From perfect to imperfect poor man's Majoranas in minimal Kitaev chains

Abstract

Poor man's Majoranas (PMMs) hold the promise to engineer Majorana bound states in a highly tunable setup consisting of a chain of quantum dots that are connected via superconductors. Due to recent progress in controlling the amplitudes of elastic cotunneling (ECT) and crossed Andreev reflection (CAR), two vital ingredients for PMMs, experimental investigations of PMMs have gained significant interest. Previously, analytic conditions for the "sweet spots" that result in PMMs have focused on systems with infinite Zeeman energy. Here, we derive analytically a sweet spot condition for PMMs in a system with finite Zeeman energy in the absence of Coulomb interaction. We then consider two numerical models, one in which ECT and CAR are transmitted via superconducting bulk states and one in which they are transmitted via an Andreev bound state. We demonstrate that the analytical sweet spot conditions can only be approximated in these more realistic models, but they cannot be satisfied exactly. As a consequence, we do not find perfect PMMs in these systems, but instead near-zero-energy states that are highly, but not perfectly, localized. These states can be considered as imperfect PMMs and their classification relies on threshold values, which adds some arbitrariness to the concept of PMMs.

References in corpus (65)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Schrieffer-Wolff transformation for quantum many-body systems
• Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks
• Majorana Fermions in Semiconductor Nanowires
• Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Realization of a minimal Kitaev chain in coupled quantum dots
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Reproducing topological properties with quasi-Majorana states
• Two terminal charge tunneling: Disentangling Majorana zero modes from partially separated Andreev bound states in semiconductor-superconductor heterostructures
• Majorana bound states in non-homogeneous semiconductor nanowires
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Quantized zero bias conductance plateau in semiconductor-superconductor heterostructures without non-Abelian Majorana zero modes
• Non-Majorana states yield nearly quantized conductance in superconductor-semiconductor nanowire devices
• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Spin-Dependent Josephson Current through Double Quantum Dots and Measurement of Entangled Electron States
• Disorder-induced zero-bias peaks in Majorana nanowires
• Ubiquitous non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices
• Nontopological zero-bias peaks in full-shell nanowires induced by flux tunable Andreev states
• Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires
• Supercurrent detection of topologically trivial zero-energy states in nanowire junctions
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• On controlling the bound states in quantum-dot hybrid-nanowire
• Topologically trivial zero bias conductance peak in semiconductor Majorana wires from boundary effects
• A two-site Kitaev chain in a two-dimensional electron gas
• Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains
• Zero-energy pinning of topologically-trivial bound states in multi-band semiconductor-superconductor nanowires
• Robust low-energy Andreev bound states in semiconductor-superconductor heterostructures: Importance of partial separation of component Majorana bound states
• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
• Controlled crossed Andreev reflection and elastic co-tunneling mediated by Andreev bound states
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Triplet correlations in Cooper pair splitters realized in a two-dimensional electron gas
• Majorana bound states in semiconducting nanostructures
• Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI
• Transport signatures of an Andreev molecule in a quantum dot -- superconductor -- quantum dot setup
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Signatures of nonlocal Cooper-pair transport and of a singlet-triplet transition in the critical current of a double-quantum-dot Josephson junction
• Detecting Topological Superconductivity with ${\phi }_0$ Josephson Junctions
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• Coupled superconducting spin qubits with spin-orbit interaction
• Kitaev chain in an alternating quantum dot-Andreev bound state array
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Fermion-parity qubit in a proximitized double quantum dot
• Flux-tunable Kitaev chain in a quantum dot array
• Coupling of quantum-dot states via elastic-cotunneling and crossed Andreev reflection in a minimal Kitaev chain

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• Fate of poor man's Majoranas in the long Kitaev chain limit
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Transport of Majorana Bound State in the presence of telegraph noise
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Entanglement dynamics in minimal Kitaev chains
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity