Persistent Current

• Aharanov-Bohm/Casher Effect in a Kondo Ring , with H.-P. Eckle and H. Johannesson. The influence of a magnetic impurity or ultrasmall quantum dot on the spin and charge persistent currents of a mesoscopic ring is investigated. The system consists of electrons in a one-dimensional ring threaded by spin--dependent Aharonov-Bohm/Casher fluxes, and coupled via an antiferromagnetic exchange interaction to a localized electron. The problem is mapped onto a Kondo model for the even-parity channel plus free electrons in the odd-parity channel. The twisted boundary conditions representing the fluxes couple states of opposite parity unless the independent twist angles for up and down spins correspond to periodic or antiperiodic boundary conditions. For these special values of the fluxes, the model is solved by the Bethe ansatz.
  
  
• Persistent current in a Moebius ladder: A new twist on the problem of interchain coherence of interacting electrons , with F. Mila and S. Capponi. Persistent currents in a Moebius ladder are shown to be very sensitive to the effects of intrachain interactions on the hopping of electrons between chains. Their periodicity as a function of flux is doubled for strong enough repulsive interactions because electrons cannot hop coherently between the chains and have to travel along the full edge of the Moebius ladder, thus encircling the flux twice. The interplay of topology and interactions is shown to lead to interesting finite-size effects on the odd harmonics of the persistent current.
  
  
• Interaction-Induced Enhancement and Oscillations of the Persistent Current , with D. F. Wang. The persistent current I in integrable models of multichannel rings with both short- and long-ranged interactions is investigated. I is found to oscillate in sign and increase in magnitude with increasing interaction strength due to interaction-induced correlations in the contributions of different channels. For sufficiently strong interactions, the contributions of all channels are found to add constructively, leading to a giant enhancement of I . Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder.
  
  
• Charge-transfer induced persistent current and capacitance oscillations , with Markus Büttiker. The polarizability of a phase-coherent mesoscopic system capacitively coupled to external voltage sources is investigated. In small-capacitance structures, where Coulomb charging effects are dominant, the polarizability is found to exhibit sharp charge transfer resonances. Charge transfer from a side branch quantum dot into a ring changes the persistent current through a sequence of plateaus of diamagnetic and paramagnetic states. In contrast, a quantum dot embedded in a ring exhibits resonances in the persistent current, whose sign is independent of the number of electrons in the dot if the total number of electrons in the system is even. It is shown that such a mesoscopic system can be polarized appreciably not only by the application of an external voltage, but also via an Aharonov-Bohm flux.
  
  
• Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension , with Andrew Millis and Sriram Shastry. The persistent current I of a mesoscopic Hubbard ring with commensurate electron density was calculated analytically via an asymptotic finite-size solution of the Bethe ansatz equations. The exponential decrease of I with the circumference of the ring allows one to define the correlation length in the insulating phase of the model. We showed that in the vicinity of the zero temperature critical point of the Mott-Hubbard metal-insulator transition the doping, system-size, and interaction-strength dependence of the frequency-dependent conductivity scale with the correlation length. These results confirm the applicability of the hyperscaling ansatz to this system, and suggest that the scaling function for the conductivity which we calculated is universal.
  

Publications

1. C. A. Stafford, A. J. Millis, and B. S. Shastry,
   Finite-size effects on the optical conductivity of a half-filled Hubbard ring ,
   Phys. Rev. B 43 , 13660 (1991).
   
   
2. C. A. Stafford and A. J. Millis,
   Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension ,
   Phys. Rev. B 48 , 1409 (1993).
   
   
3. M. Büttiker and C. A. Stafford,
   Charge Transfer Induced Persistent Current and Capacitance Oscillations ,
   Phys. Rev. Lett. 76 , 495 (1996).
   
   
4. M. Büttiker and C. A. Stafford,
   Coherent Charge Transfer Resonances and Fluctuations in a Mesoscopic Ring Coupled to a Quantum Dot ,
   in ``Correlated Fermions and Transport in Mesoscopic Systems,'' T. Martin, G. Montambaux, and J. Tran Thanh Van eds.,
   p. 491 (Editions Frontieres, Gif-sur-Yvette, 1996).
   
   
5. C. A. Stafford and D. F. Wang,
   Interaction-Induced Enhancement and Oscillations of the Persistent Current ,
   Phys. Rev. B 56 , R4383 (1997).
   
   
6. F. Mila, C. A. Stafford, and S. Capponi,
   Persistent currents in a Moebius ladder: A new twist on the problem of interchain coherence of interacting electrons ,
   Phys. Rev. B 57 , 1457 (1998).
   
   
7. R. Kotlyar, C. A. Stafford, and S. Das Sarma,
   Addition spectrum, persistent current, and spin polarization in coupled quantum-dot arrays: Coherence, correlation, and disorder ,
   Phys. Rev. B 58 , 3989 (1998).
   
   
8. C. A. Stafford, R. Kotlyar, and S. Das Sarma,
   Coherent resonant tunneling through an artificial molecule ,
   Phys. Rev. B 58 , 7091 (1998).
   
   
9. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
   Aharonov-Bohm/Casher Effect in a Kondo Ring ,
   Physica B 284 , 1872 (2000).
   
   
10. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
    Kondo Impurity in a Mesoscopic Ring: Charge Persistent Current ,
    J. Low Temp. Phys. 118 , 475 (2000).
    
    
11. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
    Persistent Currents in a Kondo Ring ,
    in ``Quantum Physics at the Mesoscopic Scale,'' D. C. Glattli, M. Sanquer, and J. Tran Thanh Van eds.
    (EDP Sciences, Les Ulis, France, 2000), pp. 445-449.
    
    
12. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
    Kondo Resonance in a Mesoscopic Ring Coupled to a Quantum Dot: Exact Results for the Aharonov-Bohm/Casher Effects ,
    Phys. Rev. Lett. 87 , 16602 (2001).