Magdalena Marganska

Spin-orbit interaction in chiral carbon nanotubes probed in pulsed magnetic fields

The magnetoconductance of an open carbon nanotube (CNT)-quantum wire was measured in pulsed magnetic fields. At low temperatures, we find a peculiar split magnetoconductance peak close to the chargeneutrality point. Our analysis of the data reveals that this splitting is intimately connected to the spin-orbit interaction and the tube chirality. Band-structure calculations suggest that the current in the peak regions is highly spin polarized, which calls for application in future CNT-based spintronic devices.

Persistent currents in carbon nanotubes

Persistent currents driven by a static magnetic flux parallel to the carbon nanotube axis are investigated. Owing to the hexagonal symmetry of graphene the Fermi contour expected for a 2D-lattice reduces to two points. However the electron or hole doping shifts the Fermi energy upwards or downwards and as a result, the shape of the Fermi surface changes. Such a hole doping leading to the Fermi level shift of (more or less) 1eV has been recently observed experimentally. In this paper we show that the shift of the Fermi energy changes dramatically the persistent currents and discuss the electronic structure and possible currents for zigzag as well as armchair nanotubes.

Broken SU(4) symmetry in a Kondo-correlated carbon nanotube

Understanding the interplay between many-body phenomena and nonequilibrium in systems with entangled spin and orbital degrees of freedom is a central objective in nanoelectronics. We demonstrate that the combination of Coulomb interaction, spin-orbit coupling, and valley mixing results in a particular selection of the inelastic virtual processes contributing to the Kondo resonance in carbon nanotubes at low temperatures. This effect is dictated by conjugation properties of the underlying carbon nanotube spectrum at zero and finite magnetic field. Our measurements on a clean carbon nanotube are complemented by calculations based on a field-theoretical Keldysh approach to the nonequilibrium Kondo problem which well reproduces the rich experimental observations in Kondo transport.

Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed that crucially depend on the tube’s chirality: (i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states. This phenomenon occurs due to the magnetic-field-dependent open boundary conditions obeyed by the carbon nanotube’s wave functions. The transport is fully suppressed above threshold values of the magnetic field, which depend on the nanotube chirality, length, and on the spin-orbit coupling. (ii) Reversible spin-polarized currents can be obtained upon tuning the magnetic field, exploiting the curvature-induced spin-orbit splitting.

Localization induced by magnetic fields in carbon nanotubes

The electronic spectra of long carbon nanotubes (CNTs) can, to a very good approximation, be obtained using the dispersion relation of graphene with both angular and axial periodic boundary conditions. In short CNTs one must account for the presence of open ends, which may give rise to states localized at the edges. We show that when a magnetic field is applied parallel to the tube axis, it modifies both momentum quantization conditions, causing hitherto extended states to localize near the ends. This localization is gradual and initially the involved states are still conducting. Beyond a threshold value of the magnetic field, which depends on the nanotube chirality and length, the localization is complete and the transport is suppressed.

The two classes of low-energy spectra in finite carbon nanotubes

We study the spectra of finite-length carbon nanotubes (CNTs) of arbitrary chirality. They divide into two classes, which arise because of different rotational symmetries of the low-energy eigenstates. In one of them (the zigzag class), the spinless spectrum is doubly degenerate and the two states can be assigned to different values of the valley degree of freedom. In the other (armchair class), the valley degeneracy is removed and the eigenstates are combinations of both valley states. Recent experimental observation of the valley mixing in ultraclean CNT quantum dots is consistent with our theory for armchair-class CNTs.

Orbital magnetic moments in pure and doped carbon nanotubes

The unusual band structure of carbon nanotubes CNs results in their remarkable magnetic properties. The application of magnetic field B parallel to the tube axis can change the conducting properties of the CN from metallic to semiconducting and vice versa. Apart from that, B induces via the Bohm-Aharonov effect orbital magnetic moments orb in the nanotube. These moments are studied both in pure and hole- or electron-doped CNs, isolated or in a circuit. Remarkably, orb in pure CNs depend uniquely on their original conducting properties, length, and temperature but do not depend on the nanotube radius or the particular chirality. In doped nanotubes the magnetic moments can be strongly altered and depend on the radius and chirality. Temperature can even change their character from diamagnetic at low T to paramagnetic at high T. A general electron-hole asymmetry increasing with the doping is found.

Topology and zero energy edge states in carbon nanotubes with superconducting pairing

We investigate the spectrum of finite-length carbon nanotubes in the presence of onsite and nearest-neighbor superconducting pairing terms. A one-dimensional ladder-type lattice model is developed to explore the low-energy spectrum and the nature of the electronic states. We find that zero energy edge states can emerge in zigzag class carbon nanotubes as a combined effect of curvature-induced Dirac point shift and strong superconducting coupling between nearest-neighbor sites. The chiral symmetry of the system is exploited to define a winding number topological invariant. The associated topological phase diagram shows regions with nontrivial winding number in the plane of chemical potential and superconducting nearest-neighbor pair potential (relative to the onsite pair potential). A one-dimensional continuum model reveals the topological origin of the zero energy edge states: a bulk-edge correspondence is proven, which shows that the condition for nontrivial winding number and that for the emergence of edge states are identical. For armchair class nanotubes, the presence of edge states in the superconducting gap depends on the nanotubes boundary shape. For the minimal boundary condition, the emergence of the subgap states can also be deduced from the winding number.

Blocking transport resonances via Kondo many-body entanglement in quantum dots

Many-body entanglement is at the heart of the Kondo effect, which has its hallmark in quantum dots as a zero-bias conductance peak at low temperatures. It signals the emergence of a conducting singlet state formed by a localized dot degree of freedom and conduction electrons. Carbon nanotubes offer the possibility to study the emergence of the Kondo entanglement by tuning many-body correlations with a gate voltage. Here we show another side of Kondo correlations, which counterintuitively tend to block conduction channels: inelastic co-tunnelling lines in the magnetospectrum of a carbon nanotube strikingly disappear when tuning the gate voltage. Considering the global SU(2) ⊗ SU(2) symmetry of a nanotube coupled to leads, we find that only resonances involving flips of the Kramers pseudospins, associated to this symmetry, are observed at temperatures and voltages below the corresponding Kondo scale. Our results demonstrate the robust formation of entangled many-body states with no net pseudospin.

Electronic spectra of commensurate and incommensurate DWNTs in parallel magnetic field

We study the electronic spectra of commensurate and incommensurate double-wall carbon nanotubes (DWNTs) of finite length. The coupling between nanotube shells is taken into account as an inter-shell electron tunneling. Selection rules for the inter-shell coupling are derived. Due to the finite size of the system, these rules do not represent exact conservation of the crystal momentum, but only an approximate one; therefore the coupling between longitudinal momentum states in incommensurate DWNTs becomes possible. The use of the selection rules allows a fast and efficient calculation of the electronic spectrum. In the presence of a magnetic field parallel to the DWNT axis, we find spectrum modulations that depend on the chiralities of the shells.