Two-channel Kondo phases in coupled quantum dots
<p>We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonst...
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| Médium: | Diplomová práce |
| Jazyk: | English |
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2009
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| _version_ | 1826316393422782464 |
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| author | Mitchell, A |
| author2 | Logan, D |
| author_facet | Logan, D Mitchell, A |
| author_sort | Mitchell, A |
| collection | OXFORD |
| description | <p>We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonstrate that a rich range of strongly correlated electron behaviour results, with non-Fermi liquid 2CK phases and non-trivial phase transitions accessible. We employ physical arguments and the numerical renormalization group (NRG) technique to analyse these systems in detail, examining in particular both thermodynamic and dynamical properties.</p> <p>When leads are coupled to either end of a chain of dots, we show that the resulting behaviour on low temperature/energy scales can be understood in terms of simpler paradigmatic quantum `impurity' models. An effective low-energy single-spin 2CK model is derived for all odd-length chains, while the behaviour of even-length chains is related fundamentally to that of the classic `two-impurity Kondo' model.</p> <p>In particular, for small interdot coupling, we show that an effective coupling mediated though incipient <em>single</em>-channel Kondo states drives all odd chains to the 2CK fixed point (FP) on the lowest temperature/energy scales. A theory is also developed to describe a phase transition in even chains. We derive an effective channel-anisotropic 2CK model, which indicates that the critical FP of such models must be the 2CK FP. This physical picture is confirmed using NRG for various chain systems.</p> <p>We also examine the effect of local frustration on 2CK physics in mirror-symmetric ring systems. The importance of geometry and symmetry is demonstrated clearly in the markedly different physical behaviour that arises in systems where two leads are either connected to the same dot, or to neighbouring dots. In the latter case, we show for all odd-membered rings that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot couplings. A frustration-induced phase transition thus occurs, the 2CK phases being separated by a novel critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilise the 2CK FPs, and the critical FP is shown to consist of a free pseudospin together with effective <em>single</em>-channel spin quenching. While connecting both leads to the same dot again results in two parity-distinct phases, a simple level-crossing transition now results due to the symmetry of the setup. The proposed geometry also allows access to a novel ferromagnetically-coupled two-channel local moment phase.</p> <p>Driven by varying the interdot couplings and occurring at the point of inherent magnetic frustration, such transitions in ring structures provide a striking example of the subtle interplay between internal spin and orbital degrees of freedom in coupled quantum dot systems, and the resulting effect on Kondo physics.</p> |
| first_indexed | 2024-03-06T21:08:28Z |
| format | Thesis |
| id | oxford-uuid:3d4e9d86-794c-441c-9d4b-20e6f1bd1de1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:44:21Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:3d4e9d86-794c-441c-9d4b-20e6f1bd1de12024-12-07T15:47:09ZTwo-channel Kondo phases in coupled quantum dotsThesishttp://purl.org/coar/resource_type/c_db06uuid:3d4e9d86-794c-441c-9d4b-20e6f1bd1de1Theoretical chemistryCondensed matter theoryCondensed Matter PhysicsTheoretical physicsPhysical SciencesChemistry & allied sciencesPhysicsPhysical & theoretical chemistryEnglishOxford University Research Archive - Valet2009Mitchell, ALogan, D<p>We investigate systems comprising chains and rings of quantum dots, coupled to two metallic leads. Such systems allow to study the competition between orbital and spin degrees of freedom in a nanodevice, and the effect this subtle interplay has on two-channel Kondo (2CK) physics. We demonstrate that a rich range of strongly correlated electron behaviour results, with non-Fermi liquid 2CK phases and non-trivial phase transitions accessible. We employ physical arguments and the numerical renormalization group (NRG) technique to analyse these systems in detail, examining in particular both thermodynamic and dynamical properties.</p> <p>When leads are coupled to either end of a chain of dots, we show that the resulting behaviour on low temperature/energy scales can be understood in terms of simpler paradigmatic quantum `impurity' models. An effective low-energy single-spin 2CK model is derived for all odd-length chains, while the behaviour of even-length chains is related fundamentally to that of the classic `two-impurity Kondo' model.</p> <p>In particular, for small interdot coupling, we show that an effective coupling mediated though incipient <em>single</em>-channel Kondo states drives all odd chains to the 2CK fixed point (FP) on the lowest temperature/energy scales. A theory is also developed to describe a phase transition in even chains. We derive an effective channel-anisotropic 2CK model, which indicates that the critical FP of such models must be the 2CK FP. This physical picture is confirmed using NRG for various chain systems.</p> <p>We also examine the effect of local frustration on 2CK physics in mirror-symmetric ring systems. The importance of geometry and symmetry is demonstrated clearly in the markedly different physical behaviour that arises in systems where two leads are either connected to the same dot, or to neighbouring dots. In the latter case, we show for all odd-membered rings that two distinct 2CK phases, with different ground state parities, arise on tuning the interdot couplings. A frustration-induced phase transition thus occurs, the 2CK phases being separated by a novel critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilise the 2CK FPs, and the critical FP is shown to consist of a free pseudospin together with effective <em>single</em>-channel spin quenching. While connecting both leads to the same dot again results in two parity-distinct phases, a simple level-crossing transition now results due to the symmetry of the setup. The proposed geometry also allows access to a novel ferromagnetically-coupled two-channel local moment phase.</p> <p>Driven by varying the interdot couplings and occurring at the point of inherent magnetic frustration, such transitions in ring structures provide a striking example of the subtle interplay between internal spin and orbital degrees of freedom in coupled quantum dot systems, and the resulting effect on Kondo physics.</p> |
| spellingShingle | Theoretical chemistry Condensed matter theory Condensed Matter Physics Theoretical physics Physical Sciences Chemistry & allied sciences Physics Physical & theoretical chemistry Mitchell, A Two-channel Kondo phases in coupled quantum dots |
| title | Two-channel Kondo phases in coupled quantum dots |
| title_full | Two-channel Kondo phases in coupled quantum dots |
| title_fullStr | Two-channel Kondo phases in coupled quantum dots |
| title_full_unstemmed | Two-channel Kondo phases in coupled quantum dots |
| title_short | Two-channel Kondo phases in coupled quantum dots |
| title_sort | two channel kondo phases in coupled quantum dots |
| topic | Theoretical chemistry Condensed matter theory Condensed Matter Physics Theoretical physics Physical Sciences Chemistry & allied sciences Physics Physical & theoretical chemistry |
| work_keys_str_mv | AT mitchella twochannelkondophasesincoupledquantumdots |