| Title | 
              | Quantized hard-x-ray phase vortices nucleated by aberrated nanolenses  |  | 
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      | Publisher | 
              | American Physical Society  |  | 
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      | Place of publication |  | 
               
                         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
                         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
                         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
                         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
                         
             
             
             
             
             
             
             
             
             
             
             
             
             
             
             
                         
             
             
             
                  
      | DOI | 
              | 10.1103/PhysRevA.83.013813  |  | 
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      | Abstract | 
              | Quantized x-ray phase vortices, namely, screw-type topological defects in the wave fronts of a coherent monochromatic scalar x-ray wave field, may be spontaneously nucleated by x-ray lenses. Phase retrieval is used to reconstruct the phase and amplitude of the complex disturbance created by aberrated gold nanolenses illuminated with hard x rays. A nanoscale quantized x-ray vortex-antivortex dipole is observed, manifest both as a pair of opposite-helicity branch points in the Riemann sheets of the multivalued x-ray phase map of the complex x-ray field and in the vorticity of the associated Poynting vector field.  |  | 
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      | Citation | 
              | Physical Review A (Atomic, Molecular and Optical Physics), 83(1), p. 013813-1-013813-7  |  | 
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