Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Samajdar, Rhine; Scheurer, Mathias S.; Turkel, Simon; Rubio-Verdú, Carmen; Pasupathy, Abhay N.; Venderbos, Jörn F.; Fernandes, Rafael M.

doi:10.1088/2053-1583/abfcd6

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Journal Article · Mon May 24 00:00:00 EDT 2021 · 2D Materials

DOI:https://doi.org/10.1088/2053-1583/abfcd6· OSTI ID:1835812

^[1]; ^[2]; Turkel, Simon ^[3]; Rubio-Verdú, Carmen ^[3]; Pasupathy, Abhay N. ^[3]; Venderbos, Jörn F. ^[4]; Fernandes, Rafael M. ^[5]

Harvard Univ., Cambridge, MA (United States); University of Minnesota
Univ. of Innsbruck (Austria)
Columbia Univ., New York, NY (United States)
Drexel Univ., Philadelphia, PA (United States)
Univ. of Minnesota, Minneapolis, MN (United States)

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data (arXiv:2009.11645) to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. Here, we compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0020045

OSTI ID:: 1835812

Journal Information:: 2D Materials, Journal Name: 2D Materials Journal Issue: 3 Vol. 8; ISSN 2053-1583

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Flat bands in twisted double bilayer graphene Chebrolu, Narasimha Raju; Chittari, Bheema Lingam; Jung, Jeil Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235417	journal	June 2019
Lattice Effects on Nematic Quantum Criticality in Metals Paul, I.; Garst, M. Physical Review Letters, Vol. 118, Issue 22 https://doi.org/10.1103/PhysRevLett.118.227601	journal	June 2017
Topological Superconductivity in Twisted Multilayer Graphene Xu, Cenke; Balents, Leon Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.087001	journal	August 2018
Chiral Spin Density Wave and d + i d Superconductivity in the Magic-Angle-Twisted Bilayer Graphene Liu, Cheng-Cheng; Zhang, Li-Da; Chen, Wei-Qiang Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.217001	journal	November 2018
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/PhysRevLett.121.257001	journal	December 2018
Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene González, J.; Stauber, T. Physical Review Letters, Vol. 122, Issue 2 https://doi.org/10.1103/PhysRevLett.122.026801	journal	January 2019
Origin of Magic Angles in Twisted Bilayer Graphene Tarnopolsky, Grigory; Kruchkov, Alex Jura; Vishwanath, Ashvin Physical Review Letters, Vol. 122, Issue 10 https://doi.org/10.1103/PhysRevLett.122.106405	journal	March 2019
Twisted Bilayer Graphene: A Phonon-Driven Superconductor Lian, Biao; Wang, Zhijun; Bernevig, B. Andrei Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.257002	journal	June 2019
Correlated Insulating States in Twisted Double Bilayer Graphene Burg, G. William; Zhu, Jihang; Taniguchi, Takashi Physical Review Letters, Vol. 123, Issue 19 https://doi.org/10.1103/PhysRevLett.123.197702	journal	November 2019
Geometric and Conventional Contribution to the Superfluid Weight in Twisted Bilayer Graphene Hu, Xiang; Hyart, Timo; Pikulin, Dmitry I. Physical Review Letters, Vol. 123, Issue 23 https://doi.org/10.1103/PhysRevLett.123.237002	journal	December 2019
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Evidence of Potts-Nematic Superfluidity in a Hexagonal s p 2 Optical Lattice Jin, Shengjie; Zhang, Wenjun; Guo, Xinxin Physical Review Letters, Vol. 126, Issue 3 https://doi.org/10.1103/PhysRevLett.126.035301	journal	January 2021
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Exact continuum model for low-energy electronic states of twisted bilayer graphene Carr, Stephen; Fang, Shiang; Zhu, Ziyan Physical Review Research, Vol. 1, Issue 1 https://doi.org/10.1103/PhysRevResearch.1.013001	journal	August 2019
Disorder in twisted bilayer graphene Wilson, Justin H.; Fu, Yixing; Das Sarma, S. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023325	journal	June 2020
Pairing in graphene-based moiré superlattices Scheurer, Mathias S.; Samajdar, Rhine Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033062	journal	July 2020
Structural relaxation and low-energy properties of twisted bilayer graphene Cantele, Giovanni; Alfè, Dario; Conte, Felice Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043127	journal	October 2020
Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality Liu, Shang; Khalaf, Eslam; Lee, Jong Yeon Physical Review Research, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevResearch.3.013033	journal	January 2021
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Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031089	journal	September 2018
Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene Isobe, Hiroki; Yuan, Noah F. Q.; Fu, Liang Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/PhysRevX.8.041041	journal	December 2018
Quantum Valley Hall Effect, Orbital Magnetism, and Anomalous Hall Effect in Twisted Multilayer Graphene Systems Liu, Jianpeng; Ma, Zhen; Gao, Jinhua Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031021	journal	August 2019
Bilayer Graphene’s Wicked, Twisted Road MacDonald, Allan H. Physics, Vol. 12 https://doi.org/10.1103/Physics.12.12	journal	May 2019
Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle Codecido, Emilio; Wang, Qiyue; Koester, Ryan Science Advances, Vol. 5, Issue 9 https://doi.org/10.1126/sciadv.aaw9770	journal	September 2019
Interaction-Driven Spectrum Reconstruction in Bilayer Graphene Mayorov, A. S.; Elias, D. C.; Mucha-Kruczynski, M. Science, Vol. 333, Issue 6044 https://doi.org/10.1126/science.1208683	journal	August 2011
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aav1910	journal	January 2019
Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene Hao, Zeyu; Zimmerman, A. M.; Ledwith, Patrick Science, Vol. 371, Issue 6534 https://doi.org/10.1126/science.abg0399	journal	February 2021
Intertwined Vestigial Order in Quantum Materials: Nematicity and Beyond Fernandes, Rafael M.; Orth, Peter P.; Schmalian, Jörg Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013200	journal	March 2019
Nematic Fermi Fluids in Condensed Matter Physics Fradkin, Eduardo; Kivelson, Steven A.; Lawler, Michael J. Annual Review of Condensed Matter Physics, Vol. 1, Issue 1 https://doi.org/10.1146/annurev-conmatphys-070909-103925	journal	August 2010

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