diff options
Diffstat (limited to 'figs')
31 files changed, 895 insertions, 0 deletions
diff --git a/figs/bands.fig/Makefile b/figs/bands.fig/Makefile new file mode 100644 index 0000000..5a6a103 --- /dev/null +++ b/figs/bands.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=bands + +all: $(PROJECTNAME).pdf + +$(PROJECTNAME).pdf: + python $(PROJECTNAME).py > $(PROJECTNAME).dat + gnuplot $(PROJECTNAME).gnuplot + pdflatex -jobname $(PROJECTNAME) $(PROJECTNAME)_plot.tex + +install: $(PROJECTNAME).pdf + cp $(PROJECTNAME).pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(PROJECTNAME).aux + rm -f $(PROJECTNAME).log + rm -f $(PROJECTNAME).dat + rm -f $(PROJECTNAME)_plot.tex + +clean-pdf: + rm -f $(PROJECTNAME).pdf + +clean: clean-aux clean-pdf diff --git a/figs/bands.fig/bands.gnuplot b/figs/bands.fig/bands.gnuplot new file mode 100644 index 0000000..f1f84ff --- /dev/null +++ b/figs/bands.fig/bands.gnuplot @@ -0,0 +1,42 @@ +#!/usr/bin/env gnuplot + +datafile="bands.dat" +# output +outfile="bands_plot.tex" +set output outfile + +# terminal +set term lua tikz size 10,6 standalone tightboundingbox + +# format axes +set key off +unset colorbox +unset border +unset xtics +unset ytics +unset ztics + +# colors +## 4169E1 (pastel blue) +## FF143C (bright red) +## 32CD32 (bright green) +## DAA520 (ochre) + +# angle camera +set view 80,30 + +# style for mesh lines +set style line 1 linetype rgbcolor "#000000" + +# splot mode +set pm3d hidden3d depthorder + +# set colors +set palette defined (0 "#DAA520",0.33 "#FF143C", 0.66 "#32CD32",1 "#4169E1") + +# plot +splot datafile using 1:2:3:4 with pm3d linestyle 1 , \ + datafile using 5:6:7:8 with pm3d linestyle 1 , \ + datafile using 9:10:11:12 with pm3d linestyle 1 , \ + datafile using 13:14:15:16 with pm3d linestyle 1 + diff --git a/figs/bands.fig/bands.py b/figs/bands.fig/bands.py new file mode 100644 index 0000000..57d03b8 --- /dev/null +++ b/figs/bands.fig/bands.py @@ -0,0 +1,55 @@ +#!/usr/bin/env python + +## compute the bands for bilayer graphene (no g4 or delta) + +from math import * +import cmath +import numpy + +g1=0.1 +g3=0.33*g1 + +def Omega(x,y): + return(1+2*cmath.exp(-3j/2*x)*cos(sqrt(3)/2*y)) + +# Hamiltonian +def H(x,y): + return(numpy.array(\ + [[0,g1,0,Omega(x,y).conjugate()],\ + [g1,0,Omega(x,y),0],\ + [0,Omega(x,y).conjugate(),0,g3*Omega(x,y)*cmath.exp(3j*x)],\ + [Omega(x,y),0,g3*(Omega(x,y).conjugate())*cmath.exp(-3j*x),0]]\ + )) + +# eigenvalues +def eigsH(x,y): + return(numpy.linalg.eigvals(H(x,y))) + + +# resolution +nrpoints=55 +# xrange +xmin,xmax=0,4*pi/3 +# yrange +ymin,ymax=-2*pi/sqrt(3),2*pi/sqrt(3) + +# sample points +x=numpy.linspace(xmin,xmax,nrpoints) +y=numpy.linspace(ymin,ymax,nrpoints) +x,y=numpy.meshgrid(x,y) + +# data points +z=numpy.zeros((4,nrpoints,nrpoints)) +for i in range(0,nrpoints): + for j in range(0,nrpoints): + eigs=numpy.sort(numpy.real(eigsH(x[i,j],y[i,j]))) + for k in range(0,4): + z[k,i,j]=(eigs[k]) + +# output +for i in range(0,nrpoints): + for j in range(0,nrpoints): + for k in range(0,4): + print("%10f %10f %10f %d " % (x[i,j],y[i,j],z[k,i,j],k),end='') + print() + print() diff --git a/figs/bands_first.fig/Makefile b/figs/bands_first.fig/Makefile new file mode 100644 index 0000000..6fbd0d6 --- /dev/null +++ b/figs/bands_first.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=bands_first + +all: $(PROJECTNAME).pdf + +$(PROJECTNAME).pdf: + python $(PROJECTNAME).py > $(PROJECTNAME).dat + gnuplot $(PROJECTNAME).gnuplot + pdflatex -jobname $(PROJECTNAME) $(PROJECTNAME)_plot.tex + +install: $(PROJECTNAME).pdf + cp $(PROJECTNAME).pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(PROJECTNAME).aux + rm -f $(PROJECTNAME).log + rm -f $(PROJECTNAME).dat + rm -f $(PROJECTNAME)_plot.tex + +clean-pdf: + rm -f $(PROJECTNAME).pdf + +clean: clean-aux clean-pdf diff --git a/figs/bands_first.fig/bands_first.gnuplot b/figs/bands_first.fig/bands_first.gnuplot new file mode 100644 index 0000000..31fdeb5 --- /dev/null +++ b/figs/bands_first.fig/bands_first.gnuplot @@ -0,0 +1,42 @@ +#!/usr/bin/env gnuplot + +datafile="bands_first.dat" +# output +outfile="bands_first_plot.tex" +set output outfile + +# terminal +set term lua tikz size 10,6 standalone tightboundingbox + +# format axes +set key off +unset colorbox +unset border +unset xtics +unset ytics +unset ztics + +# colors +## 4169E1 (pastel blue) +## FF143C (bright red) +## 32CD32 (bright green) +## DAA520 (ochre) + +# angle camera +set view 90,50 + +# style for mesh lines +set style line 1 linetype rgbcolor "#000000" + +# splot mode +set pm3d hidden3d depthorder + +# set colors +set palette defined (0 "#DAA520",0.33 "#FF143C", 0.66 "#32CD32",1 "#4169E1") + +# plot +splot datafile using 1:2:3:4 with pm3d linestyle 1 , \ + datafile using 5:6:7:8 with pm3d linestyle 1 , \ + datafile using 9:10:11:12 with pm3d linestyle 1 , \ + datafile using 13:14:15:16 with pm3d linestyle 1 + diff --git a/figs/bands_first.fig/bands_first.py b/figs/bands_first.fig/bands_first.py new file mode 100644 index 0000000..980d3b3 --- /dev/null +++ b/figs/bands_first.fig/bands_first.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python + +## compute the bands for bilayer graphene (no g4 or delta) +## first regime + +from math import * +import cmath +import numpy + +g1=0.1 +g3=0.33*g1 + +def Omega(x,y): + return(1+2*cmath.exp(-3j/2*x)*cos(sqrt(3)/2*y)) + +# Hamiltonian +def H(x,y): + return(numpy.array(\ + [[0,g1,0,Omega(x,y).conjugate()],\ + [g1,0,Omega(x,y),0],\ + [0,Omega(x,y).conjugate(),0,g3*Omega(x,y)*cmath.exp(3j*x)],\ + [Omega(x,y),0,g3*(Omega(x,y).conjugate())*cmath.exp(-3j*x),0]]\ + )) + +# eigenvalues +def eigsH(x,y): + return(numpy.linalg.eigvals(H(x,y))) + + +# resolution +nrpoints=31 +# xrange +xmin,xmax=2*pi/3-1.5,2*pi/3+1.5 +# yrange +ymin,ymax=2*pi/3/sqrt(3)-1.5,2*pi/3/sqrt(3)+1.5 + +# sample points +x=numpy.linspace(xmin,xmax,nrpoints) +y=numpy.linspace(ymin,ymax,nrpoints) +x,y=numpy.meshgrid(x,y) + +# data points +z=numpy.zeros((4,nrpoints,nrpoints)) +for i in range(0,nrpoints): + for j in range(0,nrpoints): + eigs=numpy.sort(numpy.real(eigsH(x[i,j],y[i,j]))) + for k in range(0,4): + z[k,i,j]=(eigs[k]) + +# output +for i in range(0,nrpoints): + for j in range(0,nrpoints): + for k in range(0,4): + print("%10f %10f %10f %d " % (x[i,j],y[i,j],z[k,i,j],k),end='') + print() + print() diff --git a/figs/bands_second.fig/Makefile b/figs/bands_second.fig/Makefile new file mode 100644 index 0000000..b026463 --- /dev/null +++ b/figs/bands_second.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=bands_second + +all: $(PROJECTNAME).pdf + +$(PROJECTNAME).pdf: + python $(PROJECTNAME).py > $(PROJECTNAME).dat + gnuplot $(PROJECTNAME).gnuplot + pdflatex -jobname $(PROJECTNAME) $(PROJECTNAME)_plot.tex + +install: $(PROJECTNAME).pdf + cp $(PROJECTNAME).pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(PROJECTNAME).aux + rm -f $(PROJECTNAME).log + rm -f $(PROJECTNAME).dat + rm -f $(PROJECTNAME)_plot.tex + +clean-pdf: + rm -f $(PROJECTNAME).pdf + +clean: clean-aux clean-pdf diff --git a/figs/bands_second.fig/bands_second.gnuplot b/figs/bands_second.fig/bands_second.gnuplot new file mode 100644 index 0000000..51f8949 --- /dev/null +++ b/figs/bands_second.fig/bands_second.gnuplot @@ -0,0 +1,42 @@ +#!/usr/bin/env gnuplot + +datafile="bands_second.dat" +# output +outfile="bands_second_plot.tex" +set output outfile + +# terminal +set term lua tikz size 10,6 standalone tightboundingbox + +# format axes +set key off +unset colorbox +unset border +unset xtics +unset ytics +unset ztics + +# colors +## 4169E1 (pastel blue) +## FF143C (bright red) +## 32CD32 (bright green) +## DAA520 (ochre) + +# angle camera +set view 90,50 + +# style for mesh lines +set style line 1 linetype rgbcolor "#000000" + +# splot mode +set pm3d hidden3d depthorder + +# set colors +set palette defined (0 "#DAA520",0.33 "#FF143C", 0.66 "#32CD32",1 "#4169E1") + +# plot +splot datafile using 1:2:3:4 with pm3d linestyle 1 , \ + datafile using 5:6:7:8 with pm3d linestyle 1 , \ + datafile using 9:10:11:12 with pm3d linestyle 1 , \ + datafile using 13:14:15:16 with pm3d linestyle 1 + diff --git a/figs/bands_second.fig/bands_second.py b/figs/bands_second.fig/bands_second.py new file mode 100644 index 0000000..782b300 --- /dev/null +++ b/figs/bands_second.fig/bands_second.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python + +## compute the bands for bilayer graphene (no g4 or delta) +## second regime + +from math import * +import cmath +import numpy + +g1=0.1 +g3=0.33*g1 + +def Omega(x,y): + return(1+2*cmath.exp(-3j/2*x)*cos(sqrt(3)/2*y)) + +# Hamiltonian +def H(x,y): + return(numpy.array(\ + [[0,g1,0,Omega(x,y).conjugate()],\ + [g1,0,Omega(x,y),0],\ + [0,Omega(x,y).conjugate(),0,g3*Omega(x,y)*cmath.exp(3j*x)],\ + [Omega(x,y),0,g3*(Omega(x,y).conjugate())*cmath.exp(-3j*x),0]]\ + )) + +# eigenvalues +def eigsH(x,y): + return(numpy.linalg.eigvals(H(x,y))) + + +# resolution +nrpoints=31 +# xrange +xmin,xmax=2*pi/3-0.1,2*pi/3+0.1 +# yrange +ymin,ymax=2*pi/3/sqrt(3)-0.1,2*pi/3/sqrt(3)+0.1 + +# sample points +x=numpy.linspace(xmin,xmax,nrpoints) +y=numpy.linspace(ymin,ymax,nrpoints) +x,y=numpy.meshgrid(x,y) + +# data points +z=numpy.zeros((4,nrpoints,nrpoints)) +for i in range(0,nrpoints): + for j in range(0,nrpoints): + eigs=numpy.sort(numpy.real(eigsH(x[i,j],y[i,j]))) + for k in range(0,4): + z[k,i,j]=(eigs[k]) + +# output +for i in range(0,nrpoints): + for j in range(0,nrpoints): + for k in range(0,4): + print("%10f %10f %10f %d " % (x[i,j],y[i,j],z[k,i,j],k),end='') + print() + print() diff --git a/figs/bands_third.fig/Makefile b/figs/bands_third.fig/Makefile new file mode 100644 index 0000000..fc025fa --- /dev/null +++ b/figs/bands_third.fig/Makefile @@ -0,0 +1,23 @@ +PROJECTNAME=bands_third + +all: $(PROJECTNAME).pdf + +$(PROJECTNAME).pdf: + python $(PROJECTNAME).py > $(PROJECTNAME).dat + gnuplot $(PROJECTNAME).gnuplot + pdflatex -jobname $(PROJECTNAME) $(PROJECTNAME)_plot.tex + +install: $(PROJECTNAME).pdf + cp $(PROJECTNAME).pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(PROJECTNAME).aux + rm -f $(PROJECTNAME).log + rm -f $(PROJECTNAME).dat + rm -f $(PROJECTNAME)_plot.tex + +clean-pdf: + rm -f $(PROJECTNAME).pdf + +clean: clean-aux clean-pdf diff --git a/figs/bands_third.fig/bands_third.gnuplot b/figs/bands_third.fig/bands_third.gnuplot new file mode 100644 index 0000000..2845518 --- /dev/null +++ b/figs/bands_third.fig/bands_third.gnuplot @@ -0,0 +1,41 @@ +#!/usr/bin/env gnuplot + +datafile="bands_third.dat" +# output +outfile="bands_third_plot.tex" +set output outfile + +# terminal +set term lua tikz size 10,6 standalone tightboundingbox + +# format axes +set key off +unset colorbox +unset border +unset xtics +unset ytics +unset ztics + +# colors +## FF143C (bright red) +## 32CD32 (bright green) + +# angle camera +set view 80,50 + +# style for mesh lines +set style line 1 linetype rgbcolor "#000000" + +# splot mode +set pm3d hidden3d depthorder + +# set colors +set palette defined (0 "#FF143C", 1 "#32CD32") + +# set data range +set zrange [-0.0001:0.0001] + +# plot +splot datafile using 1:2:3:4 with pm3d linestyle 1 , \ + datafile using 5:6:7:8 with pm3d linestyle 1 + diff --git a/figs/bands_third.fig/bands_third.py b/figs/bands_third.fig/bands_third.py new file mode 100644 index 0000000..f4d2290 --- /dev/null +++ b/figs/bands_third.fig/bands_third.py @@ -0,0 +1,86 @@ +#!/usr/bin/env python + +## compute the bands for bilayer graphene (no g4 or delta) +## third regime + +from math import * +import cmath +import numpy +from scipy import optimize + +g1=0.1 +g3=0.33*g1 + +def Omega(x,y): + return(1+2*cmath.exp(-3j/2*x)*cos(sqrt(3)/2*y)) + +# Hamiltonian +def H(x,y): + return(numpy.array(\ + [[0,g1,0,Omega(x,y).conjugate()],\ + [g1,0,Omega(x,y),0],\ + [0,Omega(x,y).conjugate(),0,g3*Omega(x,y)*cmath.exp(3j*x)],\ + [Omega(x,y),0,g3*(Omega(x,y).conjugate())*cmath.exp(-3j*x),0]]\ + )) + +# eigenvalues +def eigsH(x,y): + return(numpy.linalg.eigvals(H(x,y))) + +# resolution +nrpoints=101 +# xrange +xmin,xmax=2*pi/3-0.004,2*pi/3+0.004 +# yrange +ymin,ymax=2*pi/3/sqrt(3)-0.004,2*pi/3/sqrt(3)+0.004 + +# sample points +x=numpy.linspace(xmin,xmax,nrpoints) +y=numpy.linspace(ymin,ymax,nrpoints) +x,y=numpy.meshgrid(x,y) + + +## We want a data point at each Fermi point, which must first be computed + +# A function that vanishes only at the Fermi points +def fermpt(v): + eigs=numpy.sort(numpy.real(eigsH(v[0],v[1]))) + return([eigs[1]-eigs[2],0]) +# compute Fermi points +## approximate starting value +pf_app=numpy.zeros((4,2)) +pf_app[0]=[2*pi/3,2*pi/3/sqrt(3)] +pf_app[1]=[2*pi/3,2/sqrt(3)*acos(1/2-g1*g3/2)] +pf_app[2]=[acos(g1*g3/2-1/2),acos(g1*g3/2-1/2)/sqrt(3)] +pf_app[3]=[4*pi/3-acos(g1*g3/2-1/2),acos(g1*g3/2-1/2)/sqrt(3)] +pf=pf_app +for i in range(0,4): + pf[i]=optimize.root(fermpt,pf_app[i],tol=1.e-10).x + +# Reset the data point closest to each Fermi point to the fermi point +for k in range(0,4): + mini,minj=0,0 + minval=100 + for i in range(0,nrpoints): + for j in range(0,nrpoints): + if(sqrt((x[i,j]-pf[k,0])**2+(y[i,j]-pf[k,1])**2)<minval): + mini,minj=i,j + minval=sqrt((x[i,j]-pf[k,0])**2+(y[i,j]-pf[k,1])**2) + [x[mini,minj],y[mini,minj]]=pf[k] + + +# data points +z=numpy.zeros((4,nrpoints,nrpoints)) +for i in range(0,nrpoints): + for j in range(0,nrpoints): + eigs=numpy.sort(numpy.real(eigsH(x[i,j],y[i,j]))) + for k in range(0,4): + z[k,i,j]=(eigs[k]) + +# output +for i in range(0,nrpoints): + for j in range(0,nrpoints): + for k in [1,2]: + print("%10f %10f %10f %d " % (x[i,j],y[i,j],z[k,i,j],k),end='') + print() + print() diff --git a/figs/bilayer.fig/Makefile b/figs/bilayer.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/bilayer.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile
\ No newline at end of file diff --git a/figs/bilayer.fig/bilayer.tex b/figs/bilayer.fig/bilayer.tex new file mode 100644 index 0000000..0c5faa6 --- /dev/null +++ b/figs/bilayer.fig/bilayer.tex @@ -0,0 +1,17 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{} +\graphene{(-1,0)}{dashed} + +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{} +\sitelattice{a}{(0,0)}{} +\sitelattice{b}{(0,0)}{} + +\end{tikzpicture} +\end{document} diff --git a/figs/bilayer.fig/libs/graphene.sty b/figs/bilayer.fig/libs/graphene.sty new file mode 120000 index 0000000..a377638 --- /dev/null +++ b/figs/bilayer.fig/libs/graphene.sty @@ -0,0 +1 @@ +../../libs/graphene.sty
\ No newline at end of file diff --git a/figs/bilayer_cell.fig/Makefile b/figs/bilayer_cell.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/bilayer_cell.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile
\ No newline at end of file diff --git a/figs/bilayer_cell.fig/bilayer_cell.tex b/figs/bilayer_cell.fig/bilayer_cell.tex new file mode 100644 index 0000000..582d2fb --- /dev/null +++ b/figs/bilayer_cell.fig/bilayer_cell.tex @@ -0,0 +1,40 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{} +\graphene{(-1,0)}{dashed} +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{} +\sitelattice{a}{(0,0)}{} +\sitelattice{b}{(0,0)}{} + + +% cell +\draw[color=blue](120:1)++(-1.5,0)--++(1.5,\sqrttt)--++(1.5,-\sqrttt)--++(-1.5,-\sqrttt)--cycle; + +% other cells +\draw[color=blue,style=dashed](120:1)++(-1.5,0)--++\mlt; +\draw[color=blue,style=dashed](120:1)++(0,-\sqrttt)--++\lt--++\lt; +\draw[color=blue,style=dashed](120:1)++(1.5,0)--++\lt; +\draw[color=blue,style=dashed](120:1)++(0,\sqrttt)--++\mlt--++\mlt; +\draw[color=blue,style=dashed](120:1)++(0,\sqrttt)--++\lo--++\lo; +\draw[color=blue,style=dashed](120:1)++(0,-\sqrttt)--++\mlo--++\mlo; +\draw[color=blue,style=dashed](120:1)++(1.5,0)--++\lo; +\draw[color=blue,style=dashed](120:1)++(-1.5,0)--++\mlo; +\draw[color=blue,style=dashed](120:1)++(0,\sqrttt)++\mlo++\mlt--++\lo--++\lo; +\draw[color=blue,style=dashed](120:1)++(0,-\sqrttt)++\mlo++\lt--++\lo--++\lo; +\draw[color=blue,style=dashed](120:1)++(0,-\sqrttt)++\mlo++\mlt--++\lt--++\lt; +\draw[color=blue,style=dashed](120:1)++(0,\sqrttt)++\lo++\mlt--++\lt--++\lt; + +\draw[color=red](120:1)++(30:1)++(0,.2)node[rotate=30]{\scriptsize$l_1$}; +\draw[color=red](120:1)++(-30:0.8)++(0,.2)node[rotate=-30]{\scriptsize$l_2$}; +\draw[color=red,line width=1.5pt,->](120:1)--++\lo; +\draw[color=red,line width=1.5pt,->](120:1)--++\lt; + + +\end{tikzpicture} +\end{document} diff --git a/figs/bilayer_cell.fig/libs/graphene.sty b/figs/bilayer_cell.fig/libs/graphene.sty new file mode 120000 index 0000000..a377638 --- /dev/null +++ b/figs/bilayer_cell.fig/libs/graphene.sty @@ -0,0 +1 @@ +../../libs/graphene.sty
\ No newline at end of file diff --git a/figs/flow.fig/Makefile b/figs/flow.fig/Makefile new file mode 100644 index 0000000..82ff8bd --- /dev/null +++ b/figs/flow.fig/Makefile @@ -0,0 +1,21 @@ +PROJECTNAME=flow + +all: $(PROJECTNAME).pdf + +$(PROJECTNAME).pdf: + gnuplot $(PROJECTNAME).gnuplot + pdflatex -jobname $(PROJECTNAME) $(PROJECTNAME)_plot.tex + +install: $(PROJECTNAME).pdf + cp $(PROJECTNAME).pdf $(INSTALLDIR)/ + + +clean-aux: + rm -f $(PROJECTNAME).aux + rm -f $(PROJECTNAME).log + rm -f $(PROJECTNAME)_plot.tex + +clean-pdf: + rm -f $(PROJECTNAME).pdf + +clean: clean-aux clean-pdf diff --git a/figs/flow.fig/flow.gnuplot b/figs/flow.fig/flow.gnuplot new file mode 100644 index 0000000..3d8d247 --- /dev/null +++ b/figs/flow.fig/flow.gnuplot @@ -0,0 +1,53 @@ +#!/usr/bin/env gnuplot + +# output file +outfile="flow_plot.tex" +set output outfile + +# tics +set x2tics ("$\\log_2\\epsilon$" 5, "$3\\log_2\\epsilon$" 15) nomirror out +set ytics ("$1$" 1, "$\\epsilon$" 2**(-5), "$2\\epsilon|\\log_2\\epsilon|$" 2**(-5)*(15-5+1)) nomirror out +unset xtics + +set xrange [0:20] +set yrange [-0.5:1] + +# remove key +unset key + +# titles +set x2label "$h$" offset 18,-3 +set ylabel norotate "$|V_h|$" offset 10.5,-9 + +# set terminal (add color definitions for title) +set term lua tikz size 8.33,5.833 standalone font "\\footnotesize" + +# 3=1+2 draw bottom and left sides of the box +set border 6 + +# set linestyles +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 + +# extra text +set label "irrelevant" at 2.5,-0.1 center textcolor "#32CD32" +set label "$\\sim 2^{h}$" at 2.5,-0.25 center textcolor "#32CD32" +set label "marginal" at 10,-0.1 center textcolor "#DC143C" +set label "$\\sim\\epsilon|h-\\log_2\\epsilon|$" at 10,-0.25 center textcolor "#DC143C" +set label "irrelevant" at 17.5,-0.1 center textcolor "#32CD32" +set label "$\\sim\\epsilon|2\\log_2\\epsilon|2^{h-3\\log_2\\epsilon}$" at 15,-0.25 left textcolor "#32CD32" + +set samples 97 + +set arrow from 0,1 to 20,1 +set arrow from 0,1 to 0,-0.5 + +set arrow from 5,1 to 5,-0.5 nohead dashtype 2 +set arrow from 15,1 to 15,-0.5 nohead dashtype 2 + +# plots +plot \ + ((x<=5) ? 2**(-x) : 1/0) linestyle 3,\ + ((x>=5 && x<=15) ? 2**(-5)*(x-5+1) : 1/0) linestyle 2,\ + ((x>=15) ? 2**(-5)*(15-5+1)*2**(-(x-15)) : 1/0) linestyle 3 + diff --git a/figs/hoppings.fig/Makefile b/figs/hoppings.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/hoppings.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile
\ No newline at end of file diff --git a/figs/hoppings.fig/hoppings.tex b/figs/hoppings.fig/hoppings.tex new file mode 100644 index 0000000..c8fa332 --- /dev/null +++ b/figs/hoppings.fig/hoppings.tex @@ -0,0 +1,32 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{color=red} +\graphene{(-1,0)}{dashed,color=red} + +% bounding box +\path\mlo++\mlo++(-0.1,-0.1)coordinate(A); +\path\lt++(-60:1)++(0.1,-0.1)coordinate(B); +\path\lo++\mlt++\lo++(60:1)++(0.1,0.1)coordinate(C); +\path\mlt++\mlt++\lo++\mlt++(-0.1,0.1)coordinate(D); + +% interlayer hopping +\begin{scope} + \clip(A)--(B)--(C)--(D)--cycle; + \graphene{(120:1)}{densely dotted,color=blue} + \graphene{(-120:1)}{densely dotted,color=blue} +\end{scope} + +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{color=green} +\sitelattice{a}{(0,0)}{color=green} +\sitelattice{b}{(0,0)}{} + + + +\end{tikzpicture} +\end{document} diff --git a/figs/hoppings.fig/hoppings_0.tex b/figs/hoppings.fig/hoppings_0.tex new file mode 100644 index 0000000..0c8e042 --- /dev/null +++ b/figs/hoppings.fig/hoppings_0.tex @@ -0,0 +1,25 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{color=red} +\graphene{(-1,0)}{dashed,color=red} + +% bounding box +\path\mlo++\mlo++(-0.1,-0.1)coordinate(A); +\path\lt++(-60:1)++(0.1,-0.1)coordinate(B); +\path\lo++\mlt++\lo++(60:1)++(0.1,0.1)coordinate(C); +\path\mlt++\mlt++\lo++\mlt++(-0.1,0.1)coordinate(D); + +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{} +\sitelattice{a}{(0,0)}{} +\sitelattice{b}{(0,0)}{} + + + +\end{tikzpicture} +\end{document} diff --git a/figs/hoppings.fig/hoppings_1.tex b/figs/hoppings.fig/hoppings_1.tex new file mode 100644 index 0000000..ddaff19 --- /dev/null +++ b/figs/hoppings.fig/hoppings_1.tex @@ -0,0 +1,25 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{} +\graphene{(-1,0)}{dashed} + +% bounding box +\path\mlo++\mlo++(-0.1,-0.1)coordinate(A); +\path\lt++(-60:1)++(0.1,-0.1)coordinate(B); +\path\lo++\mlt++\lo++(60:1)++(0.1,0.1)coordinate(C); +\path\mlt++\mlt++\lo++\mlt++(-0.1,0.1)coordinate(D); + +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{color=green} +\sitelattice{a}{(0,0)}{color=green} +\sitelattice{b}{(0,0)}{} + + + +\end{tikzpicture} +\end{document} diff --git a/figs/hoppings.fig/hoppings_3.tex b/figs/hoppings.fig/hoppings_3.tex new file mode 100644 index 0000000..8f9b64f --- /dev/null +++ b/figs/hoppings.fig/hoppings_3.tex @@ -0,0 +1,32 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{graphene} +\begin{document} +\begin{tikzpicture} + +% draw grids +\graphene{(0,0)}{} +\graphene{(-1,0)}{dashed} + +% bounding box +\path\mlo++\mlo++(-0.1,-0.1)coordinate(A); +\path\lt++(-60:1)++(0.1,-0.1)coordinate(B); +\path\lo++\mlt++\lo++(60:1)++(0.1,0.1)coordinate(C); +\path\mlt++\mlt++\lo++\mlt++(-0.1,0.1)coordinate(D); + +% interlayer hopping +\begin{scope} + \clip(A)--(B)--(C)--(D)--cycle; + \graphene{(120:1)}{densely dotted,color=blue} + \graphene{(-120:1)}{densely dotted,color=blue} +\end{scope} + +\sitelattice{at}{(-1,0)}{} +\sitelattice{bt}{(-1,0)}{} +\sitelattice{a}{(0,0)}{} +\sitelattice{b}{(0,0)}{} + + + +\end{tikzpicture} +\end{document} diff --git a/figs/hoppings.fig/libs/graphene.sty b/figs/hoppings.fig/libs/graphene.sty new file mode 120000 index 0000000..a377638 --- /dev/null +++ b/figs/hoppings.fig/libs/graphene.sty @@ -0,0 +1 @@ +../../libs/graphene.sty
\ No newline at end of file diff --git a/figs/libs/Makefile b/figs/libs/Makefile new file mode 100644 index 0000000..5704428 --- /dev/null +++ b/figs/libs/Makefile @@ -0,0 +1,28 @@ +PROJECTNAME=$(basename $(wildcard *.tex)) +LIBS=$(notdir $(wildcard libs/*)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(LIBS) + echo $(LIBS) + pdflatex -file-line-error $(patsubst %.pdf, %.tex, $@) + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +$(LIBS): + ln -fs libs/$@ ./ + +clean-libs: + rm -f $(LIBS) + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/libs/graphene.sty b/figs/libs/graphene.sty new file mode 100644 index 0000000..40ffd03 --- /dev/null +++ b/figs/libs/graphene.sty @@ -0,0 +1,86 @@ +%% +%% Macros to draw graphene lattices +%% + +% numerical values +% sqrt(3)/2 +\def\sqrttt{0.866} +% sqrt(3) +\def\sqrtt {1.732} + +%l1 +\def\lo{(1.5,\sqrttt)} +%l2 +\def\lt{(1.5,-\sqrttt)} +%-l1 +\def\mlo{(-1.5,-\sqrttt)} +%-l2 +\def\mlt{(-1.5,\sqrttt)} + +% shapes +\def\square#1#2#3{\draw[#3]#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);} +\def\fullsquare#1#2#3{\fill[#3]#1++(-#2,-#2)--++(#2,0)--++(#2,0)--++(0,#2)--++(0,#2)--++(-#2,0)--++(-#2,0)--++(0,-#2)--++(0,-#2);} + +% atoms +\def\a#1#2{\fill[#2]#1circle(.1);} +\def\b#1#2{\fullsquare{#1}{.1}{#2}} +\def\at#1#2{\fill[color=white]#1circle(.1);\draw[#2]#1circle(.1);} +\def\bt#1#2{\fullsquare{#1}{.17}{color=white}\square{#1}{.17}{#2}} + + +% draw a hexagon +\def\hexagon#1#2{ + % draw the lines one at a time (so that dashes overlap if the line is dashed) + \draw[#2]#1++(1,0)--++(120:1); + \draw[#2]#1++(-120:1)--++(120:1); + \draw[#2]#1++(60:1)--++(-1,0); + \draw[#2]#1++(-60:1)--++(-1,0); + \draw[#2]#1++(120:1)--++(-120:1); + \draw[#2]#1++(1,0)--++(-120:1); +} + +% draw the atoms around a hexagon +\def\as#1#2{ + \a{#1++(1,0)}{#2} + \a{#1++(120:1)}{#2} + \a{#1++(-120:1)}{#2} +} +\def\ats#1#2{ + \at{#1++(1,0)}{#2} + \at{#1++(120:1)}{#2} + \at{#1++(-120:1)}{#2} +} +\def\bs#1#2{ + \b{#1++(-1,0)}{#2} + \b{#1++(60:1)}{#2} + \b{#1++(-60:1)}{#2} +} +\def\bts#1#2{ + \bt{#1++(-1,0)}{#2} + \bt{#1++(60:1)}{#2} + \bt{#1++(-60:1)}{#2} +} + +% base lattice +\def\graphene#1#2{ + \hexagon{#1}{#2} + \hexagon{#1++\lo}{#2} + \hexagon{#1++\lt}{#2} + \hexagon{#1++\mlo}{#2} + \hexagon{#1++\mlt}{#2} + \hexagon{#1++\lo++\mlt}{#2} + \hexagon{#1++\lo++\mlt++\lo}{#2} + \hexagon{#1++\lo++\mlt++\mlt}{#2} +} + +% base lattice of sites +\def\sitelattice#1#2#3{ + \csname #1s\endcsname{#2}{#3} + \csname #1s\endcsname{#2++\lo}{#3} + \csname #1s\endcsname{#2++\lt}{#3} + \csname #1s\endcsname{#2++\mlo}{#3} + \csname #1s\endcsname{#2++\mlt}{#3} + \csname #1s\endcsname{#2++\lo++\mlt}{#3} + \csname #1s\endcsname{#2++\lo++\mlt++\lo}{#3} + \csname #1s\endcsname{#2++\lo++\mlt++\mlt}{#3} +} diff --git a/figs/monolayer.fig/Makefile b/figs/monolayer.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/monolayer.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile
\ No newline at end of file diff --git a/figs/monolayer.fig/libs/graphene.sty b/figs/monolayer.fig/libs/graphene.sty new file mode 120000 index 0000000..a377638 --- /dev/null +++ b/figs/monolayer.fig/libs/graphene.sty @@ -0,0 +1 @@ +../../libs/graphene.sty
\ No newline at end of file diff --git a/figs/monolayer.fig/monolayer.tex b/figs/monolayer.fig/monolayer.tex new file mode 100644 index 0000000..59bfadc --- /dev/null +++ b/figs/monolayer.fig/monolayer.tex @@ -0,0 +1,16 @@ +\documentclass{standalone} +\usepackage{tikz} + +% macros to draw graphene lattices +\usepackage{graphene} + +\begin{document} +\begin{tikzpicture} + +\graphene{(0,0)}{} + +\sitelattice{a}{(0,0)}{} +\sitelattice{b}{(0,0)}{} + +\end{tikzpicture} +\end{document} |