|
1
|
Huang B, Leung TH, Stamper-Kurn DM, Liu WV. Discrete Time Crystals Enforced by Floquet-Bloch Scars. PHYSICAL REVIEW LETTERS 2022; 129:133001. [PMID: 36206415 DOI: 10.1103/physrevlett.129.133001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They are distinguished from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom experiments. Our analytical solutions offer a potential scheme to understand the mechanisms for more generic translation-invariant DTCs.
Collapse
Affiliation(s)
- Biao Huang
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Tsz-Him Leung
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Dan M Stamper-Kurn
- Department of Physics, University of California, Berkeley, California 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - W Vincent Liu
- Department of Physics and Astronomy and IQ Initiative, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| |
Collapse
|
|
2
|
Jin S, Zhang W, Guo X, Chen X, Zhou X, Li X. Evidence of Potts-Nematic Superfluidity in a Hexagonal sp^{2} Optical Lattice. PHYSICAL REVIEW LETTERS 2021; 126:035301. [PMID: 33543961 DOI: 10.1103/physrevlett.126.035301] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Revised: 08/29/2020] [Accepted: 12/21/2020] [Indexed: 06/12/2023]
Abstract
As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.
Collapse
Affiliation(s)
- Shengjie Jin
- State Key Laboratory of Advanced Optical Communication System and Network, Department of Electronics, Peking University, Beijing 100871, China
| | - Wenjun Zhang
- State Key Laboratory of Advanced Optical Communication System and Network, Department of Electronics, Peking University, Beijing 100871, China
| | - Xinxin Guo
- State Key Laboratory of Advanced Optical Communication System and Network, Department of Electronics, Peking University, Beijing 100871, China
| | - Xuzong Chen
- State Key Laboratory of Advanced Optical Communication System and Network, Department of Electronics, Peking University, Beijing 100871, China
| | - Xiaoji Zhou
- State Key Laboratory of Advanced Optical Communication System and Network, Department of Electronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, Department of Physics, Fudan University, Shanghai 200438, China
- Shanghai Qizhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
| |
Collapse
|
|
3
|
Lee K, Utama MIB, Kahn S, Samudrala A, Leconte N, Yang B, Wang S, Watanabe K, Taniguchi T, Altoé MVP, Zhang G, Weber-Bargioni A, Crommie M, Ashby PD, Jung J, Wang F, Zettl A. Ultrahigh-resolution scanning microwave impedance microscopy of moiré lattices and superstructures. SCIENCE ADVANCES 2020; 6:eabd1919. [PMID: 33298449 PMCID: PMC7725474 DOI: 10.1126/sciadv.abd1919] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 10/22/2020] [Indexed: 05/31/2023]
Abstract
Two-dimensional heterostructures composed of layers with slightly different lattice vectors exhibit new periodic structure known as moiré lattices, which, in turn, can support novel correlated and topological phenomena. Moreover, moiré superstructures can emerge from multiple misaligned moiré lattices or inhomogeneous strain distributions, offering additional degrees of freedom in tailoring electronic structure. High-resolution imaging of the moiré lattices and superstructures is critical for understanding the emerging physics. Here, we report the imaging of moiré lattices and superstructures in graphene-based samples under ambient conditions using an ultrahigh-resolution implementation of scanning microwave impedance microscopy. Although the probe tip has a gross radius of ~100 nm, spatial resolution better than 5 nm is achieved, which allows direct visualization of the structural details in moiré lattices and the composite super-moiré. We also demonstrate artificial synthesis of novel superstructures, including the Kagome moiré arising from the interplay between different layers.
Collapse
Affiliation(s)
- Kyunghoon Lee
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - M Iqbal Bakti Utama
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
| | - Salman Kahn
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | | | - Nicolas Leconte
- Department of Physics, University of Seoul, Seoul, South Korea
| | - Birui Yang
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
| | - Shuopei Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Quantum Matter, Beijing, China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - M Virginia P Altoé
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Guangyu Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Quantum Matter, Beijing, China
| | | | - Michael Crommie
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Paul D Ashby
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Jeil Jung
- Department of Physics, University of Seoul, Seoul, South Korea
| | - Feng Wang
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Alex Zettl
- Department of Physics, University of California at Berkeley, Berkeley, CA 94720, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| |
Collapse
|
|
4
|
Leung TH, Schwarz MN, Chang SW, Brown CD, Unnikrishnan G, Stamper-Kurn D. Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice. PHYSICAL REVIEW LETTERS 2020; 125:133001. [PMID: 33034463 DOI: 10.1103/physrevlett.125.133001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 08/28/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
Geometric frustration of particle motion in a kagome lattice causes the single-particle band structure to have a flat s-orbital band. We probe this band structure by placing a Bose-Einstein condensate into excited Bloch states of an optical kagome lattice, and then measuring the group velocity through the atomic momentum distribution. We find that interactions renormalize the band structure, greatly increasing the dispersion of the third band, which is nearly non-dispersing the single-particle treatment. Calculations based on the lattice Gross-Pitaevskii equation indicate that band structure renormalization is caused by the distortion of the overall lattice potential away from the kagome geometry by interactions.
Collapse
Affiliation(s)
- Tsz-Him Leung
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Malte N Schwarz
- Department of Physics, University of California, Berkeley, California 94720, USA
- Fakultät für Physik und Astronomie, Universität Würzburg, 97074 Würzburg, Germany
| | - Shao-Wen Chang
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Charles D Brown
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Govind Unnikrishnan
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Dan Stamper-Kurn
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| |
Collapse
|