Effect of a quantizing magnetic field on the Einstein relation in bismuth

1989 ◽  
Vol 67 (1) ◽  
pp. 72-75 ◽  
Author(s):  
M. Mondal ◽  
S. N. Banik ◽  
K. P. Ghatak
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dispersion Relation ◽  
Einstein Relation ◽  
Energy Bands ◽  
Magnetic Quantization ◽  
Quantizing Magnetic Field ◽  
Special Case

An attempt is made to study the Einstein relation of the carriers in bismuth under magnetic quantization on the basis of the Abrikosov dispersion relation, which includes various types of anisotropics in the energy spectrum. It is found, taking spin and broadening into account, that the same ratio oscillates with the inverse quantizing magnetic field and increases with increasing carrier degeneracy respectively. In addition, the corresponding well-known result of parabolic energy bands is also obtained from the generalized expression as a special case.

THE HALL CONDUCTIVITY OF A DOPED GRAPHENE IN A QUANTIZING MAGNETIC FIELD

2012 ◽  
Vol 26 (28) ◽  
pp. 1250188 ◽  
Author(s):  
MIKHAIL B. BELONENKO ◽  
ANASTASIA V. PAK ◽  
ALEXANDER V. ZHUKOV ◽  
ROLAND BOUFFANAIS
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Energy Spectrum ◽  
Applied Magnetic Field ◽  
Electron Energy Spectrum ◽  
Landau Levels ◽  
Adsorbed Atom ◽  
Doped Graphene ◽  
Quantizing Magnetic Field ◽  
Different Characteristics

In this paper we study the electron energy spectrum corresponding to Landau levels in doped graphene when an external magnetic field is applied in the direction normal to the graphene planar sheet. The derived dispersion relation for the electrons in the doped graphene allows us to determine the dependence of the electrical conductivity on the applied magnetic field. This relationship between electrical conductivity and applied magnetic field is further analyzed for different characteristics of the impurities; specifically the potential of hybridization and the energy of the adsorbed atom.

The Diffusivity-Mobilitt Ratio Under Strong Magnetic Field in III-V Superlattices with Graded Structures

1993 ◽  
Vol 300 ◽  
Author(s):  
Kamakhya P. Ghatak ◽  
Badal De
Keyword(s):  
Magnetic Field ◽  
Experimental Method ◽  
Strong Magnetic Field ◽  
Mobility Ratio ◽  
Einstein Relation ◽  
Dispersion Law ◽  
Magnetic Quantization ◽  
Graded Structures ◽  
Theoretical Results

ABSTRACTIn this paper we have studied the Einstein relation for the diffusivity-mobility ratio in III-V superlattices with graded structures under magnetic quantization by formulating a new dispersion law. It is found, taking InAs/GaSb an example that the diffusivity mobility ratio increases in an oscillatory way with increasing carrier degeneracy as a consequence4SdH effect. The Einstein relation in IIIV superlattice is greater than that of the same for the constituent materials. Besides the theoretical results are in agreement with the suggested experimental method of determining the same ratio in degenerate materials having arbitrary dispersion laws.

The Photoemission from Superlattices of III-V Semiconductors with Graded Interfaces Under Quantizing Magnetic Field

1994 ◽  
Vol 299 ◽  
Author(s):  
Kamakhya P. Ghatak ◽  
Badal De
Keyword(s):  
Magnetic Field ◽  
Theoretical Analysis ◽  
Electron Concentration ◽  
Quantum Limit ◽  
Super Lattice ◽  
Dispersion Law ◽  
Magnetic Quantization ◽  
Wide Gap ◽  
Quantizing Magnetic Field

AbstractIn this paper we have studied the photoemission from super-lattices of III-V semiconductors under magnetic quantization by formulating a new dispersion law. It is found, taking InAs/GaSb super-lattice with graded interfaces as an example that the photoemission, increases with increasing electron concentration in an oscillatory way and increases with decreasing magnetic field in the magnetic quantum limit. Besides, the photoemission in superlattices is much greater than that of the constituent materials and the well-known results for wide-gap materials have also been obtained from our generalized analysis. In addition, the theoretical analysis is in agreement with the experimental datas as given elsewhere.

Graphene

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Green’S Function ◽  
Graphene Sheet ◽  
Green's Function ◽  
Research Effort ◽  
Delta Function ◽  
High Electron ◽  
Dirac Delta ◽  
Quantizing Magnetic Field

Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quantizing magnetic field on the Green’s function of a Graphene sheet and on its energy spectrum are derived in detail: Also the magnetic-field Green’s function and energy spectrum of a Graphene sheet with a quantum dot (modelled by a 2D Dirac delta-function potential) are thoroughly examined. Furthermore, Chapter 12 similarly addresses the problem of a Graphene anti-dot lattice in a magnetic field, discussing the Green’s function for propagation along the lattice axis, with a formulation of the associated eigen-energy dispersion relation. Finally, magnetic Landau quantization effects on the statistical thermodynamics of Graphene, including its Free Energy and magnetic moment, are also treated in Chapter 12 and are seen to exhibit magnetic oscillatory features.

THE EFFECT OF A VARYING MAGNETIC FIELD ON THE DIRAC FERMION SPECTRUM OF GRAPHENE

2011 ◽  
Vol 25 (03) ◽  
pp. 365-370 ◽  
Author(s):  
M. R. SETARE ◽  
D. JAHANI
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Single Layer ◽  
The Other ◽  
Dirac Fermion ◽  
Zero Energy ◽  
Special Case

We examine the effect of a magnetic field that varies inversely as the square of distance on the Dirac fermion spectrum of graphene, a single layer of graphite. We find that unlike the case of the uniform magnetic field for which zero-energy modes exhibit half the degeneracy of the other levels in the energy spectrum, the ground state in this case, as well as the other energy levels, is doubly degenerate. We also get zero-energy solutions for the special case of ky = 0.

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