Thermopower of a Luttinger-liquid-based two-channel charge Kondo circuit: nonperturbative solution
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https://doi.org/10.15625/0868-3166/17705Keywords:
thermoelectric transport, thermopower, two-channel charge Kondo effectAbstract
Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting (\(g_\sigma = 1\)) and the interaction in the charge sector is repulsive (\(0< g_\rho \leq 1\)). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.
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P. Streda, Quantised thermopower of a channel in the ballistic regime, J. Phys.: Condens. Matter 1 (1989) 1025. DOI: https://doi.org/10.1088/0953-8984/1/5/021
L. W. Molenkamp, H. van Houten, C. W. J. Beenakker, R. Eppenga, and C. T. Foxon, Quantum oscillations in the transverse voltage of a channel in the nonlinear transport regime, Phys. Rev. Lett. 65 (1990) 1052. DOI: https://doi.org/10.1103/PhysRevLett.65.1052
C. W. J. Beenakker and A. A. M. Staring, Theory of the thermopower of a quantum dot, Phys. Rev. B 46 (1992) 9667. DOI: https://doi.org/10.1103/PhysRevB.46.9667
A. A.M. Staring, L. W. Molenkamp, B. W. Alphenaar, H. van Houten, O. J. A. Buyk, M. A. A. Mabesoone, C. W. J. Beenakker, and C. T. Foxon, Coulomb-Blockade Oscillations in the Thermopower of a Quantum Dot, Europhys. Lett. 22 (1993) 57. DOI: https://doi.org/10.1209/0295-5075/22/1/011
T. E. Humphrey, R. Newbury, R. P. Taylor, and H. Linke, Reversible Quantum Brownian Heat Engines for Electrons, Phys. Rev. Lett. 89 (2002) 116801. DOI: https://doi.org/10.1103/PhysRevLett.89.116801
M. H. Devoret and H. Grabert, Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures, New York, Plenum Press, 1992. DOI: https://doi.org/10.1007/978-1-4757-2166-9_1
Y. M. Blanter and Y. V. Nazarov, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, 2009).
K. Kikoin, M. N. Kiselev, and Y. Avishai, Dynamical Symmetry for Nanostructures. Implicit Symmetry in Single-Electron Transport Through Real and Artificial Molecules (Springer, New York, 2012). DOI: https://doi.org/10.1007/978-3-211-99724-6
R. I. Shekhter, Zero Anomalies in the Resistance of a Tunnel Junction Containing Metallic Inclusions in the Oxide Layer, Sov. Phys. JETP 36 (1972) 747; I. O. Kulik and R. I. Shekhter, Kinetic phenomena and charge discreteness effects in granulated media, Sov. Phys. JETP 41 (1975) 308.
L. I. Glazman and R. I. Shekhter, Coulomb oscillations of the conductance in a laterally confined heterostructure, J. Phys.: Condens. Matter 1, 5811 (1989). DOI: https://doi.org/10.1088/0953-8984/1/33/027
C. W. J. Beenakker, Theory of Coulomb-blockade oscillations in the conductance of a quantum dot, Phys. Rev. B 44, 1646 (1991). DOI: https://doi.org/10.1103/PhysRevB.44.1646
J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32 (1964) 37. DOI: https://doi.org/10.1143/PTP.32.37
R. Scheibner, H. Buhmann, D. Reuter, M. N. Kiselev, and L. W. Molenkamp, Thermopower of a Kondo spincorrelated quantum dot, Phys. Rev. Lett. 95 (2005) 176602. DOI: https://doi.org/10.1103/PhysRevLett.95.176602
A. Hewson, The Kondo Problem to Heavy Fermions, Cambridge Studies in Magnetism, Cambridge University Press, Cambridge, 1993. DOI: https://doi.org/10.1017/CBO9780511470752
D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav & M. A. Kastner, Kondo effect in a single-electron transistor, Nature 391 (1998) 156. DOI: https://doi.org/10.1038/34373
L. I. Glazman, and M. E. Raikh, Resonant Kondo transparency of a barrier with quasilocal impurity states, JETP Lett. 47 (1988) 452.
W. G. van der Wiel, S. De Franceschi, T. Fujisawa, J. M. Elzerman, S. Tarucha, L. P. Kouwenhoven, The Kondo effect in the unitary limit, Science 289 (2000) 2105. DOI: https://doi.org/10.1126/science.289.5487.2105
J. Nygard, D. H. Cobden, and P. E. Lindelof, Kondo physics in carbon nanotubes, Nature 408 (2000) 342. DOI: https://doi.org/10.1038/35042545
A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, andW. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59 (1987) 1. DOI: https://doi.org/10.1103/RevModPhys.59.1
K. Le Hur, Kondo resonance of a microwave photon, Phys. Rev. B 85 (2012) 140506(R). DOI: https://doi.org/10.1103/PhysRevB.85.140506
K. Le Hur, L. Henriet, L. Herviou, K. Plekhanov, A. Petrescu, T. Goren, M. Shiro, C. Mora, P. P. Orth, Driven dissipative dynamics and topology of quantum impurity systems, C. R. Physique 19 (2018) 451. DOI: https://doi.org/10.1016/j.crhy.2018.04.003
K. Flensberg, Capacitance and conductance of mesoscopic systems connected by quantum point contacts, Phys. Rev. B 48 (1993) 11156. DOI: https://doi.org/10.1103/PhysRevB.48.11156
K. A. Matveev, Coulomb blockade at almost perfect transmission, Phys. Rev. B 51 (1995) 1743. DOI: https://doi.org/10.1103/PhysRevB.51.1743
A. Furusaki, K. A. Matveev, Theory of strong inelastic cotunneling, Phys. Rev. B 52 (1995) 16676. DOI: https://doi.org/10.1103/PhysRevB.52.16676
A. V. Andreev, K. A. Matveev, Coulomb blockade oscillations in the thermopower of open quantum dots, Phys. Rev. Lett. 86 (2001) 280; Thermopower of a single-electron transistor in the regime of strong inelastic cotunneling, DOI: https://doi.org/10.1103/PhysRevLett.86.280
Phys. Rev. B 66 (2002) 045301.
Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. D. Parmentier, A. Cavanna and F. Pierre, Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states, Nature 526 (2015) 233. DOI: https://doi.org/10.1038/nature15384
Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon and F. Pierre, Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit, Science 360 (2018) 1315. DOI: https://doi.org/10.1126/science.aan5592
P. Nozieres and A. Blandin, Kondo effect in real metals, J. Phys. France 41 (1980) 193. DOI: https://doi.org/10.1051/jphys:01980004103019300
T. K. T. Nguyen and M. N. Kiselev, Thermoelectric Transport in a Three-Channel Charge Kondo Circuit, Phys. Rev. Lett. 125 (2020) 026801. DOI: https://doi.org/10.1103/PhysRevLett.125.026801
T. K. T. Nguyen, M. N. Kiselev, and V. E. Kravtsov, Thermoelectric transport through a quantum dot: Effects of asymmetry in Kondo channels, Phys. Rev. B 92 (2015) 045125.
T. K. T. Nguyen, M. N. Kiselev, Quantum Transport Through a Charge Kondo Circuit: Effects of Weak Repulsive Interaction in Luttinger Liquid, Comm. in Phys. 30 (2020) 1. DOI: https://doi.org/10.15625/0868-3166/30/1/14685
A.V. Parafilo, T. K. T. Nguyen, M. N. Kiselev, Thermoelectrics of a two-channel charge Kondo circuit: Role of electron-electron interactions in a quantum point contact, Phys Rev. B 105 (2022) L121405. DOI: https://doi.org/10.1103/PhysRevB.105.L121405
S. Tomonaga, Remarks on Bloch’s Method of Sound Waves applied to Many-Fermion Problems, Prog. Theor. Phys. 5 (1950) 544. DOI: https://doi.org/10.1143/ptp/5.4.544
J. M. Luttinger, An Exactly Soluble Model of a Many- Fermion Coefficients, J. Math. Phys. 4 (1963) 1154. DOI: https://doi.org/10.1063/1.1704046
H. J. Schulz, G. Cuniberti, and P. Pieri, Fermi liquids and Luttinger liquids In: G. Morandi et al. (eds) Field Theories for Low-Dimensional Condensed Matter Systems. Springer Series in Solid-State Sciences, Springer, Berlin, Heidelberg, 2000. DOI: https://doi.org/10.1007/978-3-662-04273-1_2
D. Senechal, An Introduction to Bosonization In: D. Senechal, A.M. Tremblay, C. Bourbonnais, (eds) Theoretical Methods for Strongly Correlated Electrons. CRM Series in Mathematical Physics, Springer, New York, 2004. DOI: https://doi.org/10.1007/b97552
T. Giamarchi, Quantum Physics in One Dimension, Oxford University Press, Oxford, UK, 2003. DOI: https://doi.org/10.1093/acprof:oso/9780198525004.001.0001
L. I. Glazman, I. M. Ruzin, B. I. Shklovskii, Quantum transport and pinning of a one-dimensional Wigner crystal, Phys. Rev. B 45 (1992) 8454. DOI: https://doi.org/10.1103/PhysRevB.45.8454
O. M. Auslaender, H. Steinberg, A. Yacoby, Y. Tserkovnyak, B. I. Halperin, K. W. Baldwin, L. N. Pfeiffer, K. W.West, Spin-charge separation and localization in one dimension, Science 308 (2005) 88. DOI: https://doi.org/10.1126/science.1107821
Y. Tserkovnyak, B. I. Halperin, O. M. Auslaender, A. Yacoby, Signatures of Spin-Charge Separation in Double-Quantum Wire Tunneling In: A. Glatz, V. I. Kozub, V. M. Vinokur, (eds) Theory of Quantum Transport in Metallic and Hybrid Nanostructures, NATO Science Series, 230, Springer, Dordrecht, 2006.
I. L. Aleiner and L. I. Glazman, Mesoscopic charge quantization, Phys. Rev. B 57 (1998) 9608. DOI: https://doi.org/10.1103/PhysRevB.57.9608
C. L. Kane, M. P. A. Fisher, Transport in a one-channel Luttinger liquid, Phys. Rev. Lett. 68 (1992) 1220; Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Phys. Rev. B 46 (1992) 15233.
I. V. Krive, E. N. Bogachek, A. G. Scherbakov, and U. Landman, Interaction enhanced thermopower in a Luttinger liquid, Phys. Rev. B 63 (2001) 113101. DOI: https://doi.org/10.1103/PhysRevB.63.113101
I. V. Krive, I. A. Romanovsky, E. N. Bogachek, A. G. Scherbakov, and U. Landman, Thermoelectric effects in a Luttinger liquid, Low Temp. Phys. 27 (2001) 821. DOI: https://doi.org/10.1063/1.1414571
I. A. Romanovsky, I. V. Krive, E. N. Bogachek, and U. Landman, Thermopower of an infinite Luttinger liquid, Phys. Rev. B 65 (2002) 075115. DOI: https://doi.org/10.1103/PhysRevB.65.075115
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Accepted 17-02-2023
Published 21-02-2023
