenging task. This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made]. Here we develop an $analytic$ approach that allows one to go beyond these limitations. Our method is general and results in analytically derived pulse shapes that correct both nonadiabatic errors as well as non-RWA errors. We also show that our approach can yield pulses requiring a smaller driving power than conventional nonadiabatic protocols. We show in detail how our ideas can be used to analytically design high-fidelity single-qubit tripod gates in a realistic superconducting fluxonium qubit.
Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e
., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.
Experiments on planar Josephson junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensi
onal channel in the junction of a two-dimensional electron gas (2DEG) proximitized by two spatially separated superconductors. The channel, which is below the break between the superconductors, is not in direct contact with the superconducting leads, so that proximity coupling is expected to be weaker and less well-controlled than in the simple nanowire configuration widely discussed in the literature. This provides a strong incentive for this paper which investigates the nature of proximitization in these Josephson architectures. At a microscopic level we demonstrate how and when it can lead to topological phases. We do so by going beyond simple tunneling models through solving self-consistently the Bogoliubov-de Gennes equations of a heterostructure multicomponent system involving two spatially separated $s$-wave superconductors in contact with a normal Rashba spin-orbit-coupled 2DEG. Importantly, within our self-consistent theory we present ways of maximizing the proximity-induced superconducting gap by studying the effect of the Rashba spin-orbit coupling, chemical potential mismatch between the superconductor and 2DEG, and sample geometry on the gap. Finally, we note (as in experiment) a Fulde-Ferrell-Larkin-Ovchinnikov phase is also found to appear in the 2DEG channel, albeit under circumstances which are not ideal for topological superconducting phase.
We theoretically study topological planar Josephson junctions (JJs) formed from spin-orbit-coupled two-dimensional electron gases (2DEGs) proximitized by two superconductors and subjected to an in-plane magnetic field $B_parallel$. Compared to previo
us studies of topological superconductivity in these junctions, here we consider the case where the superconducting leads are narrower than the superconducting coherence length. In this limit the system may be viewed as a proximitized multiband wire, with an additional knob being the phase difference $phi$ between the superconducting leads. A combination of mirror and time-reversal symmetry may put the system into the class BDI. Breaking this symmetry changes the symmetry class to class D. The class D phase diagram depends strongly on $B_{parallel}$ and chemical potential, with a weaker dependence on $phi$ for JJs with narrower superconducting leads. In contrast, the BDI phase diagram depends strongly on both $B_parallel$ and $phi$. Interestingly, the BDI phase diagram has a fan-shaped region with phase boundaries which move away from $phi = pi$ linearly with $B_parallel$. The number of distinct phases in the fan increases with increasing chemical potential. We study the dependence of the JJs critical current on $B_parallel$, and find that minima in the critical current indicate first-order phase transitions in the junction only when the spin-orbit coupling strength is small. In contrast to the case of a JJ with wide leads, in the narrow case these transitions are not accompanied by a change in the JJs topological index. Our results, calculated using realistic experimental parameters, provide guidelines for present and future searches for topological superconductivity in JJs with narrow leads, and are particularly relevant to recent experiments [A. Fornieri et al., Nature (London) 569, 89 (2019)].
Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured i
n tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference {phi} between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phase-dependent zero-bias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to {phi} ~ {pi} significantly reduces the critical field at which the zero-bias peak appears, with respect to {phi} = 0. The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.
We study fermion-parity-changing quantum phase transitions (QPTs) in platform Josephson junctions. These QPTs, associated with zero-energy bound states, are rather widely observed experimentally. They emerge from numerical calculations frequently wit
hout detailed microscopic insight. Importantly, they may incorrectly lend support to claims for the observations of Majorana zero modes. In this paper we present a fully consistent solution of the Bogoliubov-de Gennes equations for a multi-component Josephson junction. This provides insights into the origin of the QPTs. It also makes it possible to assess the standard self energy approximations which are widely used to understand proximity coupling in topological systems. The junctions we consider are complex and chosen to mirror experiments. Our full proximity calculations associate the mechanism behind the QPT as deriving from a spatially extended, proximity-induced magnetic defect. This defect arises because of the insulating region which effects a local reorganization of the bulk magnetization in the proximitized superconductor. Our results suggest more generally that QPTs in Josephson junctions generally do not require the existence of spin-orbit coupling and should not be confused with, nor are they indicators of, Majorana physics.
A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (aris
ing from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires to understand possible intrinsic deviations from the predicted conductance quantization. We find that the full temperature and the tunneling transmission dependence of the tunnel conductance does not obey any simple scaling relation, and estimating the zero-temperature conductance from finite-temperature and finite-tunnel-broadening tunneling data is difficult in general. A scaling relation, however, does hold at the extreme weak-tunneling low-temperature limit where the conductance depends only on the dimensionless ratio of the temperature and tunnel broadening. We also consider the tunneling contributions from nontopological Andreev bound states which may produce almost-zero-bias conductance peaks, which are not easy to distinguish from the Majorana-induced zero-bias peaks, finding that the nontopological almost-zero-modes associated with Andreev bound states manifest similar temperature and transmission dependence as the topological Majorana modes. We comment on the Zeeman splitting dependence of the zero-bias conductance peak for finite temperature and tunnel coupling.
A weak superconducting proximity effect in the vicinity of the topological transition of a quantum anomalous Hall system has been proposed as a venue to realize a topological superconductor (TSC) with chiral Majorana edge modes (CMEMs). A recent expe
riment [Science 357, 294 (2017)] claimed to have observed such CMEMs in the form of a half-integer quantized conductance plateau in the two-terminal transport measurement of a quantum anomalous Hall-superconductor junction. Although the presence of a superconducting proximity effect generically splits the quantum Hall transition into two phase transitions with a gapped TSC in between, in this Rapid Communication we propose that a nearly flat conductance plateau, similar to that expected from CMEMs, can also arise from the percolation of quantum Hall edges well before the onset of the TSC or at temperatures much above the TSC gap. Our Rapid Communication, therefore, suggests that, in order to confirm the TSC, it is necessary to supplement the observation of the half-quantized conductance plateau with a hard superconducting gap (which is unlikely for a disordered system) from the conductance measurements or the heat transport measurement of the transport gap. Alternatively, the half-quantized thermal conductance would also serve as a smoking-gun signature of the TSC.
