Try removing the outliers:
load('wv_prop.mat')
% Remove outliers
idx = abs(wv_prop(:,2) - nanmean(wv_prop(:,2))) > 3*nanstd(wv_prop(:,2));
wv_prop(idx,:) = [] ;
[idx,C] = kmeans(wv_prop,2);
figure;
plot(wv_prop(idx==1,1),wv_prop(idx==1,2),'r.','MarkerSize',12)
hold on
plot(wv_prop(idx==2,1),wv_prop(idx==2,2),'b.','MarkerSize',12)
plot(C(:,1),C(:,2),'kx',...
'MarkerSize',15,'LineWidth',3)
legend('Cluster 1','Cluster 2','Centroids',...
'Location','NW')
title 'Cluster Assignments and Centroids'
hold off