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Majorana Device Constructed to Investigate Non-Markovian Quantum Transport Dynamics

In an article recently published in New Journal of Physics, a Majorana device was constructed using an asymmetric superconducting chain with two leads to investigate the device’s non-Markovian quantum transport dynamics.

Majorana Device Constructed to Investigate Non-Markovian Quantum Transport Dynamics

Study: The differential conductance tunnel spectroscopy in an analytical solvable two-terminal Majorana device. Image Credit: Warongdech Digital/

Asymmetric superconducting chains were realized by either fabricating a hybrid system of superconductors and semiconductor nanowire or by using one-dimensional (1D) transverse-field Ising chains. Changing the chemical potential in asymmetric superconducting chains results in a quantum phase transition of the ground state from Majorana bound state to Andreev bound state. However, the energy of the ground state remains zero.

The accurate transitory transport current and the related differential conductance were solved. The obtained results revealed the importance of interference between the right and left Majorana zero modes to facilitate the phase transition of conductance.  This caused insulation of topologically trivial states localized at edges with zero conductance. However, the topologically nontrivial nonlocally distributed states showed a quantized conductance of 2e2/h.

The topological phase transitions at zero bias and in the differential conductance at zero-mode were independent of lead structure and its coupling strength. The superconducting chain’s finite size and the coherence effect between non-zero and zero modes were examined in the differential conductance using two-terminal Majorana device.

Majorana Bound States

Majorana-bound states are believed to be protected from quantum decoherence caused by local perturbations and are considered as potential candidates for quantum computing and quantum information applications. In addition, the Majorana bound states are distributed nonlocally at material boundaries.

On the other hand, the topological device’s edges with leads result in Andreev reflection-based Majorana resonance, where the differential conductance at the zero-bias peak is quantized to  2e2/h.  Nevertheless, when the previous attempts to identify and separate Majorana bound states from the Andreev bound states were made, the disorders and noises in these systems made the identification of Majorana zero modes a challenging process.

The use of tunneling spectroscopy through hybrid semiconductor-superconductor nanowires lead to primary detection, and the hybrid nanowires undergo a topologically non-trivial quantum phase transition under an external magnetic field. Moreover, Majorana-bound state’s existence in complex material structures has not been determined experimentally due to their zero energy and subgap states.

Although it is difficult to experimentally identify the Majorana bound state, phase transitions in topology and changes in the conductivity of Majorana nanowires remain of great interest in basic research and industrial applications. Thus, the present study is conducted on two-terminal Majorana device. 

Two-Terminal Majorana Device for Quantum Transport Dynamics

In the present study, a two-terminal Majorana device was constructed that consisted of a p-wave superconducting Kitaev chain coupled to two leads for studying its transient transport properties. Regulating the chemical potential of the asymmetric superconducting chain helped its ground state to transition from the Majorana bound state (topologically nontrivial) to the Andreev bound state (topologically trivial), while retaining the ground state energy as zero.

Furthermore, an external magnetic field or electric gate helped control the coupling of the superconductor’s edge state with the leads. Thus, the quantum Langevin and exact master equations solved the transient transport current analytically and lead’s arbitrary spectral densities for differential conductance at any temperature.

Moreover, the exact solution was used to investigate the formation of zero-bias peak through quantum transport’s non-Markovian dynamics. This exact solution also clarified the mechanism that led to the difference between zero-bias conductance from 2e2/h, and zero between the topologically trivial phase and non-trivial phases.

With the use of a large energy gap between zero and non-zero energy band in a long superconducting chain length, the zero bias conductance change from 2e2/h to phase transition point zero was substantial. Moreover, the obtained results were independent of lead’s structure and the coupling between superconducting chain and leads. These observations indicated that such a Majorana device can be used as an external-field controlled diode.

The existence of a negative differential conductance in the coupling region (led by strong chain) was observed, which was previously noticed in semiconductor heterostructures and molecular devices. Moreover, when the energy gap between zero and non-zero energy states was small, the coherence between them enhanced the zero-bias conductance peak, which exceeded 2e2/h near the critical point of the topologically non-trivial phase.


To summarize, the quantum Langevin equation and exact master equation-based quantum transport theory was used to solve the asymmetric superconductor two-terminal device’s differential conductance consisting of scattered spectral densities. This two-terminal device consisted of zero-energy modes that helped in the phase transition between Majorana bound state (topologically nontrivial) and the Andreev bound state (topologically trivial).

Majorana and Andreev-bound state’s transport properties were studied in the asymmetric superconductor two-terminal device. The results revealed that the spectral densities based on Majorana zero mode determined the differential conductance in the study state.


Yao, C. Z., Zhang, W. M. (2022) The differential conductance tunnel spectroscopy in an analytical solvable two-terminal Majorana device. New Journal of Physics

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Bhavna Kaveti

Written by

Bhavna Kaveti

Bhavna Kaveti is a science writer based in Hyderabad, India. She has a Masters in Pharmaceutical Chemistry from Vellore Institute of Technology, India, and a Ph.D. in Organic and Medicinal Chemistry from Universidad de Guanajuato, Mexico. Her research work involved designing and synthesizing heterocycle-based bioactive molecules, where she had exposure to both multistep and multicomponent synthesis. During her doctoral studies, she worked on synthesizing various linked and fused heterocycle-based peptidomimetic molecules that are anticipated to have a bioactive potential for further functionalization. While working on her thesis and research papers, she explored her passion for scientific writing and communications.


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