Electronic properties of superlattices

1990 ◽  
Vol 68 (3) ◽  
pp. 268-272 ◽  
Author(s):  
D. Aitelhabti ◽  
P. Vasilopoulos ◽  
J. F. Currie
Keyword(s):  
Wave Function ◽  
Dispersion Relation ◽  
Band Structure ◽  
Electronic Properties ◽  
Transfer Matrix ◽  
Current Density ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Tight Binding ◽  
Effective Masses

Using the transfer-matrix method, we evaluate the exact normalized wave function analytically, the band structure, and the current density associated with an electron in a superlattice, with different or equal effective masses between wells and barriers. Also, we evaluate numerically the dispersion relation, the bandwidth, and the current density (in the tight-binding limit) for both equal and different effective masses between wells and barriers.

scholarly journals Selective spin transport through a quantum heterostructure: Transfer matrix method

2016 ◽  
Vol 30 (25) ◽  
pp. 1650184 ◽  
Author(s):  
Moumita Dey ◽  
Santanu K. Maiti
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Spin Transport ◽  
Tight Binding ◽  
Transmission Probability ◽  
Applied Bias Voltage ◽  
One Dimensional ◽  
Wide Range ◽  
Nanoscale Level

In the present work, we propose that a one-dimensional quantum heterostructure composed of magnetic and non-magnetic (NM) atomic sites can be utilized as a spin filter for a wide range of applied bias voltage. A simple tight-binding framework is given to describe the conducting junction where the heterostructure is coupled to two semi-infinite one-dimensional NM electrodes. Based on transfer matrix method, all the calculations are performed numerically which describe two-terminal spin-dependent transmission probability along with junction current through the wire. Our detailed analysis may provide fundamental aspects of selective spin transport phenomena in one-dimensional heterostructures at nanoscale level.

scholarly journals MODELLING CHARGE TRANSPORT IN DNA USING TRANSFER MATRICES WITH DIAGONAL TERMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4138-4149 ◽  
Author(s):  
STEPHEN A. WELLS ◽  
CHI-TIN SHIH ◽  
RUDOLF A. RÖMER
Keyword(s):  
Damage Detection ◽  
Charge Transport ◽  
Transport Properties ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Tight Binding ◽  
Transfer Matrices ◽  
Dna Charge Transport ◽  
Binding Models

There is increasing evidence that DNA can support a considerable degree of charge transport along the strand by hopping of holes from one base to another, and that this charge transport may be relevant to DNA regulation, damage detection and repair. A surprisingly useful amount of insight can be gained from the construction of simple tight-binding models of charge transport, which can be investigated using the transfer-matrix method. The data thus obtained indicate a correlation between DNA charge-transport properties and the locations of cancerous mutation. We review models for DNA charge transport and their extension to include more physically realistic diagonal-hopping terms.

DISPERSION OF ACOUSTIC PHONONS IN QUASIPERIODIC SUPERLATTICES

2004 ◽  
Vol 11 (06) ◽  
pp. 541-551 ◽  
Author(s):  
R. K. MISHRA ◽  
K. D. MISRA ◽  
R. P. TIWARI
Keyword(s):  
Dispersion Relation ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Acoustic Phonon ◽  
Multilayered Structure ◽  
Angle Of Incidence ◽  
Semiconducting Materials ◽  
Acoustic Phonons ◽  
Normal Angle

The aim of this work is to present an up-to-date study of acoustic phonon excitations that can propagate in multilayered structure with constituents arranged in quasiperiodic fashion. In this paper, the dispersion relation of acoustic phonons for the quasiperiodic superlattice using different semiconducting materials, with the help of transfer matrix method, is derived at normal angle of incidence. Calculation is presented for (a) Ge / Si and (b) Nb / Cu semiconductor superlattices from 5th to 9th generations and dispersion diagrams are plotted using the famous Kronning–Penny model obtained from the transfer matrix of the structure. The concept of allowed and forbidden bands with the help of these dispersion curves in various generations of Fibonacci superlattices and the relation between imaginary value of propagation vector and the existence of forbidden bands is demonstrated.

Modeling of Electron Tunneling Current in a p-n Junction Based on Strained Armchair Graphene Nanoribbons with Extended Tight Binding and Transfer Matrix Method

2015 ◽  
Vol 1112 ◽  
pp. 102-105
Author(s):  
Rifky Syariati ◽  
Endi Suhendi ◽  
Fatimah A. Noor ◽  
Khairurrijal
Keyword(s):  
Band Gap ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Electron Tunneling ◽  
Graphene Nanoribbons ◽  
Tight Binding ◽  
Tunneling Current ◽  
Computation Method ◽  
Armchair Graphene Nanoribbons

A theoretical model of electron tunneling current in a p-n junction based on strained armchair graphenenanoribbons (AGNRs) is developed. The effects of strain to the energy dispersion relation and the band gap of AGNR are formulated under the extended tight binding method. The electron transmittance was derived by utilizing the transfer matrix method. The calculated transmittance was then used to obtain the tunneling current by employing the Landauer formula with Gauss Quadrature computation method. The effects of strain to the energy band gap, AGNR width, and tunneling current are studied thoroughly.

TRANSFER-MATRIX METHOD FOR SOLVING THE SPIN 1/2 ANTIFERROMAGNETIC HEISENBERG CHAIN

1988 ◽  
Vol 02 (05) ◽  
pp. 1035-1036 ◽  
Author(s):  
M. A. Garcia-Bach ◽  
D. J. Klein ◽  
R. Valenti
Keyword(s):  
Wave Function ◽  
Transfer Matrix ◽  
Ground State ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Valence Bond ◽  
Exact Results ◽  
Matrix Elements ◽  
Heisenberg Chain ◽  
Spin Configuration

Following the discovery of high Tc superconductivity in the copper oxides, there has been a great deal of interest in the RVB wave function proposed by Anderson [1]. As a warm-up exercise we have considered a valence-bond wave function for the one dimensional spin-1/2 Heisenberg chain. The main virtue of our work is to propose a new variational singlet wavefunction which is almost analytically tractable by a transfer-matrix technique. We have obtained the ground state energy for finite as well as infinite chains, in good agreement with exact results. Correlation functions, excited states, and the effects of other interactions (e.g., spin-Peierls) are also accessible within this scheme [2]. Since the ground state of the chain is known to be a singlet (Lieb & Mattis [3]), we write the appropriate wave function as a superposition of valence-bond singlets, [Formula: see text], where | k > is a spin configuration obtained by pairing all spins into singlet pairs, in a way which is common in valence-bond calculations of large molecules. As in that case, each configuration, | k >, can be represented by a Rümer diagram, with directed bonds connecting each pair of spins on the chain. The c k 's are variational co-efficients, the form of which is determined as follows: Each singlet configuration (Rümer diagram) is divided into "zones", a "zone" corresponding to the region between two consecutive sites. Each zone is indexed by its distance from the end of the chain and by the number of bonds crossing it. Our procedure assigns a variational parameter, x ij , to the j th zone, when crossed by i bonds. The resulting wavefunction for an N-site chain is written as [Formula: see text] where m ij(k) equals 1 when zone j is crossed by i bonds and zero otherwise. To make the calculation tractable we reduce the number of variational parameters by disallowing configurations with bonds connecting any two sites separated by more than 2M lattice points. (For simplicity, we have limited ourselves to M=3, but the scheme can be used for any M). With the simple ansatz, matrix elements can be calculated by a transfer-matrix method. To understand the transfer-matrix method note that since only local zone parameters appear in the description of each state | k >, matrix elements and overlaps, [Formula: see text] and < k | k '>, are completely specified by a small number of "local states" associated with each zone. Within a given zone a local state is defined by (i) the number of bonds crossing the zone and (ii), by whether the bonds originate from the initial (| k >) or final (| k '>) state. It is then easy to see that "local states" of consecutive zones are connected by a 15 × 15 transfer matrix (for the case M=3). Furthermore, the overlap matrix element can be written as a product of transfer-matrices associated with each zone of the chain. When calculating matrix elements of the Hamiltonian, an additional matrix, U , must be defined, to represent the particular zone involving the two spins connected by the Heisenberg interaction. The relevant details as well as the comparison with exact results will be given elsewhere. We are planning to ultimately apply this method to the two dimensional case, and hope to include the effects of holes.

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