Option 1: use boxplotGroup()
See boxplotGroup() on the file exchange. If your boxplot data are matrices with the same number of columns, you can use this function to group them and provide primary and secondary labels.
Option 2: Use newline to create two rows of tick labels
Pro: Easy and clean
Con: Less control of the alignment between the upper and lower labels.
ax = axes();
xlim([0,12])
ticks = {'a_peaks','b','a_concat','b','a_F0','b','a_Fs','b'};
ticks = strrep(ticks,'_','\newline'); % replace underscore with \newline
ax.XTick = [1 2 4 5 7 8 10 11];
ax.XTickLabel = ticks;
This variation below controls the alignment between the upper and lower labels but adds an additional tick between the upper labels.
ax = axes();
xlim([0,12])
ticks = {'a','_peaks','b','a','_concat','b','a','_F0','b','a','_Fs','b'};
ticks = strrep(ticks,'_','\newline'); % replace underscore with \newline
ax.XTick = [1 1.5 2 4 4.5 5 7 7.5 8 10 10.5 11];
ax.XTickLabel = ticks;
Option 2.1: Use cell array with justified text
Added to answer 11-Feb-2021
Pro: Intuitive label arrangement & text justification
ax = axes();
xlim([0,12])
ticks = {'a','','b','a','','b','a','','b','a','','b'; ... % 1st row of labels
'','peaks','','','concat','','','F0','','','Fs',''}; % 2nd row of labels
ticksJust = strjust(pad(ticks),'center'); % Justify: 'left'(default)|'right'|'center
% ticksJust =
% 2×9 cell array
% {' a '} {' '} {' b '} {' a '} {' '} {' b '} {' a '} {' '} {' b '}
% {' '} {'peaks'} {' '} {' '} {'peaks'} {' '} {' '} {'peaks'} {' '}
tickLabels = strtrim(sprintf('%s\\newline%s\n', ticksJust{:}));
ax.XTick = [1 1.5 2 4 4.5 5 7 7.5 8 10 10.5 11];
ax.XTickLabel = tickLabels;
Option 3: Use text() to create a second row of tick lables
Pro: More control over the placement of the tick labels.
Con: Axis limits must be set and the lower tick labels will move if the pan feature is used.
ax = axes();
% Set axis limits before labeling
xlim([0,12])
ylim([0,1]);
% Shorten the height of the axes to 90% and shift
% upward to make room for the 2-layers of labels.
upperPosition = sum(ax.Position([2,4]));
ax.Position(4) = ax.Position(4) * .9;
ax.Position(2) = minus(upperPosition, ax.Position(4));
% label the upper row using xtick and xticklabel
ax.XTick = [1 2 4 5 7 8 10 11];
ax.XTickLabel = {'a' 'b'};
% use text() to creat the lower row of tick labels
% The 2nd layer will be 6% of the y axis range below the axis.
lowerLevel = min(ylim(ax))-range(ylim(ax))*.06;
lowerLabels = {'peaks','concat','F0','FS'};
text([1.5, 4.5, 7.5, 10.5], repmat(lowerLevel,1,numel(lowerLabels)), lowerLabels,...
'VerticalAlignment','Top','HorizontalAlignment','Center')
