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Register a new userMajorana fermion arcs and the local density of states of UTe$_2$
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$text{UTe}_2$ is a leading candidate for chiral p-wave superconductivity, and for hosting exotic Majorana fermion quasiparticles. Motivated by recent STM experiments in this system, we study particle-hole symmetry breaking in chiral p-wave superconductors. We compute the local density of states from Majorana fermion surface states in the presence of Rashba surface spin-orbit coupling, which is expected to be sizeable in heavy-fermion materials like UTe$_2$. We show that time-reversal and surface reflection symmetry breaking lead to a natural pairing tendency towards a triplet pair density wave state, which naturally can account for broken particle-hole symmetry.
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The recently discovered superconductor, UTe$_2$, has attracted immense scientific interest due to the experimental observations that suggest odd-parity superconductivity. It is believed that the material becomes a heavy-fermion metal at low temperatures although details of the normal state are unclear. Using Fourier transform infrared spectroscopy (FTIR), the normal state electronic structure of UTe$_2$ was investigated at zero applied magnetic field. Combining the measured reflectivity with the dc resistivity, the complex optical conductivity was obtained over a large frequency range. The frequency dependence of the real part of the optical conductivity exhibits a MIR peak around 4000 cm$^{-1}$ and a narrow Drude peak that develops below 40 K. A combination of density functional and dynamic mean field theory (DFT + DMFT) gives spectra in close correspondence to the experiment. Via this comparison we attribute the prominent MIR peak to inter-band transitions involving a narrow U 5$f$ feature that develops near the Fermi level. In this regard, our data gives spectroscopic evidence for the existence of a low energy Kondo resonance at temperatures just above the onset of superconductivity and implicates heavy electrons in the formation of the superconducting state. We find that the coherent Kondo resonance is primarily associated with a collapse of scattering and less with a transfer of spectral weight.
We have performed the $^{125}$Te-nuclear magnetic resonance (NMR) measurement in the field along the $b$ axis on the newly discovered superconductor UTe$_2$, which is a candidate of a spin-triplet superconductor. The nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ abruptly decreases below a superconducting (SC) transition temperature $T_c$ without showing a coherence peak, indicative of UTe$_2$ being an unconventional superconductor. It was found that the temperature dependence of $1/T_1T$ in the SC state cannot be understood by a single SC gap behavior but can be explained by a two SC gap model. The Knight shift, proportional to the spin susceptibility, decreases below $T_c$, but the magnitude of the decrease is much smaller than the decrease expected in the spin-singlet pairing. Rather, the small Knight-shift decrease as well as the absence of the Pauli-depairing effect can be interpreted by the spin triplet scenario.
We study the topology and symmetry of surface Majorana arcs in superconductors with nonunitary cyclic pairing. Cyclic $p$-wave pairing may be realized in a cubic or tetrahedral crystal, while it is a candidate for the interior $^3P_2$ superfluids of neutron stars. The cyclic state is an admixture of full gap and nodal gap with eight Weyl points and the low-energy physics is governed by itinerant Majorana fermions. We here show the evolution of surface states from Majorana cone to Majorana arcs under rotation of surface orientation. The Majorana cone is protected solely by an accidental spin rotation symmetry and fragile against spin-orbit coupling, while the arcs are attributed to two topological invariants: the first Chern number and one-dimensional winding number. Lastly, we discuss how topologically protected surface states inherent to the nonunitary cyclic pairing can be captured from surface probes in candidate compounds, such as U$_{1-x}$Th$_{x}$Be$_{13}$. We examine tunneling conductance spectra for two competitive scenarios in U$_{1-x}$Th$_{x}$Be$_{13}$---the degenerate $E_u$ scenario and the accidental scenario.
We study the formation of Majorana states in superconductors using the Majorana polarization, which can locally evaluate the Majorana character of a given state. We introduce the definition of the Majorana polarization vector and the corresponding criterion to identify a Majorana state, and we apply it to some simple cases such as a one-dimensional wire with spin-orbit coupling, subject to a Zeeman magnetic field, and proximitized by a superconductor, as well as to an NS junction made with such a wire. We also apply this criterion to two-dimensional finite-size strips and squares subject to the same physical conditions. Our analysis demonstrates the necessity of using the Majorana polarization local order parameter to characterize the Majorana states, particularly in finite-size systems.
We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in Ref. [R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016)], under a strong magnetic field can be seen in LDOS without smeared out by non-zero-energy states. The spin-resolved LDOS further reveals that the spin of the exterior Majorana state is strongly polarized. Accordingly, the induced odd-frequency spin-triplet pairs are found to be spin-polarized as well. In order to detect the exterior Majorana states, however, the Fermi energy should be closed to the Dirac point to avoid contributions from continuum levels. We also study a different two-dimensional topological-superconducting system where a two-dimensional electron gas with the spin-orbit coupling is sandwiched between an s-wave superconductor and a ferromagnetic insulator. We show that the radius of an exterior Majorana state can be tuned by an applied magnetic field. However, on the contrary to the results at a TI surface, neither the exterior Majorana state nor the induced odd-frequency spin-triplet pairs are spin-polarized. We conclude that the spin-polarization of the Majorana state is attributed to the spin-polarized Landau level which is characteristic for systems with the Dirac-like dispersion.
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