scholarly journals An elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulators

2021 ◽  
Vol 35 (04) ◽  
pp. 2150050
Author(s):  
Bo-Hung Chen ◽  
Dah-Wei Chiou
Keyword(s):  
Energy Spectrum ◽  
Integral Formula ◽  
Generic Model ◽  
Band Model ◽  
Linear Difference Equations ◽  
Boundary Correspondence ◽  
Chern Numbers ◽  
Cauchy’S Integral Formula ◽  
Chern Insulators ◽  
Two Band Model

With the inclusion of arbitrary long-range hopping and (pseudo)spin–orbit coupling amplitudes, we formulate a generic model that can describe any two-dimensional two-band bulk insulators, thus providing a simple framework to investigate arbitrary adiabatic deformations upon the systems of any arbitrary Chern numbers. Without appealing to advanced techniques beyond the standard methods of solving linear difference equations and applying Cauchy’s integral formula, we obtain a mathematically elementary yet rigorous proof of the bulk-boundary correspondence on a strip, which is robust against any adiabatic deformations upon the bulk Hamiltonian and any uniform edge perturbation along the edges. The elementary approach not only is more transparent about the underlying physics but also reveals various intriguing nontopological features of Chern insulators that have remained unnoticed or unclear so far. Particularly, if a certain condition is satisfied (as in most renowned models), the loci of edge bands in the energy spectrum and their (pseudo)spin polarizations can be largely inferred from the bulk Hamiltonian alone without invoking any numerical computation for the energy spectrum of a strip.

scholarly journals О структуре энергетического спектра дырок в материалах A-=SUP=-IV-=/SUP=-B-=SUP=-VI-=/SUP=- под иным углом зрения

2019 ◽  
Vol 53 (7) ◽  
pp. 890
Author(s):  
Л.В. Прокофьева ◽  
П.П. Константинов
Keyword(s):  
Energy Spectrum ◽  
Hole Concentration ◽  
Small Addition ◽  
Band Model ◽  
Temperature Hysteresis ◽  
Charge Process ◽  
The Common ◽  
Heavy Doping ◽  
Two Band Model ◽  
Twofold Decrease

The twofold decrease in hole concentration of all PbTe <NaTe> samples at 77–450 K and the same effect achieved at 77 K and heavy doping only due to introduction in PbTe of tin small addition, supplemented by observation in indicated range of temperature hysteresis in hole concentration, are the grounds for developing an other approach to a study of the energy spectrum in A(IV)B(VI) materials, an alternative two-band model. It is based on the common for these materials phenomenon — compensation of current carriers as a reaction on electroactive doping. The appearance of compensation is associated with initial (at temperatures below 77 K) two-charge process — participation in a single doping act of the pair of electrons due to their mutual attraction. With a rise in temperature, as with introduction of tin, the situation is changed. The study of all aspects of transformation is a task for further research.

scholarly journals Meromorphic or Holomorphic Completion of a Reinhardt Domain

1970 ◽  
Vol 38 ◽  
pp. 1-12 ◽  
Author(s):  
Eiichi Sakai
Keyword(s):  
Meromorphic Function ◽  
Power Series ◽  
Meromorphic Functions ◽  
Integral Formula ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Reinhardt Domain ◽  
Continuity Theorem ◽  
Cauchy’S Integral Formula ◽  
Long Time

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.

IONIZATION ENERGY AND IMPURITY BAND CONDUCTION OF SHALLOW DONORS IN n-GALLIUM ARSENIDE

1967 ◽  
Vol 45 (1) ◽  
pp. 119-126 ◽  
Author(s):  
J. Basinski ◽  
R. Olivier
Keyword(s):  
Ionization Energy ◽  
Impurity Band ◽  
Shallow Donor ◽  
Band Model ◽  
A Value ◽  
Transition Concentration ◽  
Temperature Electron ◽  
Two Band Model ◽  
Band Conduction ◽  
Made In

Hall effect and resistivity measurements have been made in the temperature range 4.2–360 °K on several samples of n-type GaAs grown under oxygen atmosphere and without any other intentional dopings. The principal shallow donor in this material is considered to be Si. All samples exhibited impurity-band conduction at low temperature. Electron concentrations in the conduction band were calculated, using a two-band model, and then fitted to the usual equation expressing charge neutrality. A value of 2.3 × 10−3 eV was obtained for the ionization energy of the donors, for donor concentration ranging from 5 × 1015 cm−3 to 2 × 1016 cm−3. The conduction in the impurity band was of the hopping type for these concentrations. A value of 3.5 × 1016 cm−3 was obtained for the critical transition concentration of the impurity-band conduction to the metallic type.

ENERGY BAND OVERLAPPING IN HIGH-Tc SUPERCONDUCTORS

1996 ◽  
Vol 10 (30) ◽  
pp. 1483-1490 ◽  
Author(s):  
M. MORENO ◽  
R. M. MÉNDEZ-MORENO ◽  
M. A. ORTIZ ◽  
S. OROZCO
Keyword(s):  
Weak Coupling ◽  
Cuprate Superconductors ◽  
Weak Coupling Limit ◽  
Band Model ◽  
Coupling Constant ◽  
High Tc Superconductors ◽  
Energy Bands ◽  
Effective Coupling ◽  
High Tc ◽  
Two Band Model

Multi-band superconductors are analyzed and the relevance of overlapping energy bands to the high-T c of these materials is studied. Within the BCS framework, a two band model with generalized Fermi surface topologies is developed. Values of the overlapped occupancy parameters for typical cuprate superconductors are obtained as a function of the ratio R and the effective coupling constant, λ, in the weak-coupling limit. The overlap scale is of the order or lower than the cutoff (Debye) energy. The typical behavior of the isotope effect is obtained. As these superconductors have transition temperatures above the phonon barrier, the results of this approach are important to the generic understanding of the high-T c superconducting mechanism.

Thermoelectric Power of the Liquid Sn—Te Alloy

1982 ◽  
Vol 37 (10) ◽  
pp. 1127-1131 ◽  
Author(s):  
D. H. Kurlat ◽  
M. Rosen
Keyword(s):  
Thermoelectric Power ◽  
Hard Sphere ◽  
Stoichiometric Composition ◽  
Band Model ◽  
Liquid Alloys ◽  
Sphere Approximation ◽  
The Difference ◽  
Predicted Values ◽  
Experimental Values ◽  
Two Band Model

The Seebeck coefficient (S) of Sni1-x- Tex liquid alloys was measured as a function of concentration and temperature. For 0 ≦ x <0.45 the behaviour is metallic; S values are small and negative, rising linearly with temperature. The predicted values of Ziman's theory when using the hard sphere approximation disagree with the experimental ones. The change in sign occurs for 0.45. For x = 0.5 (stoichiometric composition) the thermoelectric power decreases linearly with temperature. This fact is explained assuming a two-band model. For x ≧ 0.6 the liquid alloy becomes more semiconducting and presents a maximum in the isotherms of S for x = 0.65. For the excess tellurium concentration range we have calculated the difference EF - EV and γ/kB, assuming a S(1/T) law. The experimental values are compared with those of Dancy and Glazov.

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