Temperature Dependence Quantum State of Electron in One Dimensional Carbon Nano Tubes and The Expression for Temperature Co-efficient of Resistance in Terms of Quantum State

Ashrafuz Zaman Sk., Dr. Ranjit Chowdhury

The Field of Carbon nano tube (CNT) is an promising area of research theoretically as well as experimentally [1],[2]. In fact the band structure of CNT determines its conductivity and in carbon nano tubes the structural pattern affects the conductivity type i.e the conductivity of CNT depends upon how graphene sheet is rolled up. So, CNT can be made to behave as conductor as well as semiconductor [2] It is well established that the samples of single wall carbon nano tubes with an arm chair wrapping have been produced and exhibit metallic behavior with an intrinsic resistivity which increases approximately linearly with temperature over a wide temperature range (see for instance ref.[4]. In this paper the quantized value of electric conductivity [1],[2] is used in an attempt to show theoretically that the quantum state of the electron of the carbon nano tube is directly related to temperature of the CNT as resistivity of CNT depends on quantum state and also found to depend on temperature. Finally, an effort has been made to find an approximate  expression for the temperature co-efficient of resistance of the CNT.