Chandan Basu

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.

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.

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.

On the occurence of band gaps in one-dimensional disordered systems

Abstract We show that the occurence of band gaps in one-dimensional disordered systems with short-range order is subjected to an upper limit to the “deviation parameter” characterizing the disorder. We discuss the implications of our findings in the light of other results in this regard.

Density of states of generalised Thue-Morse lattice and related issues

Abstract We have investigated the density of states (DOS) of the generalised Thue-Morse (GTM) lattice, and compared by that means the degrees of aperiodicity and relevant electronic states of various GTM lattices. Further, we have correlated the DOS of various GTM lattices with the corresponding energy spectrum. Among other things, we find that GTM lattices with higher ratios of relevant exponents are likely to be more periodic than other varieties of it.

Upper limits on the deviation parameter for the occurrence of band gaps in one-dimensional disordered systems

Abstract The non-relativistic upper limits on the deviation parameter ( d for the occurrence of band gaps in one-dimensional disordered systems are correctly derived. The results now reported with regard to the upper limit on d remove a discrepancy pointed out recently by Clerk and McKellar.

On the derivation of zitterbewegung

Abstract We show how we can remove the inconsistencies recently pointed out by Sherry in regard to Diracs derivation of zitterbewegung.