Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators
We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0\lt K\lt 1$ . The model was studied...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/17/1/013005 |
| _version_ | 1797751219774554112 |
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| author | Chung-Hou Chung Salman Silotri |
| author_facet | Chung-Hou Chung Salman Silotri |
| author_sort | Chung-Hou Chung |
| collection | DOAJ |
| description | We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0\lt K\lt 1$ . The model was studied by Law et al (2010 Phys. Rev. B http://dx.doi.org/10.1103/PhysRevB.81.041305 81 http://dx.doi.org/10.1103/PhysRevB.81.041305 ), and was mapped onto an anisotropic two-channel Kondo model via bosonization. For $K\lt 1$ , the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between the dot and the 2DTI based on a simple scaling dimensional analysis (Law et al 2010 Phys. Rev. B http://dx.doi.org/10.1103/PhysRevB.81.041305 81 http://dx.doi.org/10.1103/PhysRevB.81.041305 . We re-examine this model beyond the bare scaling dimension analysis via a one-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for a fixed value of $K\lt 1$ that the 2CK fixed point can be unstable towards the 1CK fixed point and the system is expected to undergo a quantum phase transition between 1CK and 2CK fixed points with changing Kondo couplings. Our RG approach is controlled near K = 1. In general, this QPT can also occur upon tuning the Luttinger parameter K to a critical value ${{K}_{{\rm c}}}$ smaller than unity ( $0\lt {{K}_{{\rm c}}}\lt 1$ ) for fixed Konodo couplings. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for $\frac{1}{2}\lt K\lt 1$ . |
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| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:45:23Z |
| publishDate | 2015-01-01 |
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| spelling | doaj.art-3c91881c91884bc78fe7845848a2f29e2023-08-08T14:15:39ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117101300510.1088/1367-2630/17/1/013005Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulatorsChung-Hou Chung0Salman Silotri1Department of Electrophysics, National Chiao-Tung University , HsinChu, Taiwan, 300, Republic of China; National Center for Theoretical Sciences , HsinChu, Taiwan 300, Republic of ChinaDepartment of Electrophysics, National Chiao-Tung University , HsinChu, Taiwan, 300, Republic of ChinaWe investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0\lt K\lt 1$ . The model was studied by Law et al (2010 Phys. Rev. B http://dx.doi.org/10.1103/PhysRevB.81.041305 81 http://dx.doi.org/10.1103/PhysRevB.81.041305 ), and was mapped onto an anisotropic two-channel Kondo model via bosonization. For $K\lt 1$ , the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between the dot and the 2DTI based on a simple scaling dimensional analysis (Law et al 2010 Phys. Rev. B http://dx.doi.org/10.1103/PhysRevB.81.041305 81 http://dx.doi.org/10.1103/PhysRevB.81.041305 . We re-examine this model beyond the bare scaling dimension analysis via a one-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for a fixed value of $K\lt 1$ that the 2CK fixed point can be unstable towards the 1CK fixed point and the system is expected to undergo a quantum phase transition between 1CK and 2CK fixed points with changing Kondo couplings. Our RG approach is controlled near K = 1. In general, this QPT can also occur upon tuning the Luttinger parameter K to a critical value ${{K}_{{\rm c}}}$ smaller than unity ( $0\lt {{K}_{{\rm c}}}\lt 1$ ) for fixed Konodo couplings. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for $\frac{1}{2}\lt K\lt 1$ .https://doi.org/10.1088/1367-2630/17/1/013005Kondo effectquantum criticalityquantum dottopological insulators72.15.Qm7.23.-b |
| spellingShingle | Chung-Hou Chung Salman Silotri Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators New Journal of Physics Kondo effect quantum criticality quantum dot topological insulators 72.15.Qm 7.23.-b |
| title | Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators |
| title_full | Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators |
| title_fullStr | Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators |
| title_full_unstemmed | Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators |
| title_short | Quantum criticality in a Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators |
| title_sort | quantum criticality in a kondo quantum dot coupled to helical edge states of interacting 2d topological insulators |
| topic | Kondo effect quantum criticality quantum dot topological insulators 72.15.Qm 7.23.-b |
| url | https://doi.org/10.1088/1367-2630/17/1/013005 |
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