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Topological nodal $i$-wave superconductivity in PtBi$_2$

Susmita Changdar, Oleksandr Suvorov, Andrii Kuibarov, Setti Thirupathaiah, Grigoriy Shipunov, Saicharan Aswartham, Sabine Wurmehl, Iryna Kovalchuk, Klaus Koepernik, Carsten Timm, Bernd Büchner, Ion Cosma Fulga, Sergey Borisenko, Jeroen van den Brink

Abstract

Most superconducting materials are well-understood and conventional in the sense that the pairs of electrons that cause the superconductivity by their condensation have the highest possible symmetry. Famous exceptions are the enigmatic high-$T_c$ cuprate superconductors. Nodes in their superconducting gap are the fingerprint of their unconventional character and imply superconducting pairing of $d$-wave symmetry. Here, using angle-resolved photoemission spectroscopy, we observe that the Weyl semimetal PtBi$_2$ harbors nodes in its superconducting gap, implying unconventional $i$-wave pairing symmetry. At temperatures below $10\,\mathrm{K}$, the superconductivity in PtBi$_2$ gaps out its topological surface states, the Fermi arcs, while its bulk states remain normal. The nodes in the superconducting gap that we observe are located exactly at the center of the Fermi arcs, and imply the presence of topologically protected Majorana cones around this locus in momentum space. From this, we infer theoretically that robust zero-energy Majorana flat bands emerge at surface step edges. This not only establishes PtBi$_2$ surfaces as unconventional, topological $i$-wave superconductors but also as a promising material platform in the ongoing effort to generate and manipulate Majorana bound states.

Topological nodal $i$-wave superconductivity in PtBi$_2$

Abstract

Most superconducting materials are well-understood and conventional in the sense that the pairs of electrons that cause the superconductivity by their condensation have the highest possible symmetry. Famous exceptions are the enigmatic high- cuprate superconductors. Nodes in their superconducting gap are the fingerprint of their unconventional character and imply superconducting pairing of -wave symmetry. Here, using angle-resolved photoemission spectroscopy, we observe that the Weyl semimetal PtBi harbors nodes in its superconducting gap, implying unconventional -wave pairing symmetry. At temperatures below , the superconductivity in PtBi gaps out its topological surface states, the Fermi arcs, while its bulk states remain normal. The nodes in the superconducting gap that we observe are located exactly at the center of the Fermi arcs, and imply the presence of topologically protected Majorana cones around this locus in momentum space. From this, we infer theoretically that robust zero-energy Majorana flat bands emerge at surface step edges. This not only establishes PtBi surfaces as unconventional, topological -wave superconductors but also as a promising material platform in the ongoing effort to generate and manipulate Majorana bound states.

Paper Structure

This paper contains 6 sections, 3 figures.

Table of Contents

  1. ARPES characterization
  2. Evidence for nodes in the superconducting gap
  3. Comparison to electronic structure calculations
  4. Step-edge Majorana modes
  5. Acknowledgements

Figures (3)

  • Figure 1: Progress in experimental accuracy.(a) Fermi surface (FS) map observed with FeSuMa and He-I lamp $h\nu=21.2\,\mathrm{eV}$ from KT-termination. Collected LEED image on PtBi$_2$ single crystal is demonstrated in the inset. The yellow box marks the position of the arc at the FS map. (b) The arc becomes well resolved in the FS observed with Laser ARPES with $h\nu=6\,\mathrm{eV}$ (KT-termination). (c) Momentum-energy intensity distribution corresponding to the momentum cut through the arc (DH-termination). (d) MDC and EDC plotted along the red and green arrows of panel (c).
  • Figure 2: Anisotropic superconducting gap.(a) leading edge gap across different points of the arc (KT-termination). (b) Angular dependence of the gap, showing a node at $\theta=0^\circ$ and a maximum gap at $\pm 90^\circ$ for Cleave 1 of sample 1 (top panel). Middle panel shows the leading edge gap from EDCs taken along $\theta = 0^\circ$ and $\pm 90^\circ$ at $2.5\,\mathrm{K}$. This is equivalent to the gap observed from EDCs taken at $+90^\circ$ with $2.5\,\mathrm{K}$ and $30\,\mathrm{K}$ (bottom panel). (c) Energy distribution curves (EDCs) taken at the node, $+90^{\circ}$, and $-90^{\circ}$ respectively for 2.5 K and 20 K. For $\pm 90^{\circ}$, the temperature is cycled back to 2.5 K, which overlap with the initial 2.5 K EDCs. (d) Angular dependence for Cleave 2 of sample 1 (left panel) and for three other PtBi$_2$ single crystals from different batches. (e) Temperature dependence of the EDC corresponding to the arc exhibiting the gradual closing of the leading edge gap at higher temperature.
  • Figure 3: Calculated properties of the $i$-wave superconductor -- Majorana cones and hinge states.(a) Calculated spectral density at the Fermi level in a DFT-BdG Wannier model for the $\left(00\bar{1}\right)$ surface (DH termination Vocaturo2024, top panels) and for the $(001)$ surface (bottom panels) with superconducting $i$-wave pairing $V_{0} \sin\left(6\varphi\right)$ on the first three surface layers for coupling strengths $V_{0}=0$ (no superconductivity) and $V_0 = 21$ meV. The points at which the gap was determined are indicated in the normal state panel using labels 0 to 6. Spectral weights larger than $200$ are shown in yellow. (b) The SC gap as a function of distance from the node for three coupling strengths $V_{0}=7$ (black), 15 (red), and 21 meV (green), in the case of the DH termination, as in the top panels of (a). Circles are calculated values, the lines are guides to the eyes. (c) Electronic structure of the effective model. The color scale denotes the probability density of the states in real space. Bulk Weyl cones are shown in green, and top and bottom Majorana cones are shown in red and blue, respectively. Dispersionless zero-energy Majorana hinge modes are shown in black. (d) Sketch of the prism geometry used in the effective model. The system is infinite in the $y$ direction and finite in $x$ and $z$. The superconducting top surface is shown in blue, and the Majorana hinge modes are shown in red. (e) Probability density of the four Majorana hinge modes in the prism geometry of panel (d), computed for $k_y=1.3$, corresponding to the green arrow in panel (c).