Accessing nanotube bands via crossed electric and magnetic fields

We investigate the properties of conduction electrons in single-walled armchair carbon nanotubes in the presence of mutually orthogonal electric and magnetic fields transverse to the tube’s axis. We find that the fields give rise to an asymmetric dispersion in the right- and left-moving electrons along the tube as well as a band-dependent interaction. We predict that such a nanotube system would exhibit spin-band-charge separation and a band-dependent tunneling density of states. We show that in the quantum dot limit, the fields serve to completely tune the quantum states of electrons added to the nanotube. For each of the predicted effects, we provide examples and estimates that are relevant to experiment.

Figure 1

(Color online) An armchair carbon nanotube in the presence of transverse magnetic (pointing in the $-\widehat{y}$ direction) and electric fields (pointing in the $\widehat{z}$ direction). The carbon atoms belonging to the $A$ and $B$ sublattices are indicated by dark and light shading, respectively.

Figure 2

(Color online) Plasmon velocities $v_{1,R}$ and $v_{1,L}$ and band structure velocities $v_R$ and $v_L$ (solid, dotted, dashed, and dotted-dashed, respectively) for a $1\text{−}\mu \text{m}$-long, 4.75-nm-diameter armchair tube in a 12 T magnetic field as a function of electric field strength.

Figure 3

(Color online) Plasmon velocities $v_{2,R}$ and $v_{2,L}$ (solid and dashed, respectively) for a $1\text{−}\mu \text{m}$-long, 4.75-nm-diameter armchair tube in a 12 T magnetic field as a function of electric field strength. The field-free charge plasmon velocity of this tube would be $v_{\rho }=4.52v_F$.

Figure 4

(Color online) Examples of shell filling. Figure indicates the order, $\alpha$ point, and spin of tunneled electron with increasing chemical potential $\mu$ (not drawn to scale). (a) Filling order for a tube in the absence of fields and with ${\Delta }_b\ne 0$. (b) Shell filling for $N_{c+}=N_{c-}$ exhibits twofold periodicity and complete polarization into band $\alpha =+$. This condition is approximately met for a $1\mu \text{m}$ tube of diameter 6.78 nm in the presence of magnetic and electric fields 4.93 T and 0.0242 V/nm, respectively (see text for specific values of the Coulomb blockade parameters for this case and other details).