Chapter 6
Ballistic Transport in Nanowires
B. G. Sidharth and Abhishek Das
Abstract In this chapter, we endeavour to investigate the phenomenon of electrical
conduction through nanowires. To be precise we derive a novel expression for the
conductance resorting to the uncertainty principle.
6.1 Introduction
It is known that ballistic conduction or ballistic transport is a term associated with the
transport of electrons through a medium where the electrical resistivity can be
neglected. Sharvin (1965) led the foundation of the phenomenon of ballistic transport while visualizing an experiment. Since then, it has been a subject of widespread
interest. There is a plethora of literature on ballistic conduction (Choi et al. 1985;
Thornton et al. 1986; Wees et al. 1988; Wharam et al. 1988; Houten and Beenakker
1996; Frank et al. 1998).
However, even before Sharvin a significant nexus between conductance and
transmission probability was put forward by Landauer (1957) which was essentially
in contradistinction to the Drude model (Drude 1900a, b) or the quantum mechanically modified Drude-Sommerfeld model. In this chapter, we use the Heisenberg
uncertainty principle to derive an expression for the conductance and then coalesce it
with the Landauer–Buttiker formalism (Landauer 1957; Buttiker 1988) to find out if
the transmission probability can be unity altogether, thereby allowing ballistic
transport. Interestingly, very recently it has been experimentally found that electrons
exhibit superballistic flow in the ballistic regime (Kumar et al. 2017).
On another track Sidharth had argued in the mid-1990s (Sidharth 1999) that in
one dimensions and two dimensions, the transport would be luminal mimicking
superconductivity. It must be remembered that by this time nanotubes had not yet
been found and only 10 years later graphene was discovered, exhibiting the same
properties. Sidharth’s arguments were quantum mechanical, using the Dirac equations in one and two dimensions.
B. G. Sidharth (*) · A. Das
B.M. Birla Science Centre, Adarsh Nagar, Hyderabad, India
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_6
61
Ballistic Transport in Nanowires
B. G. Sidharth and Abhishek Das
Abstract In this chapter, we endeavour to investigate the phenomenon of electrical
conduction through nanowires. To be precise we derive a novel expression for the
conductance resorting to the uncertainty principle.
6.1 Introduction
It is known that ballistic conduction or ballistic transport is a term associated with the
transport of electrons through a medium where the electrical resistivity can be
neglected. Sharvin (1965) led the foundation of the phenomenon of ballistic transport while visualizing an experiment. Since then, it has been a subject of widespread
interest. There is a plethora of literature on ballistic conduction (Choi et al. 1985;
Thornton et al. 1986; Wees et al. 1988; Wharam et al. 1988; Houten and Beenakker
1996; Frank et al. 1998).
However, even before Sharvin a significant nexus between conductance and
transmission probability was put forward by Landauer (1957) which was essentially
in contradistinction to the Drude model (Drude 1900a, b) or the quantum mechanically modified Drude-Sommerfeld model. In this chapter, we use the Heisenberg
uncertainty principle to derive an expression for the conductance and then coalesce it
with the Landauer–Buttiker formalism (Landauer 1957; Buttiker 1988) to find out if
the transmission probability can be unity altogether, thereby allowing ballistic
transport. Interestingly, very recently it has been experimentally found that electrons
exhibit superballistic flow in the ballistic regime (Kumar et al. 2017).
On another track Sidharth had argued in the mid-1990s (Sidharth 1999) that in
one dimensions and two dimensions, the transport would be luminal mimicking
superconductivity. It must be remembered that by this time nanotubes had not yet
been found and only 10 years later graphene was discovered, exhibiting the same
properties. Sidharth’s arguments were quantum mechanical, using the Dirac equations in one and two dimensions.
B. G. Sidharth (*) · A. Das
B.M. Birla Science Centre, Adarsh Nagar, Hyderabad, India
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_6
61