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Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3

We study the quasiparticle excitations around a single vortex in the superconducting topological insulator Cu$_{x}$Bi$_{2}$Se$_{3}$, focusing on a superconducting state with point nodes. Inspired by the recent Knight shift measurements, we propose two ways to detect the positions of point nodes, using an explicit formula of the density of states with Kramer-Pesch approximation in the quasiclassical treatment. The zero-energy local density of states around a vortex parallel to the $c$-axis has a twofold shape and splits along the nodal direction with increasing energy; these behaviors can be detected by the scanning tunneling microscopy. An angular dependence of the density of states with a rotating magnetic field on the $a$-$b$ plane has deep minima when the magnetic field is parallel to the directions of point nodes, which can be detected by angular-resolved heat capacity and thermal conductivity measurements. All the theoretical predictions are detectable via standard experimental techniques in magnetic fields.