New directions in the pursuit of Majorana fermions in solid state systems (1202.1293v1)

Abstract: The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible toengineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

• The paper introduces novel techniques to realize Majorana modes in 1D and 2D superconductors using heterostructure designs.
• It details experimental detection methods such as tunneling spectroscopy and the fractional Josephson effect to identify zero-energy excitations.
• The study highlights the implications for fault-tolerant quantum computing through the use of non-Abelian exchange statistics.

Overview of Majorana Fermions in Solid State Systems

The paper "New directions in the pursuit of Majorana fermions in solid state systems" by Jason Alicea provides an extensive review of the efforts to realize Majorana fermions in condensed matter settings. Majorana fermions are exotic quasi-particles theorized to be their own antiparticles. Their potential manifestations in condensed matter physics, particularly in topological superconductors, have recently garnered significant attention due to their implications for quantum computing.

Theoretical Background

Ettore Majorana first conceptualized these fermions within the field of high-energy physics, where they have been proposed as candidates for neutrinos and dark matter components. In condensed matter physics, Majorana modes arise as zero-energy excitations bound to defects or boundaries in certain superconductors. A central interest lies in their predicted non-Abelian exchange statistics, which are robust to local perturbations and hold promise for fault-tolerant quantum computing.

Topological Superconductors

The paper highlights two primary manifestations of Majorana fermions in solid-state systems: in one-dimensional (1D) spinless $p$-wave superconductors and two-dimensional (2D) $p+ip$ superconductors. The former can be realized using chains of spinless fermions that exhibit topological phases distinguished by $Z_2$ invariants. Under these conditions, Majorana modes localize at the chain's ends. The latter are characterized by a $p+ip$ pairing symmetry, where Majorana zero modes are bound to vortices, contributing to a ground state manifold that is described by a nontrivial Chern number.

Engineering Majorana Modes

Recent advancements suggest that Majorana modes can be engineered using heterostructures that combine conventional $s$-wave superconductors with materials exhibiting strong spin-orbit coupling and time-reversal symmetry breaking. For instance, proposals involve semiconductor wires with strong spin-orbit coupling, proximate to $s$-wave superconductors and subject to a magnetic field. Alternatively, 2D topological insulators provide a versatile platform; their edge states, when proximitized by $s$-wave superconductors, potentially realize a robust topological superconducting phase.

Detection and Implications

Detecting Majorana modes in these systems is nontrivial. The paper reviews several experimental approaches, including tunneling spectroscopy, which predicts a quantized zero-bias conductance anomaly when Majorana zero modes are present. Additionally, the fractional Josephson effect—where the periodicity of the current-phase relationship is doubled—serves as an indicator of Majorana physics. Interferometric setups further provide a means to demonstrate non-Abelian statistics experimentally.

Quantum Computation and Future Perspectives

Majorana fermions are promising candidates for topological qubits owing to their non-Abelian exchange statistics, enabling quantum operations that are inherently protected from decoherence. Nevertheless, the realization of Majorana-based quantum computation requires precise control and manipulation of these modes. Future advancements in materials design, fabrication, and measurement techniques are critical for transitioning from theoretical predictions to practical devices.

The ongoing research across various experimental platforms underscores the interdisciplinary nature of this quest and holds promise for realizing a new paradigm in quantum computation. The creation and manipulation of Majorana fermions represent a significant frontier in the paper of topological phases of matter, with profound implications for fundamental physics and technology.