Roman M. Lutchyn

We propose and analyze theoretically an experimental setup for detecting the elusive Majorana particle in semiconductor-superconductor heterostructures. The experimental system consists of one-dimensional semiconductor wire with strong spin-orbit Rashba interaction embedded into a superconducting quantum interference device. We show that the energy spectra of the Andreev bound states at the junction are qualitatively different in topologically trivial (i.e., not containing any Majorana) and nontrivial phases having an even and odd number of crossings at zero energy, respectively. The measurement of the supercurrent through the junction allows one to discern topologically distinct phases and observe a topological phase transition by simply changing the in-plane magnetic field or the gate voltage. The observation of this phase transition will be a direct demonstration of the existence of Majorana particles.

We show that a film of a semiconductor in which s-wave superconductivity and Zeeman splitting are induced by the proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. Since time-reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose-a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator-is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

We theoretically investigate the influence of designed pulse sequences in restoring quantum coherence lost due to background noise in superconducting qubits. We consider both $1/f$ noise and random telegraph noise and show that the qubit coherence time can be substantially enhanced by carefully engineered pulse sequences. Conversely, the time dependence of qubit coherence under external pulse sequences could be used as a spectroscopic tool for extracting the noise mechanisms in superconducting qubits, i.e., by using Uhrig's pulse sequence [Phys. Rev. Lett. 98, 100504 (2007)], one can obtain information about moments of the spectral density of noise. We also study the effect of pulse sequences on the evolution of the qubit affected by a strongly coupled fluctuator and show that the non-Gaussian features in decoherence are suppressed by the application of pulses.

We show that an ordinary semiconducting thin film with spin-orbit coupling can, under appropriate circumstances, be in a quantum topologically ordered state supporting exotic Majorana excitations which follow non-Abelian statistics. The key to the quantum topological order is the coexistence of spin-orbit coupling with proximity-induced $s$-wave superconductivity and an externally induced Zeeman coupling of the spins. For the Zeeman coupling below a critical value, the system is a nontopological (proximity-induced) $s$-wave superconductor. However, for a range of Zeeman coupling above the critical value, the lowest energy excited state inside a vortex is a zero-energy Majorana fermion state. The system, thus, has entered into a non-Abelian $s$-wave superconducting state via a topological quantum phase transition (TQPT) tuned by the Zeeman coupling. In the topological phase, since the time-reversal symmetry is explicitly broken by the Zeeman term in the Hamiltonian, the edge of the film constitutes a chiral Majorana wire. Just like the $s$-wave superconductivity, the Zeeman coupling can also be proximity induced in the film by an adjacent magnetic insulator. We show this by an explicit model tight-binding calculation for both types of proximity effects in the heterostructure geometry. Here we show that the same TQPT can be accessed by varying the interface transparency between the film and the superconductor. For the transparency below (above) a critical value, the system is a topological (regular) $s$-wave superconductor. In the one-dimensional version of the same structure and for the Zeeman coupling above the critical value, there are localized Majorana zero-energy modes at the two ends of a semiconducting quantum nanowire. In this case, the Zeeman coupling can be induced more easily by an external magnetic field parallel to the wire, obviating the need for a magnetic insulator. We show that, despite the fact that the superconducting pair potential in the nanowire is explicitly $s$ wave, tunneling of electrons to the ends of the wire reveals a pronounced zero-bias peak. Such a peak is absent when the Zeeman coupling is below its critical value, i.e., the nanowire is in the nontopological $s$-wave superconducting state. We argue that the observation of this zero-bias tunneling peak in the semiconductor nanowire is possibly the simplest and clearest experiment proposed so far to unambiguously detect a Majorana fermion mode in a condensed-matter system.