Abstract
We investigate possible nontrivial phases of a two-subband quantum wire. It is found that inter- and intra-subband interactions may drive the electron system of the wire into a gapped state. If the nominal electron densities in the two subbands are sufficiently close to each other, then the leading instability is the inter-subband charge-density wave (CDW). For larger difference in the densities, the interaction in the inter-subband Cooper channel may lead to a superconducting instability. The total charge density mode, responsible for the conductance of an ideal wire, always remains gapless, which enforces the two-terminal conductance to be at the universal value of 2e 2/hper occupied subband. On the contrary, the tunneling density of states (DOS) in the bulk of the wire acquires a hard gap, above which the DOS has a non-universal singularity. This singularity is weaker than the square-root divergency characteristic for non-interacting quasiparticles near a gap edge due to the “dressing” of massive modes by a gapless total charge density mode. The DOS for tunneling into the end of a wire in a CDW-gapped state, however, preserves the power-law behavior due to the frustration the edge introduces into the CDW order. This work is related to the vast literature on coupled 1D systems, and most of all, on two-leg Hubbard ladders. Whenever possible, we give derivations of the important results by other authors, adopted for the context of our study.
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References
H. J. Schulz, in Proceedings of Les Houches Summer School LXI, ed. E. Akkermans, G. Montambaux, J. Pichard, and J. Zinn-Justin (Elsevier, Amsterdam, 1995), p.533.
M. P. A. Fisher and L. I. Glazman in Mesoscopic Electron Transport, edited by L. P. Kouwenhoven, L. L. Sohn and G. Schön, Kluwer Academic, Boston, 1997.
M. Bockrath et al., Nature 397, 598 (1999); cond-mat/9812233.
C. Dekker, Physics Today 52, 22 (1999).
C. Ilani et al., cond-mat/9910116.
S. V. Zaitsev-Zotov et al., cond-mat/990756.
C. L. Kane and M. P. A. Fisher, Phys. Rev. B 46, 15233 (1992).
K. A. Matveev and L. I. Glazman, Phys. Rev. Lett 70, 990 (1993).
S. Tarucha, T. Honda, and T. Saku, Sol. St. Commun. 94, 413 (1995).
K. J. Thomas et al., Phys. Rev. Lett 77, 135 (1996).
A. Yacoby et al., Phys. Rev. Lett 77, 4612 (1996); Solid State Communications 101, 77 (1997).
A. M. Finkelstein and A. I. Larkin, Phys. Rev. B 47, 10461 (1993).
M. Fabrizio, Phys. Rev. B 48, 15838 (1993).
H. J. Schulz, Phys. Rev. B 53, R2959 (1996).
L. Balents and M. P. A. Fisher, Phys. Rev. B 53, 12133 (1996).
H. J. Schulz, cond-mat/9808167.
V. J. Emery, S. A. Kivelson, and O. Zachar, Phys. Rev. B 56, 6120 (1997).
H. H. Lin, L. Balents, and M. P. A. Fisher, Phys. Rev. B 56, 6569 (1997); condmat/ 9801285.
C. L. Kane, L. Balents and M. P. A. Fisher, Phys. Rev. Lett 79, 5086 (1997).
Yu. A. Krotov, D. H. Lee. and S. G. Louie, Phys. Rev. Lett 78, 4245 (1997).
R. Egger and A. O. Gogolin, Phys. Rev. Lett 79, 5082 (1997).
R. Egger, A. O. Gogolin, Eur. Phys. J. B 3, 281 (1998).
H. Yoshioka and A. Odintsov, Phys. Rev. Lett. 82, 374 (1999).
Yu. A. Firsov, V. N. Prigodin, and Chr. Seidel, Phys. Rep. 126, 245 (1985).
C. M. Varma and A. Zawadowski, Phys. Rev. B 32, 7399 (1985).
J. Voit, Eur. Phys. J. B 5, 505 (1999).
P. B. Wiegmann, Phys. Rev. B 59, 15705 (1999).
E. Orignac and T. Giamarchi, Phys. Rev. B 56, 7167 (1997).
M. Mori, M. Ogata and H. Fukuyama, J. Phys. Soc. Jpn. 66, 3363 (1997).
O. A. Starykh and D. L. Maslov, Phys. Rev. Lett. 80, 1694 (1998).
L. P. Kouwenhoven et al., Phys. Rev. Lett. 65, 361 (1990).
K. B. Efetov and A. I. Larkin, Zh. Exp. Teor. Phys. 69, 764 (1975) [Sov. Phys.-JETP 42, 390 (1976)].
H. Frölich, J. Phys. C 1, 544 (1968).
J. Ruvalds, Adv. Phys. 30, 677 (1981).
F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980).
T. Giamarchi, Phys. Rev. B 44, 2905 (1991).
W. Metzner and C. Di Castro, Phys. Rev. B 47, 16107 (1993).
G. D. Mahan, Many-Particle Physics, 2nd ed., Plenum Press, New York, 1990, section 4.4.
J. M. Luttinger, J. Math.. Phys. 4, 1154 (1963).
V. J. Emery, Highly Conducting One-Dimensional Solids, eds. J. T. Devreese, R. E. Evrard and V. E. van Doren, New York, Plenum, p. 247 (1979).
S. Capponi, D. Poilblanc and T. Giamarchi, cond-mat/9909360.
K.A. Matveev, D. Yue, and L.I. Glazman, Phys. Rev. Lett. 71, 3351 (1993).
V. L. Pokrovsky and A. L. Talapov, Sov. Phys. JETP 48, 570 (1978).
H. J. Schulz, Phys. Rev. B 22, 5274 (1980).
A. Luther, Phys. Rev. B 15, 403 (1977).
T. Giamarchi and H. Schulz, Phys. Rev. B 39, 4620 (1989)
J. B. Kogut, Rev. Mod. Phys. 51, 701 (1979).
I. Sa. and H. J. Schulz, Phys. Rev. B 52, R17040 (1995).
D. L. Maslov and M. Stone, Phys. Rev. B 52, R5539 (1995).
V. V. Ponomarenko, Phys. Rev. B 52, R8666 (1995).
T. Giamarchi and H. Maurey, in Correlated Fermions and Transport in Mesoscopic Systems, edited by T. Martin, G. Montambaux, and J. Tran Thanh Van (Editions Frontieres, 1996), p. 13.
I. E. Dzyaloshinskii and A. I. Larkin, Sov. Phys. JETP 38, 202 (1974).
A. M. Chang, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 77, 2538 (1996).
A. V. Shytov, L. S. Levitov, and B. I. Halperin, Phys. Rev. Lett. 80, 141 (1998).
A. Alekseev, V. Cheianov, A. P. Dmitriev, and V. Yu. Kachorovskii, condmat/9904076.
S. T. Chui and P. A. Lee, Phys. Rev. Lett. 35, 315 (1975).
Z. Gulacsi and K. S. Bedell, Phys. Rev. Lett. 72, 2765 (1994).
A. Luther and V. J. Emery, Phys. Rev. Lett. 33, 589 (1974).
S. Sachdev, T. Senthil and R. Shankar, Phys. Rev. B 50, 258 (1994).
D. G. Shelton, A. A. Nersesyan, and A. M. Tsvelik, Phys. Rev. B 53, 8561 (1996).
A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics, Cambridge University Press, 1995.
R. Konik, F. Lesage, A. W. W. Ludwig, H. Saleur, cond-mat/9806334.
L. Balents, cond-mat/9902159.
M. Fabrizio and A. O. Gogolin, Phys. Rev. B 51, 17827 (1995).
M. Fuentes, A. Lopez, E. Fradkin, and E. Moreno, Nucl. Phys. B 450, 603 (1995).
A. O. Gogolin, A. A. Nersesyan and A. M. Tsvelik, Bosonization and Strongly Correlated Systems, Cambridge University Press, 1998.
U. Weiss, Quantum Dissipative Systems, Vol. 2 of Modern Condensed Matter Physics, World Scientific, Singapore, 1993; M. Sassetti and U. Weiss, Europhys. Lett. 27, 311 (1994).
U. Weiss, Solid State Comm. 100, 281 (1996).
U. Weiss et al., Z. Phys. B 84, 471 (1991).
A. O. Gogolin, A. A. Nersesyan, A. M. Tsvelik, and Lu Yu, Nucl. Phys. B 540, 705 (1999).
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Starykh, O.A., Maslov, D.L., Häusler, W., Glazman, L.I., Glazman (1999). Gapped Phases of Quantum Wires. In: Brandes, T. (eds) Low-Dimensional Systems. Lecture Notes in Physics, vol 544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46438-7_3
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DOI: https://doi.org/10.1007/3-540-46438-7_3
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