Ferdinand Kuemmeth

Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube

A Wigner molecule—a localized pair of interacting electrons—is now created in a carbon nanotube. The high-quality, electronically pristine tubes enable a full characterization of the energy spectrum, laying the groundwork for future studies of interacting fermion systems in one and two dimensions.

Coupling of spin and orbital motion of electrons in carbon nanotubes

Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion, leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes are widely believed to be four-fold degenerate, owing to independent spin and orbital symmetries, and also to possess electron–hole symmetry. Here we report measurements demonstrating that in clean nanotubes the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin–orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and antiparallel alignment for holes. Our measurements are consistent with recent theories that predict the existence of spin–orbit coupling in curved graphene and describe it as a spin-dependent topological phase in nanotubes. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of quantum bits (qubits) in nanotubes and providing a mechanism for all-electrical control of spins in nanotubes.

Exponential protection of zero modes in Majorana islands

Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a ‘Majorana island’) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.

Metal-nanoparticle single-electron transistors fabricated using electromigration

We have fabricated single-electron transistors from individual metal nanoparticles using a geometry that provides improved coupling between the particle and the gate electrode. This is accomplished by incorporating a nanoparticle into a gap created between two electrodes using electromigration, all on top of an oxidized aluminum gate. We achieve sufficient gate coupling to access more than ten charge states of individual gold nanoparticles (5–15 nm in diameter). The devices are sufficiently stable to permit spectroscopic studies of the electron-in-a-box level spectra within the nanoparticle as its charge state is varied.

Hole spin relaxation in Ge-Si core-shell nanowire qubits

Controlling decoherence is the biggest challenge in efforts to develop quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among implementations of solid-state quantum bits, but their strong coupling to nuclear spins produces high decoherence rates. Group IV semiconductors, on the other hand, have relatively low nuclear spin densities, making them an attractive platform for spin quantum bits. However, device fabrication remains a challenge, particularly with respect to the control of materials and interfaces. Here, we demonstrate state preparation, pulsed gate control and charge-sensing spin readout of hole spins confined in a Ge-Si core-shell nanowire. With fast gating, we measure T(1) spin relaxation times of up to 0.6 ms in coupled quantum dots at zero magnetic field. Relaxation time increases as the magnetic field is reduced, which is consistent with a spin-orbit mechanism that is usually masked by hyperfine contributions.

Hard gap in epitaxial semiconductor–superconductor nanowires

Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunnelling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on the proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunnelling conductance below the superconducting gap, suggesting a continuum of subgap states--a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by the proximity effect in a semiconductor, using epitaxial InAs-Al semiconductor-superconductor nanowires. The hard gap, together with favourable material properties and gate-tunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.

Nanometer-scale scanning sensors fabricated using stencil lithography

We describe a flexible technique for fabricating 10-nm-scale devices for use as high-resolution scanning sensors and functional probes. Metallic structures are deposited directly onto atomic force microscope tips by evaporation through nanoscale holes fabricated in a stencil mask. We report on the lithographic capabilities of the technique and discuss progress in one initial application, to make high-spatial-resolution magnetic force sensors.

Measurement of Discrete Energy-Level Spectra in Individual Chemically Synthesized Gold Nanoparticles

We form single-electron transistors from individual chemically synthesized gold nanoparticles, 5-15 nm in diameter, with monolayers of organic molecules serving as tunnel barriers. These devices allow us to measure the discrete electronic energy levels of individual gold nanoparticles that are, by virtue of chemical synthesis, well-defined in their composition, size and shape. We show that the nanoparticles are nonmagnetic and have spectra in good accord with random-matrix-theory predictions taking into account strong spin-orbit coupling.

Relaxation and Dephasing in a Two-Electron \(^{13}C\) Nanotube Double Quantum Dot

We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time T1 first decreases with a parallel magnetic field and then goes through a minimum in a field of 1.4 T. We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which at high field enhances relaxation due to bending-mode phonons. The inhomogeneous dephasing time T{2} is consistent with previous data on hyperfine coupling strength in 13C nanotubes.