Sumanta Tewari

Generic new platform for topological quantum computation using semiconductor heterostructures.

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.

px+ipy superfluid from s-wave interactions of fermionic cold atoms.

Two-dimensional (p(x)+ip(y)) superfluids or superconductors offer a playground for studying intriguing physics such as quantum teleportation, non-Abelian statistics, and topological quantum computation. Creating such a superfluid in cold fermionic atom optical traps using p-wave Feshbach resonance is turning out to be challenging. Here we propose a method to create a p(x)+ip(y) superfluid directly from an s-wave interaction making use of a topological Berry phase, which can be artificially generated. We discuss ways to detect the spontaneous Hall mass current, which acts as a diagnostic for the chiral p-wave superfluid.

BCS-BEC crossover and topological phase transition in 3D spin-orbit coupled degenerate fermi gases

We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.

Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems

We show that an ordinary semiconducting thin film with spin-orbit coupling can, under ap- propriate 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 non-topological (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 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 non-topological 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.

Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortices in a p x + i p y superconductor

We propose a simple way to stabilize half-quantum vortices in superconducting strontium ruthenate, assuming the order parameter is of chiral

Topological Invariants for Spin-Orbit Coupled Superconductor Nanowires

{p}_{x}+i{p}_{y}

Axionic field theory of (3+1)-dimensional Weyl semimetals

symmetry, as is suggested by recent experiments. The method, first given by Salomaa and Volovik in the context of Helium-3, is very naturally suited for strontium ruthenate, which has a layered, quasi-two-dimensional, perovskite crystal structure. We propose possible experiments to detect their non-Abelian braiding statistics. These experiments are of potential importance for topological quantum computation.

Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires

We show that the Hamiltonian of a multiband spin-orbit coupled semiconductor nanowire with Zeeman splitting and s-wave superconductivity is approximately chiral symmetric. The chiral symmetry becomes exact when only one pair of confinement bands is occupied and the Zeeman splitting is parallel to the nanowire. In this idealized case the Hamiltonian is in the BDI symmetry class of the topological classification of band Hamiltonians, allowing an arbitrary integer number of zero-energy Majorana fermion modes at each end. In the realistic case of multiband wires (Zeeman splitting still parallel to the length) the chiral symmetry is approximate and results in multiple near-zero-energy end states with increasing Zeeman splitting. The existence of such low energy end states implies the vanishing of the minigap with increased Zeeman splitting which can only be restored by breaking the approximate chiral symmetry by a second Zeeman field.

Blue Quantum Fog: Chiral Condensation in Quantum Helimagnets

From a direct calculation of the anomalous Hall conductivity and an effective electromagnetic action obtained via Fujikawas chiral rotation technique, we conclude that an axionic field theory with a nonquantized coefficient describes the electromagnetic response of the

Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: Searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

(3+1)