This paper proposes a theoretical method to detect Majorana fermions in semiconductor-superconductor heterostructures. The setup involves a one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded in a superconducting quantum interference device (SQUID). The energy spectra of Andreev bound states at the junction differ between topologically trivial and nontrivial phases, with an even or odd number of zero-energy crossings. The supercurrent through the junction can be used to distinguish these phases and observe a topological phase transition by varying the in-plane magnetic field or gate voltage. The observation of this phase transition would confirm the existence of Majorana particles. Majorana fermions, self-antiparticles, are of interest for topological quantum computation due to their non-Abelian statistics and immunity to local noise. The paper discusses the experimental realization of Majorana fermions in solid-state systems, focusing on a 1D semiconductor/superconductor heterostructure. The setup uses a semiconductor with strong spin-orbit coupling and a superconductor, where the spin-orbit coupling leads to the formation of Majorana modes at the ends of the wire. The system undergoes a phase transition from a superconducting state with Majorana modes to a normal superconducting state without them. Theoretical analysis shows that the Andreev spectrum exhibits an odd number of crossings in the topologically nontrivial phase, while an even number in the trivial phase. This difference allows distinguishing between the two phases. The phase transition is protected by particle-hole symmetry and is associated with the presence of Majorana zero-energy modes. The paper also discusses the experimental techniques for detecting these modes, including measuring the Josephson current and using inductively coupled rf-driven tank circuits to monitor the effective Josephson inductance. The results suggest that the proposed setup is experimentally feasible for observing Majorana fermions in semiconductor-superconductor heterostructures.This paper proposes a theoretical method to detect Majorana fermions in semiconductor-superconductor heterostructures. The setup involves a one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded in a superconducting quantum interference device (SQUID). The energy spectra of Andreev bound states at the junction differ between topologically trivial and nontrivial phases, with an even or odd number of zero-energy crossings. The supercurrent through the junction can be used to distinguish these phases and observe a topological phase transition by varying the in-plane magnetic field or gate voltage. The observation of this phase transition would confirm the existence of Majorana particles. Majorana fermions, self-antiparticles, are of interest for topological quantum computation due to their non-Abelian statistics and immunity to local noise. The paper discusses the experimental realization of Majorana fermions in solid-state systems, focusing on a 1D semiconductor/superconductor heterostructure. The setup uses a semiconductor with strong spin-orbit coupling and a superconductor, where the spin-orbit coupling leads to the formation of Majorana modes at the ends of the wire. The system undergoes a phase transition from a superconducting state with Majorana modes to a normal superconducting state without them. Theoretical analysis shows that the Andreev spectrum exhibits an odd number of crossings in the topologically nontrivial phase, while an even number in the trivial phase. This difference allows distinguishing between the two phases. The phase transition is protected by particle-hole symmetry and is associated with the presence of Majorana zero-energy modes. The paper also discusses the experimental techniques for detecting these modes, including measuring the Josephson current and using inductively coupled rf-driven tank circuits to monitor the effective Josephson inductance. The results suggest that the proposed setup is experimentally feasible for observing Majorana fermions in semiconductor-superconductor heterostructures.