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Register a new userDetecting the universal fractional entropy of Majorana zero modes
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A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is $log 2$. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of $frac{1}{2}log 2$ is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment [Hartman et. al., Nat. Phys. 14, 1083 (2018)] to the case of a proximitized topological system hosting MZMs, and propose a method to measure this $frac{1}{2}log 2$ entropy change --- an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non-topological states.
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Proposals for realizing Majorana fermions in condensed matter systems typically rely on magnetic fields, which degrade the proximitizing superconductor and plague the Majoranas detection. We propose an alternative scheme to realize Majoranas based only on phase-biased superconductors. The phases (at least three of them) can be biased by a tiny magnetic field threading macroscopic superconducting loops, focusing and enhancing the effect of the magnetic field onto the junction, or by supercurrents. We show how a combination of the superconducting phase winding and the spin-orbit phase induced in closed loops (Aharonov-Casher effect) facilitates a topological superconducting state with Majorana end states. We demontrate this scheme by an analytically tractable model as well as simulations of realistic setups comprising only conventional materials.
Among the major approaches that are being pursued for realizing quantum bits, the Majorana-based platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologically-protected manner. The quantum information is protected by its nonlocal storage in localized and well-separated Majorana zero modes, and manipulated by exploiting their nonabelian quantum exchange properties. Realizing these topological qubits is experimentally challenging, requiring superconductivity, helical electrons (created by spin-orbit coupling) and breaking of time reversal symmetry to all cooperate in an uncomfortable alliance. Over the past decade, several candidate material systems for realizing Majorana-based topological qubits have been explored, and there is accumulating, though still debated, evidence that zero modes are indeed being realized. This paper reviews the basic physical principles on which these approaches are based, the material systems that are being developed, and the current state of the field. We highlight both the progress made and the challenges that still need to be overcome.
The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of quantum quench to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${cal L}(t)=| < psi(0) | psi(t) > |^2sim t^{-alpha}$ for large times after the quench, with a universal critical exponent $alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.
We study the low-energy transport properties of a hybrid device composed by a native quantum dot coupled to both ends of a topological superconducting nanowire section hosting Majorana zero-modes. The account of the coupling between the dot and the farthest Majorana zero-mode allows to introduce the topological quality factor, characterizing the level of topological protection in the system. We demonstrate that Coulomb interaction between the dot and the topological superconducting section leads to the onset of the additional overlap of the wavefunctions describing the Majorana zero-modes, leading to the formation of trivial Andreev bound states even for spatially well-separated Majoranas. This leads to the spoiling of the quality factor and introduces a constraint for the braiding process required to perform topological quantum computing operations.
In this work, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing superconductivity on the helical channel through proximity effect will create Majorana zero energy modes (MZMs) at the ends of the cut. In this geometry, there is no need for the proximity gap to overcome the bulk insulating gap of the QAHI to create MZMs as in the two-dimensional QAHI/superconductor (QAHI/SC) heterostructures. Therefore, the topological regime with MZMs is greatly enlarged. Furthermore, due to the presence of a single helical channel, the generation of low energy in-gap bound states caused by multiple conducting channels is avoided such that the MZMs can be well separated from other in-gap excitations in energy. This simple but practical approach allows the creation of a large number of MZMs in devices with complicated geometry such as hexons for measurement-based topological quantum computation. We further demonstrate how braiding of MZMs can be performed by controlling the coupling strength between the counter-propagating electron modes.
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