Mapping a non-linear Luttinger Liquid using 1D-2D magnetotunelling spectroscopy
Lead Research Organisation:
University of Cambridge
Department Name: Physics
Abstract
One-dimensional (1D) systems behave in a significantly different way from their higher-dimensional counterparts as electron-electron interactions can now no longer be neglected. The Tomonaga-Luttinger Liquid (TLL) model is a theory that describes such systems. This model makes a number of predictions, such as spin-charge separation and suppression of tunnelling conductance at zero bias, both of which have been experimentally observed. It makes however some simplifications, such as assuming 1D systems of infinite length and only considering low-energy excitations.
Recent theoretical work has focused on extending the TLL theory to include higher energy excitations and finite length systems. This led to the prediction that, at higher order excitations, 'replica' parabolas with higher momenta should be observed, in addition to the simple single-particle parabolic dispersion. My work focuses on the experimental detection and quantification of these higher order excitations using the method of 1D-2D tunnelling spectroscopy in order to map the dispersion of the system. In addition, we are also interested in measuring the temperature dependence of tunnelling at zero bias and at other interesting features as well as observing asymmetric current flow (i.e. charge fractionalisation) in 1D wires.
Recent theoretical work has focused on extending the TLL theory to include higher energy excitations and finite length systems. This led to the prediction that, at higher order excitations, 'replica' parabolas with higher momenta should be observed, in addition to the simple single-particle parabolic dispersion. My work focuses on the experimental detection and quantification of these higher order excitations using the method of 1D-2D tunnelling spectroscopy in order to map the dispersion of the system. In addition, we are also interested in measuring the temperature dependence of tunnelling at zero bias and at other interesting features as well as observing asymmetric current flow (i.e. charge fractionalisation) in 1D wires.
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
| 1948695 | Studentship | EP/N509620/1 | 01/10/2017 | 31/03/2021 | Pedro Vianez |
| Description | This award was used to study interaction effects in many-body one-dimensional systems. The current established theory, that of a Luttinger liquid, has been amply verified experimentally, with several of its seminal predictions (e.g. spin-charge separation, threshold power-law behaviour) having been confirmed across several experimental platforms. This theory is, however, based on a number of approximations, most importantly that of linearity, making its applicability limited to low-energy regimes. We used this award to explore newly proposed theories beyond the Luttinger paradigm which hadn't yet been put under the experimental probe, specifically those concerning the newly proposed nonlinear Luttinger liquids. We were able to verify several of the new predictions, including a length-dependent hierarchy of modes and separation of different types of excitations (charge and spin) beyond the low energy regime. We have also, for the first time, obtained data showing screening effects between two one-dimensional systems, as well as the contribution of the many-body effects to the carrier mass. This work has now resulted in the following outcomes: - Y. Jin, M. Moreno, P. M. T. Vianez, J. P. Griffiths, I. Farrer, D. A. Ritchie, C. J. B. Ford, Microscopic metallic air-bridge arrays for connecting quantum devices, Appl. Phys. Lett. 118, 162108 (2021) [doi: 10.1063/5.0045557]; - P. Vianez, O. Tsyplyatyev, C. Ford, Semiconductor nanodevices as a probe of strong electron correlations. In: Semiconductors Nanodevices: Physics, Technology and Applications, David Ritchie (Ed.), Elsevier (2021) [doi: 10.1016/B978-0-12-822083-2.00007-1]; - P. M. T. Vianez, Y. Jin, M. Moreno, A. Anirban, A. Anthore, W. K. Tan, J. P. Griffiths, I. Farrer, D. A. Ritchie, A. J. Schofield, O. Tsyplyatyev, C. J. B. Ford, Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor, Science Advances 8, eabm2781 (2022) [doi: 10.1126/sciadv.abm2781]; - P. M. T. Vianez, Y. Jin, W. K. Tan, J. P. Griffiths, I. Farrer, D. A. Ritchie, O. Tsyplyatyev, C. J. B. Ford, Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality, Phys. Rev. B (2023) [doi: 10.1103/PhysRevB.00.005100]; - P. M. T. Vianez, C. J. B. Ford, Quantum transport and interactions in one dimension, Encyclopedia of Condensed Matter Physics 2nd edition, Tapash Chakraborty (Ed.), Elsevier [in press] |
| Exploitation Route | The study of interaction effects in one-dimensional (1D) systems could potentially contribute to a better understanding of the mechanisms behind superconductivity. In particular, this work could contribute towards better understanding of the mechanisms behind high-temperature superconductivity, something which would significantly reduce energy losses, while also allowing for more efficient uses. On this front, substantial efforts are currently being made in order to expand both the theoretical tools as well as experimental techniques developed in 1D to higher dimensions (e.g. 2D). Another possible outcome is the development of new, more powerful, energy harvesting devices and platforms based on the resonant tunnelling technique developed in this work. This is currently being explored by Pedro Vianez as part of their postdoctoral research. Finally, two recent European Microkelvin Platform (2022 and 2023) have been secured by Pedro Vianez and Christopher Ford in order to investigate the formation of spontaneous nuclear spin magnetism in 1D systems when cooled down to sufficiently low temperatures. |
| Sectors | Digital/Communication/Information Technologies (including Software),Electronics,Energy |
| Description | Clare-Yale Fellowship Award |
| Amount | £2,000 (GBP) |
| Organisation | University of Cambridge |
| Department | Clare College |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 08/2019 |
| End | 08/2019 |
| Description | EPSRC Doctoral Prize |
| Amount | £50,000 (GBP) |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2021 |
| End | 05/2023 |
| Description | Graduate Research Expenses Fund |
| Amount | £400 (GBP) |
| Organisation | University of Cambridge |
| Department | Clare College |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 03/2020 |
| End | 03/2020 |
| Description | Mapping a non-linear Luttinger Liquid using 1D-2D magnetotunelling spectroscopy |
| Amount | £80,000 (GBP) |
| Funding ID | 1948695 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 10/2017 |
| End | 03/2021 |
| Description | Research Student Conference Fund |
| Amount | £300 (GBP) |
| Organisation | Institute of Physics (IOP) |
| Sector | Learned Society |
| Country | United Kingdom |
| Start | 03/2020 |
| End | 03/2020 |
| Title | Supporting Data for "Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality" |
| Description | Description Data used in the figures in the paper and in its Supplementary Material. See README.txt files for full details. Format While the data can be loaded manually, convenient, free programs and scripts are available to load it into MATLAB (from http://www.repository.cam.ac.uk/handle/1810/247429) or Origin (from http://www.repository.cam.ac.uk/handle/1810/247432). .mat and .m files need MATLAB (or free equivalent GNU Octave from https://www.gnu.org/software/octave/ ) Keywords Luttinger liquid, Nonlinear Luttinger Liquid, Electronic transport |
| Type Of Material | Database/Collection of data |
| Year Produced | 2023 |
| Provided To Others? | Yes |
| Impact | P. M. T. Vianez, Y. Jin, W. K. Tan, Q. Liu, J. P. Griffiths, I. Farrer, D. A. Ritchie, O. Tsyplyatyev, and C. J. B. Ford, Phys. Rev. B 107, 115128 (2023). Supporting Data for "Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality" [Dataset]. See full publication at https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.115128. |
| URL | https://doi.org/10.17863/CAM.94403 |
| Title | Supporting Data for "Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor" |
| Description | Description Data used in the figures in the paper and in its Supplementary Material. See README.txt files for full details. Format While the data can be loaded manually, convenient, free programs and scripts are available to load it into MATLAB (from http://www.repository.cam.ac.uk/handle/1810/247429) or Origin (from http://www.repository.cam.ac.uk/handle/1810/247432). .mat and .m files need MATLAB (or free equivalent GNU Octave from https://www.gnu.org/software/octave/ ) Keywords Luttinger liquid, Nonlinear Luttinger Liquid, Electronic transport |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| Impact | P. M. T. Vianez, Y. Jin, M. Moreno, A. S. Anirban, A. Anthore, W. K. Tan, J. P. Griffiths, I. Farrer, D. A. Ritchie, A. J. Schofield, O. Tsyplyatyev, C. J. B. Ford, Sci. Adv. 8, eabm2781 (2022). Supporting Data for "Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor" [Dataset]. See full publication at https://www.science.org/doi/10.1126/sciadv.abm2781. |
| URL | https://www.repository.cam.ac.uk/handle/1810/336189 |
| Title | Supporting data for "Microscopic metallic air-bridge arrays for connecting quantum devices" |
| Description | Description Numerical data in text format, produced by CryoMeas (written by C J B Ford). Fig.1- N/A Fig.2- AFM scans data Fig.3- Contrast curves data for Copolymer, 100k, 495k and 950k Fig.4- Matlab routine for estimating the evolution of the resist profile Fig.5- CryoMeas data files and MatLab routine to load them Format While the data can be loaded manually, convenient, free programs and scripts are available to load it into MATLAB (from http://www.repository.cam.ac.uk/handle/1810/247429) or Origin (from http://www.repository.cam.ac.uk/handle/1810/247432). .mat and .m files need MATLAB (or free equivalent GNU Octave from https://www.gnu.org/software/octave/ ) AFM images can be viewed using free software gwyddion from gwyddion.net . Keywords Electron-beam lithography, Air-bridge, Water-IPA developer |
| Type Of Material | Database/Collection of data |
| Year Produced | 2021 |
| Provided To Others? | Yes |
| Impact | Citation Jin, Y., Moreno, M., Vianez, P. M., & Ford, C. (2021). Supporting data for "Microscopic metallic air-bridge arrays for connecting quantum devices" [Dataset]. See full publication at https://aip.scitation.org/doi/10.1063/5.0045557 |
| URL | https://doi.org/10.17863/CAM.66595 |
| Description | Leonid Glazman |
| Organisation | Yale University |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | We have fabricated and successfully measured a series of samples designed to work beyond the regime of validity of the Luttinger Liquid model. We have collected extensive amounts of data to compare against theoretical proposals that try to push the currently established model into the nonlinear domain. |
| Collaborator Contribution | Prof. Leonid Glazman is a world-renowned theorist in many-body physics. He pioneered the current established theory on nonlinear Luttinger Liquids (i.e. the mobile impurity model). |
| Impact | We have successfully analysed extensive amounts of data showing evidence for the emergence of a length-dependent hierarchy of modes, a key prediction going beyond the Luttinger approximation. This work has now been published, Vianez et al., Science Advances (2022) [doi: 10.1126/sciadv.abm2781]. This collaboration also allowed Pedro Vianez to have a two month placement at the Yale Quantum Institute as a Visiting Assistant in Research. This collaboration is not multi-disciplinary. |
| Start Year | 2019 |
| Description | Oleksandr Tsyplyatyev |
| Organisation | Goethe University Frankfurt |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | We have fabricated and successfully measured a set of samples designed to work beyond the assumptions made in the Luttinger Liquid model. Our work has focused on providing experimental feedback to current theoretical proposals trying to push the model into finite-length and/or high-energy regimes. |
| Collaborator Contribution | Dr. Oleksandr Tsyplyatyev is a condensed matter theorist working at the Institute of Theoretical Physics in the University of Frankfurt. Our collaboration was established based on his expertise in the microscopic theory of correlated quantum systems, specifically regarding strong correlations in one dimension. Dr. Tsyplyatyev developed the model which we are currently using in order to interpret and analyse our data. |
| Impact | We have observed two key predictions regarding nonlinear Luttinger liquids: - the emergence of a length-dependent hierarchy of modes; - the observation of charge and spin modes at high-energies; In addition, we have also observed: - the first experimental study on screening effects between two one-dimensional systems; - the effect of the many-body effects on the carrier mass of the electron. These results have now been published, see Vianez et al, Science Advances (2022) [doi: 10.1126/sciadv.abm2781] and Vianez et al., Phys. Rev. B 107, 115128 (2023) [doi: 10.1103/PhysRevB.107.115128]. This collaboration is not multi-disciplinary. |
| Start Year | 2018 |
| Description | Invited talk at CBPF (Brazilian Center for Physical Research) in Brazil |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Gave invited talk to CBPF's condensed matter physics group, sparking interested questions and discussions with both experimentalists and theorists. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://www.gov.br/cbpf/pt-br |
| Description | Invited talk at ICPS conference in Australia |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Gave invited talk at large international conference, with many researchers discussing the work afterwards and a possible collaboration with a theorist. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://icps2022.org/ |
| Description | Invited talk at Mahidol University in Bangkok, Thailand |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Gave invited talk at a university Physics Department, receiving interested questions afterwards, and strengthening a current collaboration. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Invited talk at SKKU University in South Korea |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Gave invited talk at University Physics Department, sparking interested questions and discussions and a likely collaboration. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Invited talk at Workshop in South Korea |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Gave invited talk at a Workshop on Solid-State Quantum Devices for mainly Korean researchers in South Korea, sparking interested questions and several possible collaborations. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://sites.google.com/view/wseqt |