C.L. Roy

A study of Landauer resistance and related issues of the generalized Thue-Morse lattice

We have carried out an elaborate study of electrical conduction in the generalized Thue-Morse (GTM) lattice. We have studied (i) the Landauer resistance, trace map and localization length of GTM structures, and (ii) the effects of deviations of inter-barrier distances from ideal GTM structures on electrical conduction. Among other things, our results indicate clearly the conditions under which a GTM lattice is likely to be most akin to a periodic system.

Lifetime of resonant tunnelling states in multibarrier systems

Abstract We have studied the variation of the resonant tunnelling lifetime with resonant energies for multibarrier systems (MBS) consisting of rectangular barrier type potentials and going beyond the usual double barrier case. Among other things, this variation shows a special kind of minima for MBS with more than three barriers.

Localization of relativistic electrons in a one-dimensional disordered system

We address the question as to whether relativistic effects have any influence on localization phenomena in disordered systems. Starting from the Schrodinger and Dirac equations for Kronig-Penney potentials, we derive their discrete counterparts within the framework of the linear combination of atomic orbitals and tight-binding approaches. As a specific example we subsequently focus on substitutional binary alloys. We show that taking relativity into account leads to many important differences with respect to the results obtained in the non-relativistic approximation. The predicted behaviour of localization length can be very relevant in several experimental contexts.

Relativistic impacts on tunnelling through multi-barrier systems

We have studied relativistic effects on the tunnelling of electrons through a multi-barrier system (MBS) consisting of rectangular barrier potentials, by deriving, for the purpose, relativistic formulae for the transmission coefficient and associated relativistic conditions for resonant tunnelling. Among other things, we have discussed critically the quantitative extents of relativistic impacts on tunnelling through MBSS, especially in the context of their measurability.

Correlation between trace map and Landauer resistance of Fibonacci lattice

Abstract We have studied the trace map and Landauer resistance (LR) of the Fibonacci lattice, and indicate how diverse features of the LR of this kind of system can be correlated in a meaningful way with the energy spectrum provided by the corresponding trace map. A study of this kind would facilitate the interpretation of the experimental results on the LR of the Fibonacci lattice.

Some special features of relativistic tunnelling through multi-barrier systems with δ-function barriers

Abstract We have carried out a comparative study of relativistic and non-relativistic tunnelling through a multi-barrier system consisting of an arbitrary number of δ-function barriers. Among other things, our study reveals that relativistic resonant tunnelling occurs at all energies for any number of barriers when the strength of the δ-function barriers assumes certain quantised values, while the corresponding non-relativistic treatment does not display this property.

Some features of resonant tunnelling

Abstract We show how the condition for resonant tunnelling in a system of two rectangular barriers can be interpreted in terms of the band structure and phase change of Bloch electrons in an infinite periodic system having a part of the two-barrier system as the periodicity.

A relativistic treatment about the existence of band gaps in one-dimensional disordered systems

Abstract We have investigated the relativistic criteria for the occurrence of band gaps in one-dimensional disordered systems, with the intention of elucidating the circumstances under which the relativistic effects would be significant with respect to various issues concerned with band gaps in such systems. Our model consists of an infinite chain of atoms lacking long range order, the atomic potentials being represented by rectangular wells or barriers. Our treatment is a relativistic generalisation of a non-relativistic approach due to Borland [Proc. Phys. Soc. 78, 926 (1961)]. We find that the relativistic effects on various aspects concerning the occurrence of band gaps in our models, are quite significant. Also, we show that there exists an upper limit to the deviation parameter for occurrence of band gaps in disordered systems, for both relativistic and non-relativistic cases.

A study of the relativistic electronic state of disordered systems

Abstract We have carried out a quantitative study of the relativistic density of states (DOS) of a one-dimensional system, using analytical results of a related treatment previously reported by Roy (J. Phys. Chem. Solids 50, 111, 1989). We have examined various features of the quantitative results of the relativistic DOS of our model of a 1D disordered system, in light of (i) non-relativistic (NR) DOS of the same disordered system, (ii) relativistic and non-relativistic DOS of free electrons, and (iii) relativistic and non-relativistic band structure of 1D periodic systems relevant to our disordered systems. Among many other things, our investigation brings out clearly the circumstances under which the relativistic effects on the DOS of disordered systems can become substantially larger; in this regard, it is found that the relativistic effects on the DOS of disordered systems are very large in the simultaneous presence of low concentration of scatterers and low values of height (depth) of potential barriers (wells) which represent the potentials due to scatterers in our model of disordered systems.

LCAO approach to non-relativistic and relativistic Kronig-Penney models

We have reported a comparative study of dynamics of non-relativistic and relativistic electrons in Kronig-Penney models with the use of discretized Hamiltonians in the context of the linear combination of atomic orbitals approach. We have carried out general formulations of both non-relativistic and relativistic cases, by taking the atomic potentials appropriately as δ-function potentials; then, we have applied these general formulations to obtain significant results regarding relativistic impacts on certain important aspects of the electronic energy spectrum of periodic, quasiperiodic and disordered systems.