Polarons in Suspended Carbon Nanotubes

Abstract

We prove theoretically the possibility of electric-field controlled polaron formation involving flexural (bending) modes in suspended carbon nanotubes. Upon increasing the field, the ground state of the system with a single extra electron undergoes a first-order phase transition between an extended state and a localized polaron state. For a common experimental setup, the threshold electric field is only of the order of ' 5  10 À2 V= m. [5], this allows for resonant excitation and coherent manipulation of discrete degrees of freedom. The envisioned devices may find application in quantum information processing.In current devices, a discrete spectrum is obtained by embedding a quantum dot on a suspended nanotube [2,3]. In this Letter, we prove the possibility of the controllable formation of discrete states of a different kind, namely, polarons. A polaron is an electron localized inside a lattice deformation that the electron itself produces. Our setup is shown in Fig. 1. It consists of an ultraclean semiconducting single wall carbon nanotube cantilever. The setup is similar to the nanorelay proposed in Ref. [6] and to the experimental setup of Ref. [7] but operated in a different regime, namely, that of a single electron on the cantilever. This is achieved by putting the Fermi energy of the tube just below the energy of the bottom of the conduction band. The Fermi energy is tuned by adjusting the voltage bias on the metallic electrode A in Fig. 1.If the electron enters the suspended part of the tube, it experiences a force F ¼ ÀeE. The electric field E may be due to an external source or to the image charge induced by the electron in the substrate below the cantilever. The force F deforms the tube. As a result, the potential energy of the electron is lowered. Thus, the tube deformation produces a potential well that may trap the electron.This allows for unprecedented manipulation possibilities. One can, for instance, envisage the coherent manipulation of the quantum state of the polaron by the excitation (with a high frequency source) of the tube's flexural modes. These possibilities are present neither for the well-studied polarons in bulk solids [8] nor for previously studied polarons in carbon nanotubes [9] that originate from axial stretching and radial bending modes of the tube rather than from macroscopic flexural modes.Our main results are contained in Fig. 2. At small electric fields, the ground state consists of an undeformed tube without a polaron. As the field is increased beyond a critical value, the system undergoes a first-order phase transition to a localized polaron state. For realistic values of a suspended tube length L ¼ 1 m and tube radius r ¼ 1 nm, the threshold electric field is 0:051 V= m, and the tip deviation is 0.89 nm. This is the field that would be produced by an image charge induced in a metallic substrate 0:12 m below the tube.The typical energy scale for the polaron state is set by the electron confinement energy " e ¼ @ 2 =2m à L 2 , where m à is the effective electron mass. The...

Tunable spin-polaron state in a singly clamped semiconducting carbon nanotube

“…the use of ferromagnetic leads inducing magnetic exchange fields E ex /µ B (with µ B the Bohr magneton) on the electronic spin is currently actively investigated [10][11][12][13]. More surprisingly such exchange fields can have remarkable consequences also on the dynamics of a nano-mechanical system for which dynamical (shuttle) instabilities, strong spin-polarized currents, and cooling have been predicted [14][15][16] In this paper we show that the system discussed by Snyman and Nazarov [8] in presence of a magnetic dielectric substrate allows the formation of a localized fully polarized polaronic state. The experimentally observed exchange energy E ex (see Ref.…”

“…1 of Ref. [8]). The mechanical bending of the suspended part of the nanotube induces then a spatial inhomogeneity of the electrostatic potential along the CNT forming a minimum at the deformable end of the wire.…”

“…Recently I. Snyman and Yu.V. Nazarov [8] considered a semiconducting CNT laying on an insulating substrate with one end of it suspended. A metallic gate below both the insulating substrate and the suspended part of the CNT generates an homogeneous electric field (cf.…”

The asymmetric quantum Rabi model in the polaron picture

“…It should be noted here that, unlike the trial wave function (12), the displacement amplitudes of the two coherent states are not the same. Keeping only up to the second order of λ 1,2 , the ground state energy is:…”

“…[8] for an early review, or for a more recent review, see Ref. [9]) but also in a variety of other fields such as, for example, BoseEinstein condensation [10,11], nanoscience [12], biophysics [13], polymers [14][15][16], and so on. Recently, it has also been extended to study spin coherence [17,18] in a dissipative quantum system, namely, the spin-boson model [19,20].…”