arXiv subjects

Rodrigo A. Dourado

Publications and source records attributed to Rodrigo A. Dourado.

6 recordsLinked to original sources

arXiv2026

Assessing Majorana states and qubits through quantum capacitance

Quantum capacitance (QC) has recently emerged as a promising tool for parity readout in topological qubits based on Majorana bound states (MBSs). Here, we show that this capability can be extended further: by employing an auxiliary quantum dot (QD) as a sensor, we demonstrate that QC measurements simultaneously resolve two fundamental figures of merit of the device, the ground-state energy splitting and the MBS overlap, thus providing direct access to the underlying internal degrees of freedom. Using a low-energy effective model, we provide analytic expressions for these two figures of merit that can be determined from the relative position and magnitude of the QC maxima in the even and odd parity sectors as functions of the auxiliary-QD energy. We further validate these results with a microscopic model of QD-based Kitaev chains and qubits, demonstrating their applicability in a wide range of MBS-based devices. Our results establish QC as a probe of MBS quality and a tool for topological-device optimization that preserves fermion parity.

cond-mat.mes-hall↗

arXiv2025

Machine-learned tuning to protected states by probing noise resilience

Protected states are promising for quantum technologies due to their intrinsic resilience against noise. However, such states often emerge at discrete points or small regions in parameter space and are thus difficult to find in experiments. In this work, we present a machine-learning method for tuning to protected regimes, based on injecting noise into the system and searching directly for the most noise-resilient configuration. We illustrate this method by considering short quantum dot-based Kitaev chains which we subject to random parameter fluctuations. Using the covariance matrix adaptation evolutionary strategy we minimize the typical resulting ground state splitting, which makes the system converge to a protected configuration with well-separated Majorana bound states. We verify the robustness of our method by considering finite Zeeman fields, electron-electron repulsion, asymmetric couplings, and varying the length of the Kitaev chain. Our work provides a reliable method for tuning to protected states, including but not limited to isolated Majorana bound states.

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arXiv2025

Measuring coherence factors of states in superconductors through local current

The coherence factors of quasiparticles in a superconductor determine their properties, including transport and susceptibility to electric fields. In this work, we propose a way to infer the local coherence factors using local transport to normal leads. Our method is based on measuring the local current through a lead as the coupling to a second one is varied: the shape of the current is determined by the ratio between the local coherence factors, becoming independent of the coupling to the second lead in the presence of local electron-hole symmetry, {\it i.e.} coherence factors $|u|=|v|$. We apply our method to minimal Kitaev chains: arrays of quantum dots coupled via narrow superconducting segments. These chains feature Majorana-like quasiparticles (zero-energy states with $|u|=|v|$) at discrete points in parameter space. We demonstrate that the local current allows us to estimate the local Majorana polarization (MP) -- a measurement of the local Majorana properties of the state. We derive an analytical expression for the MP in terms of local currents and benchmark it against numerical calculations for 2- and 3-sites chains that include a finite Zeeman field and electron-electron interactions. These results provide a way to quantitatively assess the quality of Majorana states in short Kitaev chains.

cond-mat.mes-hall↗

arXiv2025

Majorana sweet spots in 3-site Kitaev chains

Minimal Kitaev chains, composed of two quantum dots (QDs) connected via a superconductor, have emerged as an attractive platform to realize Majorana bound states (MBSs). These excitations exist when the ground state is degenerate. The additional requirement of isolating the MBS wavefunctions further restricts the parameter space to discrete sweet spots. While scaling up to Kitaev chains with more than two sites has the potential to improve the stability of the MBSs, longer chains offer more features to optimize, including the MBS localization length and the excitation gap. In this work, we theoretically investigate 3-site Kitaev chains and show that there are three different types of sweet spots, obtained by maximizing distinct MBS properties: genuine 3-site sweet spots with well-localized MBSs at the ends, effective 2-site sweet spots, where the middle site acts as a barrier, and sweet spots with delocalized MBSs that overlap in the middle of the chain. These three cases feature different degrees of robustness against perturbations, with the genuine 3-site being the most stable. We analyze the energy spectrum, transport, and microwave absorption associated with these three cases, showing how to distinguish them.

cond-mat.mes-hall↗

arXiv2025

Two-site Kitaev sweet spots evolving into topological islands

Artificial Kitaev chains based on arrays of quantum dots are promising platforms for realizing Majorana Bound States (MBSs). In a two-site Kitaev chain, it is possible to find these non-Abelian zero-energy excitations at certain points in parameter space (sweet spots). These states, commonly referred to as Poor man's Majorana bound states (PMMs), are challenging to find and stabilize experimentally. In this work, we investigate the evolution of the sweet spots as we increase the number of sites of the Kitaev chain. To this end, we use the Bogoliubov-de Gennes representation to study the excitations of the system, and the scattering matrix and Green functions formalisms to calculate the zero-bias conductance. Our results show that the sweet spots evolve into a region that grows bigger and becomes gradually more protected as the number of sites $N$ increases. Due to the protection of the MBSs, we refer to this region as a topological island. We obtain similar results by considering a realistic spinful model with finite magnetic fields in a chain of normal-superconducting quantum dots. For long chains, $N \geq 20$, we show the emergence of strictly zero-energy plateaus robust against disorder. Finally, we demonstrate that the topological islands can be observed by performing conductance measurements via a quantum dot side-coupled to the Kitaev chain. Our work shows that the fine-tuning required to create and detect PMMs in a 2-site Kitaev chain is significantly relaxed as the length of the chain increases and details how PMMs evolve into MBSs. Our results are consistent with experimental reports for 2 and 3-site chains.

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arXiv2024

Nonlocality of local Andreev conductances as a probe for topological Majorana wires

We propose a protocol based only on local conductance measurements for distinguishing trivial from topological phases in realistic three-terminal superconducting nanowires coupled to normal leads, capable of hosting Majorana zero modes (MZMs). By using Green functions and the scattering matrix approach, we calculate the conductance matrix and the local density of states (LDOS) as functions of the asymmetry in the couplings to the left ($Γ_L$) and right ($Γ_R$) leads. In the trivial phase, we find that the zero-bias local conductances are distinctively affected by variations in $Γ_R$ (for fixed $Γ_L$): while $G_{LL}$ is mostly constant, $G_{RR}$ decays exponentially as $Γ_R$ is decreased. In the topological phase, surprisingly, $G_{LL}$ and $G_{RR}$ are both suppressed with $G_{LL} \sim G_{RR}$. This \textit{nonlocal} suppression of $G_{LL}$ with $Γ_R$ scales with the MZM hybridization energy $\varepsilon_m$ and arises from the emergence of a dip in the LDOS near zero energy at the left end of the wire, which affects the local Andreev reflection. We further exploit this nonlocality of the local Andreev processes and the gate-controlled suppression of the LDOS by proposing a Majorana-based transistor. Our results hold for zero and low electron temperatures $T<20$ mK. For $T = 30, 40$ mK, $G_{LL}$ and $G_{RR}$ become less correlated. As an additional nonlocal fingerprint of the topological phase at higher $T$'s, we predict modulations in our \textit{asymmetric} conductance deviation $δG^{asym}_{LL}= G_{LL}^{Γ_R = Γ_L} - G_{LL}^{Γ_R \ll Γ_L}$ that remains commensurate with the Majorana oscillations in $\varepsilon_m$ over the range $30<T< 150~\rm{mK}$.

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