🔬 mesoscale physics

Spectral Bifurcation and Anomalous Supercurrent in Dissipative Topological Insulator-based Josephson Junctions

This study demonstrates that coupling a topological insulator-based Josephson junction to a dissipative environment induces spectral bifurcation and finite lifetimes for Majorana bound states, ultimately driving an anomalous supercurrent with a non-vanishing value at zero phase difference.

Original authors: Ardamon Sten, Paramita Dutta, Sudeep Kumar Ghosh

Published 2026-07-22

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CC BY 4.0

Original authors: Ardamon Sten, Paramita Dutta, Sudeep Kumar Ghosh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where electricity doesn't just flow like water in a pipe, but dances like a synchronized troupe of acrobats. This is the realm of quantum physics, specifically the study of superconductors—materials that conduct electricity with zero resistance, allowing electrons to pair up and move in perfect unison. When two superconductors are separated by a tiny gap, they form a "Josephson junction," a magical bridge where these electron pairs can tunnel through, creating a supercurrent that depends on the "phase" of their dance. Now, imagine adding a twist: what if the dance floor itself is slightly slippery, or if the acrobats are constantly losing energy to the air around them? This is the world of "dissipation," or energy loss, which usually ruins delicate quantum states. Scientists are obsessed with a special type of material called a "topological insulator." Think of these as materials that act like insulators on the inside (blocking electricity) but conduct electricity perfectly on their surface, protected by a kind of quantum "force field" that makes them incredibly robust against disturbances. The big question in modern physics is: What happens when you try to build a superconducting bridge using these protected materials, but you also introduce the messy, energy-draining reality of the real world?

This paper, titled "Spectral Bifurcation and Anomalous Supercurrent in Dissipative Topological Insulator-based Josephson Junctions," dives into exactly that scenario. The authors, Ardamon Sten, Paramita Dutta, and Sudeep Kumar Ghosh, set up a theoretical experiment where they take a Josephson junction built on the surface of a 3D topological insulator and attach a "lossy" metallic lead to it. Think of this lead as a sponge soaking up energy from the system, introducing dissipation. Instead of using standard math, they use a special "non-Hermitian" toolkit (a mathematical way to describe systems that lose energy) to model how this sponge affects the quantum dance.

What they find is a fascinating and somewhat chaotic reshaping of the rules. In a perfect, loss-free world, the energy levels of the electrons crossing the junction would behave in a very predictable, symmetric way. However, once the "sponge" is introduced, the symmetry breaks. The energy spectrum (the map of allowed energy levels) splits apart, or "bifurcates," in a strange way. One branch of the energy levels merges with the surrounding chaos, while the other dives just below the superconducting gap. Most importantly, the point where the energy hits zero—which usually happens at a specific, predictable moment in the dance—gets pushed off-center and gains a "fuzzy" lifetime. In plain terms, the special "Majorana" states (exotic particles that are their own antiparticles) that usually live here become unstable and start to decay because of the energy loss.

The most surprising result is what happens to the electric current. In a normal junction, if you don't apply any voltage or phase difference, the current should be zero. But in this dissipative setup, the authors find an "anomalous supercurrent." Even when the phase difference is zero, a current still flows! It's as if the bridge has a built-in current that refuses to stop, driven by the very asymmetry caused by the energy loss. The paper suggests that this happens because the dissipation interacts with the topological protection in a unique way that ordinary metals don't experience. While the authors note that these results are based on theoretical models and simulations (specifically using a "short" junction approximation), they point out that this behavior could be tested in real devices, such as those made with Niobium superconductors on HgTe or Bi2Te3 surfaces. Ultimately, the paper reveals that dissipation doesn't just ruin quantum devices; it can fundamentally rewrite how they transport electricity, opening up new possibilities for engineering quantum systems that use energy loss as a feature rather than a bug.

Technical Summary: Spectral Bifurcation and Anomalous Supercurrent in Dissipative Topological Insulator-based Josephson Junctions

Problem Statement
The interplay between topological protection and environmental dissipation represents a critical frontier in the development of hybrid quantum devices. While Josephson junctions (JJs) based on topological insulators (TIJJs) are known to host exotic states such as helical Andreev bound states (ABSs) and non-chiral Majorana modes, the impact of intrinsic dissipation on these systems remains largely unexplored. Specifically, it is unclear how coupling a "lossy" metallic lead to a topological Josephson junction affects quantum transport properties, the stability of Majorana bound states, and the current-phase relationship (CPR). Unlike Hermitian systems where dissipation is often treated perturbatively, non-Hermitian systems exhibit complex spectra and exceptional points (EPs) that may fundamentally alter transport signatures.

Methodology
The authors model a dissipative planar Josephson junction formed on the surface of a 3D topological insulator (3DTI) sandwiched between two $s$ -wave singlet superconductors.

Non-Hermitian Modeling: Dissipation is introduced by coupling the junction to a "lossy" metallic lead connected to an electron reservoir. This is described effectively using a non-Hermitian Hamiltonian derived via the Lindblad formalism, neglecting quantum jumps. The dissipation manifests as an imaginary potential barrier at the junction interface.
Effective Hamiltonian: The system is treated using an effective Bogoliubov-de Gennes (BdG) Hamiltonian. The contact potential barrier is defined as $U(x) = (V_1 - iV_2)\delta(x)$ , where $V_1$ represents the real barrier strength (tunable via a top gate) and $V_2$ represents the imaginary barrier strength induced by the lead.
Transport Calculation: The authors solve for the complex Andreev bound state (ABS) spectrum in the "short" junction limit (junction width $\ll$ coherence length). To calculate the supercurrent, they employ the Furusaki-Tsukada (FT) formula, which sums over Andreev reflection processes. This approach is chosen over alternative non-Hermitian supercurrent formulas to avoid divergences at "gap-exit points" (GEPs) and to properly account for contributions from Green's function branch cuts, not just bound state poles.

Key Results

Complex Andreev Spectrum and Bifurcation:
- The ABS spectrum becomes complex, possessing both real (energy) and imaginary (lifetime/broadening) components.
- For oblique incidence, the real part of the spectrum undergoes bifurcation beyond specific phase intervals ( $\phi_1, \phi_2$ ). One branch merges with the continuum (supra-gap), while the other remains sub-gap. These points are termed Gap-Exit Points (GEPs).
- Unlike the Hermitian case, the zero-energy crossing for normally incident quasiparticles shifts away from $\phi = \pi$ and acquires a non-zero imaginary component. This indicates that the associated Majorana bound states acquire a finite lifetime, signaling a loss of robustness against dissipation.
Spectral Asymmetry:
- The interplay between the real barrier ( $V_1$ ) and the non-Hermitian dissipation ( $V_2$ ) induces a fundamental asymmetry in the spectrum with respect to $\phi = \pi$ .
- In contrast, an "ordinary" non-Hermitian Josephson junction (replacing the TI with a normal metal) exhibits symmetric gap-exit points and lacks this specific asymmetry, highlighting the unique role of the topological surface states and Kramers degeneracy in the TIJJ.
Anomalous Supercurrent:
- The spectral asymmetry drives an anomalous supercurrent, manifested as a non-vanishing current at zero phase difference ( $\phi = 0, 2\pi$ ).
- The current-phase relationship (CPR) is $2\pi$ -periodic but non-sinusoidal and asymmetric about $\phi = \pi$ .
- The critical current decreases with increasing dissipation strength ( $Z_2$ ) due to decoherence and quasiparticle escape to the reservoir.
- The authors note that standard ABS-based formulas (which only consider bound state poles) predict "Josephson gaps" (zero current) beyond GEPs, whereas the FT formula correctly yields a finite supercurrent in these regions by including continuum contributions.

Significance and Claims
The paper claims to reveal how dissipation fundamentally reshapes superconducting transport in topological junctions. The primary significance lies in demonstrating that:

Dissipation does not merely dampen transport but qualitatively alters the spectral topology, causing bifurcations and shifting zero-energy crossings.
The robustness of Majorana bound states against dissipation is compromised, as they acquire finite lifetimes and lose their characteristic zero-energy crossing at $\phi = \pi$ .
The interplay between topological protection and non-Hermiticity generates a unique "anomalous" supercurrent that persists even at zero phase bias, a signature distinct from ordinary non-Hermitian junctions.

The authors suggest these findings open new directions for "dissipation-engineered" quantum devices. They propose that the described physics could be realized in experimental setups such as Nb-superconductors on HgTe 3DTI surfaces or Nb-Bi $_2$ Te $_3$ -Nb junctions, provided the junction dimensions and material parameters (e.g., induced gap, tunneling rate) fall within specific regimes. The study focuses on the "short" junction limit, noting that the "long" junction regime remains a subject for future investigation.

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