Four probe measurements in bilayer sheets

Calculating resistance of bilayer systems aprroximating them as a coupled network of resistors. Each layer is assumed to have uniform values for the value of each resistor element. The network and the four probes are as follows:

We try to look at the effect on the DUT resistance by varying the various paramters in the system.

Input paramters

The input paramters are specified in the file input.dat.

The various input parameters are:

        Layer 1 size          <number of rows in layer 1>   <number of columns in layer 1>   
        Layer 2 size          <number of rows in layer 2>   <number of columns in layer 2>   
        R_top                 <Resistance in layer 1>  
        R_bottom              <Resistance in layer 2>  
        R_cross               <Resistance in the cross sectional region>   
        I+ position           <layer number>   <row number>   <column number>  
        I- position           <layer number>   <row number>   <column number>  
        V+ position           <layer number>   <row number>   <column number>    
        V- position           <layer number>   <row number>   <column number> 
        Convergence           <Value of convergence threshold>  
        Maximum Iterations    <Maxium number of iterations>  
	Append		       String you want to append to output files	

Note that if you are scanning over a series of R_cross you can enter all the values seperated by spaces

Running the Code

After specifying the input parameters run

        python main.py
	python plot_planes.py

The final voltage distribution will be saved as an image and the Results.txt will contain all the necessary probe data.

Reference

Misorientation-Controlled Cross-Plane Thermoelectricity in Twisted Bilayer Graphene

Phanibhusan S. Mahapatra, Bhaskar Ghawri, Manjari Garg, Shinjan Mandal, K. Watanabe, T. Taniguchi, Manish Jain, Subroto Mukerjee, and Arindam Ghosh

Phys. Rev. Lett. 125, 226802 – Published 24 November 2020