Index in fraction in exponent in fraction looks wonky

Question

I'm trying to write

\[ \frac{1}{1+e^{\frac{\varepsilon-\mu}{k_B T}}} \]

but it looks really wonky. In particular the B in the subscript is just as big as everything else. I've seen this written in a way that looked nice (without using \exp or writing (...)/(...) instead of \frac{}{}. Is there any nicer way of doing this?

Answer 1

Consider the following four representations of the same mathematical expression.

• The first row is from your posting. TeX knows about scriptstyle (for first-level subscripts and superscripts) and scriptscriptstyle (for second-level subscripts and superscripts) math, but not about scriptscriptscriptstyle. That's why the letter B looks too big relative to k and T.

• The second row succeeds in making the overall expression less tall, by replacing \frac{1}{...} with [...]^{-1}. However, the letter B still looks too big.

• The third row replaces e^{...} with \exp(...). This change, finally, succeeds in getting the relative sizes about right.

• The fourth row replaces frac{a}{b} with (a)/(b), with inline-fraction notation.

In my view, the expressions in rows 3 and 4 both look good.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\addtolength\jot{4pt}
\begin{align*} 
&\frac{1}{1+e^{\frac{\varepsilon-\mu}{k_B T}}} \\
&\Bigl[1+e^{\frac{\varepsilon-\mu}{k_B T}}\Bigr]^{-1} \\
&\Bigl[1+\exp\Bigl(\frac{\varepsilon-\mu}{k_B T}\Bigr)\Bigr]^{-1} \\
&\bigl[1+\exp\bigl((\varepsilon-\mu)/(k_B T)\bigr)\bigr]^{-1}
\end{align*}
\end{document}

Answer 2

You can use\tfrac in the exponent (and \mathrm{e}, but that's another problem). Compare:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}

\[ \frac{1}{1+\mathrm{e}^{\frac{\varepsilon-\mu}{k_B T}}} \]

\[ \frac{1}{1+\mathrm{e}^{\tfrac{\varepsilon-\mu}{k_B T}}} \]

\end{document} 

Answer 3

If you prefer to have a smaller B you can use scalerel package with the command \scaleobj. Here's an example with a scaling factor of 0.7.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{scalerel}
\begin{document}
\[ \frac{1}{1+e^{\frac{\varepsilon-\mu}{k_{\scaleobj{.7}{B}} T}}} \]
\end{document}