One-dimensional electron systems

• 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.
  
  
• Correlated charge polarization of coupled quantum dots , with R. Kotlyar and S. Das Sarma. Coherent charge transfer in a linear array of tunnel-coupled quantum dots, electrostatically coupled to external gates, is investigated using the Bethe ansatz for a symmetrically biased Hubbard chain. Charge polarization in this correlated system is shown to proceed by two distinct processes: formation of bound states in the metallic phase, and charge transfer processes corresponding to a superposition of antibound states at opposite ends of the chain in the Mott-insulating phase. The polarizability in the insulating phase of the system exhibits a universal scaling form, while the polarization charge in the metallic phase is shown to be quantized in units of e /2.
  
  
• 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.
  
  
• Thermopower in a system with spin-charge separation . Using an asymptotic Bethe ansatz for holons and spinons, the low-temperature thermopower of the one-dimensional Hubbard model was evaluated for the case of repulsive interactions. The competition between the entropy carried by the holons and that carried by the backflow of the spinons gives rise to an unusual temperature and doping dependence of the thermopower which is qualitatively similar to that observed in the normal state of high- T c superconductors and certain quasi-one-dimensional organic conductors. In particular, it is shown that the sign of the thermopower near the metal-insulator transition is opposite to that of noninteracting electrons, consistent with the notion of a ``doped Mott insulator.''
  
  
• 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. C. A. Stafford,
   Unusual low-temperature thermopower in the one-dimensional Hubbard model ,
   Phys. Rev. B 48 , 8430 (1993).
   
   
4. C. A. Stafford and D. F. Wang,
   Parity-locking effect in a strongly-correlated ring ,
   Z. Phys. B 103 , 323 (1997).
   
   
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,
   Correlated charge polarization in a chain of coupled quantum dots ,
   Phys. Rev. B 58 , R1746 (1998).
   
   
8. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
   Aharonov-Bohm/Casher Effect in a Kondo Ring ,
   Physica B 284 , 1872 (2000).
   
   
9. 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).
   
   
10. H.-P. Eckle, H. Johannesson, and C. A. Stafford,
    Persistent Currents in a Kondo Ring ,
    to appear in ``Quantum Physics at the Mesoscopic Scale,'' D. C. Glattli and M. Sanquer eds. (Editions Frontieres, Gif-sur-Yvette, 2000).
    
    
11. 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).