Slide 1:Antibonding Hole Ground Statein Artificial Molecules J.I. Climente G. Goldoni M.F. Doty M. Scheibner A. Bracker D. Gammon M. Korkusinski P. Hawrylak Virtual Conference on Nanoscience and Technolgoy July 2008


Slide 2:The Motivation


Slide 3:Discrete energy spectrum Shell structure Pauli principle, Aufbau logic... Discrete energy spectrum Shell structure Pauli principle, Aufbau logic... But differences are more interesting: Charged with electrons Charged with electrons or holes Sort of positively charged, heavy electrons but with some exotic properties violate Aufbau logic? PRL 94 (2005) 026808 weak decoherence Nature 451 (2008) 441 Similarities enabled fast learning of quantum dot physics Artificial atoms


Slide 4:Molecular states are formed in both cases Electrons in double dots behave very much as in natural diatomic molecules But holes do not always do so... Artificial molecules


Slide 5:Electron vs Hole tunneling in DQDs TUNNELING NO TUNNELING EQD EQD ?


Slide 6:Antecedents: atomistic calculations Bester el al. PRL 93, 047401 (2004); PRB 71, 075325 (2005) Jaskólski el al. Acta Phys. Pol. A 106, 193 (2004); PRB 74, 195339 (2006) Korkusinski et al. ICPS (2004) Antibonding ground state related to large light-hole pz atomic orbital component Asymmetric DQDs (hole mostly localized in one QD)


Slide 7:Holes as Luttinger spinors Conduction Band Valence Band E k Eg Heavy Hole |Jz|=3/2 Light Hole |Jz|=1/2 Split Off Electrons: l=0 J = l+s = 1/2 Holes: l=1 J = l+s = 3/2, 1/2 Heavy Hole Light Hole Luttinger & Kohn Phys. Rev. 97, 869 (1955). Energy Heavy hole


Slide 8:Holes as Luttinger spinors


Slide 9:Luttinger-Kohn spinors in QDs Each component has a well-defined vertical parity Do not couple in-plane and vertical coordinates Each component has a well-defined m=0, +1, -1, +2, -2 ...


Slide 10:...but The spinor has well-defined total (envelope+Bloch) angular momentum Fz=m+Jz Luttinger-Kohn spinors in QDs


Slide 11:...but we can define a chirality operator which is isomorphic to spin: Rego et al. PRB 55, 15694 (1997) Andreani et al. PRB 36, 5887 (1987) Luttinger-Kohn spinors in QDs


Slide 12:Luttinger spinors in DQDs QD1 QD2 z Chirality up (~97% bonding) Chirality down (~95% antibonding) z The Luttinger spinor contains the ingredients of the ground state reversal


Slide 13:The Role of Spin-Orbit Interaction


Slide 14:Spin-orbit interaction mixes: Bonding HH with antibonding LH (chirality up) Antibonding HH with bonding LH (chirality down) Spin-orbit acts as a negative correction to the tunneling rate 2t < 0 Antibonding g.s.


Slide 15:Ground state reversal induced with magnetic fields bonding antibonding D


Slide 16:Luttinger-Kohn k∙p Hamiltonian diagonalization sp3d5s* tight-binding numerical computation including strain Comparison with more realistic models Effective mass heavy hole Hamiltonian Resonant Electric Field Bracker, et al. APL 89 233110 (2006)


Slide 17:Looking for experimental evidence


Slide 18:The antibonding state shows enhanced Zeeman splitting The bonding state shows decreased Zeeman splitting Tunneling-dependent Zeeman splitting Image courtesy of L.J Whitman, NRL Electric field Doty, et al. Phys. Rev. Lett. 97 197202 (2006) GaAs InAs InAs QD2 QD1 Bonding Antibonding At the resonant field:


Slide 19:Antibonding hole ground state detected Antibonding ground state! Ground state Excited state The antibonding state shows enhanced Zeeman splitting The bonding state shows decreased Zeeman splitting


Slide 20:Conclusions In DQDs, holes need to be described as Luttinger spinors Doty et al. arxiv:0804.3097 Climente et al. submitted (2008) Theory: Experiment and theory: The strong valence band spin-orbit interaction induces a bonding-to-antibonding ground state transition Experimental evidence of the predicted behavior is found Molecular states with novel properties ahead?