 the ability 
 of core  shell nanowires to overcome existing 
 limitations of heterostructures is one of the key ingredients for 
 the design of next generation devices . 
 this requires a detailed understanding 
 of the mechanism for strain relaxation in these systems in order to 
 eliminate strain - induced defect formation and thus to boost important 
 electronic properties such as carrier mobility . here 
 we demonstrate 
 how the hole mobility of [ 110]-oriented ge  
 si core  
 shell 
 nanowires can be substantially enhanced thanks to the realization 
 of large band offset and coherent strain in the system , reaching values 
 as high as 4200 cm2/(vs ) at 4 k and 1600 cm2/(vs ) at room temperature for high hole densities of 1019 cm3 . 
 we present a direct correlation of ( i ) mobility , 
 ( ii ) crystal direction , ( iii ) diameter , and ( iv ) coherent strain , 
 all of which are extracted in our work for individual nanowires . 
 our 
 results imply [ 110]-oriented ge  
 si core  
 shell nanowires 
 as a promising candidate for future electronic and quantum transport 
 devices . 
Supplementary Material