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Register a new userDeconfinement of Majorana vortex modes produces a superconducting Landau level
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Added by
Micha{\\l} Jan Pacholski
Publication date
2021
fields
Physics
and research's language is
English
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A spatially oscillating pair potential $Delta(r)=Delta_0 e^{2i Kcdot r}$ with momentum $K>Delta_0/hbar v$ drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity $v$, on a superconducting substrate with gap $Delta_0$, in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector $sqrt{K^2-(Delta_0/hbar v)^2}$. The striped pattern also provides a means to measure the chirality of the Majorana fermions.
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The combination of two-dimensional Dirac surface states with s-wave superconductivity is expected to generate localized topological Majorana zero modes in vortex cores. Putative experimental signatures of these modes have been reported for heterostructures of proximitized topological insulators, iron-based superconductors or certain transition metal dichalcogenides. Despite these efforts, the Majorana nature of the observed excitation is still under debate. We propose to identify the presence of Majorana vortex modes using a non-local transport measurement protocol originally proposed for one-dimensional settings. In the case of an isolated subgap state, the protocol provides a spatial map of the ratio of local charge- and probability-density which offers a clear distinction between Majorana and ordinary fermionic modes. We show that these distinctive features survive in the experimentally relevant case of hybridizing vortex core modes.
The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of textit{d}-wave superconductivity, with a negative answer: The scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: The chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value $G=tfrac{1}{2}g_0 Phi/Phi_0$, with $Phi$ the magnetic flux through the system, $Phi_0$ the superconducting flux quantum, and $g_0$ the thermal conductance quantum.
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.
Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures, we consider a realistic tight-binding model and analyze its transport behavior numerically. In particular, we take into account the presence of a superconducting contact, used in real experiments to extract the current, which is usually not included in theoretical calculations. We show that important features emerge that are absent in simpler models, such as the shift in energy of the proximity gap signal, and the enhanced visibility of the topological gap for increased spin-orbit interaction. We find oscillations of the zero bias peak as a function of the magnetic field and study them analytically. We argue that many of the experimentally observed features hint at an actual spin-orbit interaction larger than the one typically assumed. However, even taking into account all the known ingredients of the experiments and exploring many parameter regimes for MFs, we are not able to reach full agreement with the reported data. Thus, a different physical origin for the observed zero-bias peak cannot be excluded.
Tunneling two level systems (TLS), present in dielectrics at low temperatures, have been recently studied for fundamental understanding and superconducting device development. According to a recent theory by Burin textit{et al.}, the TLS bath of any amorphous dielectric experiences a distribution of Landau-Zener transitions if exposed to simultaneous fields. In this experiment we measure amorphous insulating films at millikelvin temperatures with a microwave field and a swept electric field bias using a superconducting resonator. We find that the maximum dielectric loss per microwave photon with the simultaneous fields is approximately the same as that in the equilibrium state, in agreement with the generic material theory. In addition, we find that the loss depends on the fields in a way which allows for the separate extraction of the TLS bath dipole moment and density of states. This method allows for the study of the TLS dipole moment in a diverse set of disordered films, and provides a technique for continuously inverting their population.
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