Orbital magnetization of Floquet topological systems
Abstract
A general expression for the orbital magnetization of a Floquet system is derived. The expression holds for a clean system, and is valid for any driving protocol, and arbitrary occupation of the bands. The orbital magnetization is shown to be large not only for Chern insulators, but also for anomalous phases where the Chern number does not fully account for the topology. In addition, the orbital magnetization is shown to take significant values both for a thermal equilibrium occupation of the Floquet bands, and for occupations determined by a quantum quench from an initial state with zero orbital magnetization. For the latter case, the orbital magnetization is shown to be highly sensitive to van Hove singularities of the Floquet bands.
- Authors:
-
- Aalto Univ., Otaniemi (Finland)
- RWTH Aachen Univ. (Germany); Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany)
- New York Univ. (NYU), NY (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- New York Univ. (NYU), NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1869395
- Grant/Contract Number:
- SC0010821
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 19; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Chern insulators; Magnetization dynamics
Citation Formats
Topp, Gabriel E., Törmä, Päivi, Kennes, Dante M., and Mitra, Aditi. Orbital magnetization of Floquet topological systems. United States: N. p., 2022.
Web. doi:10.1103/physrevb.105.195426.
Topp, Gabriel E., Törmä, Päivi, Kennes, Dante M., & Mitra, Aditi. Orbital magnetization of Floquet topological systems. United States. https://doi.org/10.1103/physrevb.105.195426
Topp, Gabriel E., Törmä, Päivi, Kennes, Dante M., and Mitra, Aditi. Mon .
"Orbital magnetization of Floquet topological systems". United States. https://doi.org/10.1103/physrevb.105.195426. https://www.osti.gov/servlets/purl/1869395.
@article{osti_1869395,
title = {Orbital magnetization of Floquet topological systems},
author = {Topp, Gabriel E. and Törmä, Päivi and Kennes, Dante M. and Mitra, Aditi},
abstractNote = {A general expression for the orbital magnetization of a Floquet system is derived. The expression holds for a clean system, and is valid for any driving protocol, and arbitrary occupation of the bands. The orbital magnetization is shown to be large not only for Chern insulators, but also for anomalous phases where the Chern number does not fully account for the topology. In addition, the orbital magnetization is shown to take significant values both for a thermal equilibrium occupation of the Floquet bands, and for occupations determined by a quantum quench from an initial state with zero orbital magnetization. For the latter case, the orbital magnetization is shown to be highly sensitive to van Hove singularities of the Floquet bands.},
doi = {10.1103/physrevb.105.195426},
journal = {Physical Review. B},
number = 19,
volume = 105,
place = {United States},
year = {Mon May 23 00:00:00 EDT 2022},
month = {Mon May 23 00:00:00 EDT 2022}
}
Works referenced in this record:
Critical properties of the Floquet time crystal within the Gaussian approximation
journal, January 2021
- Natsheh, Muath; Gambassi, Andrea; Mitra, Aditi
- Physical Review B, Vol. 103, Issue 1
Colloquium: Atomic quantum gases in periodically driven optical lattices
journal, March 2017
- Eckardt, André
- Reviews of Modern Physics, Vol. 89, Issue 1
Topological characterization of periodically driven quantum systems
journal, December 2010
- Kitagawa, Takuya; Berg, Erez; Rudner, Mark
- Physical Review B, Vol. 82, Issue 23
Low-frequency and Moiré–Floquet engineering: A review
journal, March 2021
- Rodriguez-Vega, Martin; Vogl, Michael; Fiete, Gregory A.
- Annals of Physics
Floquet topological phases protected by time glide symmetry
journal, May 2017
- Morimoto, Takahiro; Po, Hoi Chun; Vishwanath, Ashvin
- Physical Review B, Vol. 95, Issue 19
Effective Theory of Floquet Topological Transitions
journal, December 2014
- Kundu, Arijit; Fertig, H. A.; Seradjeh, Babak
- Physical Review Letters, Vol. 113, Issue 23
Topological Floquet engineering of twisted bilayer graphene
journal, September 2019
- Topp, Gabriel E.; Jotzu, Gregor; McIver, James W.
- Physical Review Research, Vol. 1, Issue 2
Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires
journal, June 2011
- Jiang, Liang; Kitagawa, Takuya; Alicea, Jason
- Physical Review Letters, Vol. 106, Issue 22
Emergence of orbital angular moment at van Hove singularity in graphene/h-BN moiré superlattice
journal, October 2020
- Moriya, Rai; Kinoshita, Kei; Crosse, J. A.
- Nature Communications, Vol. 11, Issue 1
Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
journal, May 1965
- Shirley, Jon H.
- Physical Review, Vol. 138, Issue 4B
Floquet topological systems in the vicinity of band crossings: Reservoir-induced coherence and steady-state entropy production
journal, June 2016
- Dehghani, Hossein; Mitra, Aditi
- Physical Review B, Vol. 93, Issue 24
Moiré heterostructures as a condensed-matter quantum simulator
journal, February 2021
- Kennes, Dante M.; Claassen, Martin; Xian, Lede
- Nature Physics, Vol. 17, Issue 2
Floquet Time Crystals
journal, August 2016
- Else, Dominic V.; Bauer, Bela; Nayak, Chetan
- Physical Review Letters, Vol. 117, Issue 9
Prethermal Phases of Matter Protected by Time-Translation Symmetry
journal, March 2017
- Else, Dominic V.; Bauer, Bela; Nayak, Chetan
- Physical Review X, Vol. 7, Issue 1
Chiral Floquet Phases of Many-Body Localized Bosons
journal, December 2016
- Po, Hoi Chun; Fidkowski, Lukasz; Morimoto, Takahiro
- Physical Review X, Vol. 6, Issue 4
Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems
journal, June 2010
- Inoue, Jun-ichi; Tanaka, Akihiro
- Physical Review Letters, Vol. 105, Issue 1
Colloquium: Nonthermal pathways to ultrafast control in quantum materials
journal, October 2021
- de la Torre, Alberto; Kennes, Dante M.; Claassen, Martin
- Reviews of Modern Physics, Vol. 93, Issue 4
Floquet topological phases with symmetry in all dimensions
journal, May 2017
- Roy, Rahul; Harper, Fenner
- Physical Review B, Vol. 95, Issue 19
Out-of-equilibrium electrons and the Hall conductance of a Floquet topological insulator
journal, April 2015
- Dehghani, Hossein; Oka, Takashi; Mitra, Aditi
- Physical Review B, Vol. 91, Issue 15
Floquet Engineering of Quantum Materials
journal, March 2019
- Oka, Takashi; Kitamura, Sota
- Annual Review of Condensed Matter Physics, Vol. 10, Issue 1
Effective response theory for Floquet topological systems
journal, February 2021
- Glorioso, Paolo; Gromov, Andrey; Ryu, Shinsei
- Physical Review Research, Vol. 3, Issue 1
Interacting invariants for Floquet phases of fermions in two dimensions
journal, February 2019
- Fidkowski, Lukasz; Po, Hoi Chun; Potter, Andrew C.
- Physical Review B, Vol. 99, Issue 8
Orbital Magnetization in Periodic Insulators
journal, September 2005
- Thonhauser, T.; Ceresoli, Davide; Vanderbilt, David
- Physical Review Letters, Vol. 95, Issue 13
The electronic properties of graphene
journal, January 2009
- Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.
- Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162
Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene
journal, April 2020
- He, Wen-Yu; Goldhaber-Gordon, David; Law, K. T.
- Nature Communications, Vol. 11, Issue 1
The marvels of moiré materials
journal, March 2021
- Andrei, Eva Y.; Efetov, Dmitri K.; Jarillo-Herrero, Pablo
- Nature Reviews Materials, Vol. 6, Issue 3
Classification of topological phases in periodically driven interacting systems
journal, May 2016
- Else, Dominic V.; Nayak, Chetan
- Physical Review B, Vol. 93, Issue 20
Quantized transport and steady states of Floquet topological insulators
journal, June 2018
- Esin, Iliya; Rudner, Mark S.; Refael, Gil
- Physical Review B, Vol. 97, Issue 24
Discrete Time Crystals: Rigidity, Criticality, and Realizations
journal, January 2017
- Yao, N. Y.; Potter, A. C.; Potirniche, I. -D.
- Physical Review Letters, Vol. 118, Issue 3
Dissipative Floquet topological systems
journal, November 2014
- Dehghani, Hossein; Oka, Takashi; Mitra, Aditi
- Physical Review B, Vol. 90, Issue 19
Topological Index for Periodically Driven Time-Reversal Invariant 2D Systems
journal, March 2015
- Carpentier, David; Delplace, Pierre; Fruchart, Michel
- Physical Review Letters, Vol. 114, Issue 10
Quantum Theory of Orbital Magnetization and Its Generalization to Interacting Systems
journal, November 2007
- Shi, Junren; Vignale, G.; Xiao, Di
- Physical Review Letters, Vol. 99, Issue 19
Abelian Floquet symmetry-protected topological phases in one dimension
journal, September 2016
- Roy, Rahul; Harper, Fenner
- Physical Review B, Vol. 94, Issue 12
Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems
journal, July 2013
- Rudner, Mark S.; Lindner, Netanel H.; Berg, Erez
- Physical Review X, Vol. 3, Issue 3
Entanglement properties of Floquet-Chern insulators
journal, November 2016
- Yates, Daniel J.; Lemonik, Yonah; Mitra, Aditi
- Physical Review B, Vol. 94, Issue 20
Classification of Matrix-Product Unitaries with Symmetries
journal, March 2020
- Gong, Zongping; Sünderhauf, Christoph; Schuch, Norbert
- Physical Review Letters, Vol. 124, Issue 10
Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
journal, July 2006
- Ceresoli, Davide; Thonhauser, T.; Vanderbilt, David
- Physical Review B, Vol. 74, Issue 2
Chiral one-dimensional Floquet topological insulators beyond the rotating wave approximation
journal, July 2019
- Kennes, Dante M.; Müller, Niclas; Pletyukhov, Mikhail
- Physical Review B, Vol. 100, Issue 4
Photovoltaic Hall effect in graphene
journal, February 2009
- Oka, Takashi; Aoki, Hideo
- Physical Review B, Vol. 79, Issue 8
Optical Hall conductivity of a Floquet topological insulator
journal, October 2015
- Dehghani, Hossein; Mitra, Aditi
- Physical Review B, Vol. 92, Issue 16
Band structure engineering and non-equilibrium dynamics in Floquet topological insulators
journal, May 2020
- Rudner, Mark S.; Lindner, Netanel H.
- Nature Reviews Physics, Vol. 2, Issue 5
Periodic table for Floquet topological insulators
journal, October 2017
- Roy, Rahul; Harper, Fenner
- Physical Review B, Vol. 96, Issue 15
Quantized Magnetization Density in Periodically Driven Systems
journal, October 2017
- Nathan, Frederik; Rudner, Mark S.; Lindner, Netanel H.
- Physical Review Letters, Vol. 119, Issue 18
Absolute stability and spatiotemporal long-range order in Floquet systems
journal, August 2016
- von Keyserlingk, C. W.; Khemani, Vedika; Sondhi, S. L.
- Physical Review B, Vol. 94, Issue 8
Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field
journal, June 1973
- Sambe, Hideo
- Physical Review A, Vol. 7, Issue 6
Phase Structure of Driven Quantum Systems
journal, June 2016
- Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich
- Physical Review Letters, Vol. 116, Issue 25
Experimental realization of the topological Haldane model with ultracold fermions
journal, November 2014
- Jotzu, Gregor; Messer, Michael; Desbuquois, Rémi
- Nature, Vol. 515, Issue 7526
Critical properties of the prethermal Floquet time crystal
journal, June 2021
- Natsheh, Muath; Gambassi, Andrea; Mitra, Aditi
- Physical Review B, Vol. 103, Issue 22
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 18
Occupation probabilities and current densities of bulk and edge states of a Floquet topological insulator
journal, May 2016
- Dehghani, Hossein; Mitra, Aditi
- Physical Review B, Vol. 93, Issue 20
Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump
journal, May 2016
- Titum, Paraj; Berg, Erez; Rudner, Mark S.
- Physical Review X, Vol. 6, Issue 2
Topology and Broken Symmetry in Floquet Systems
journal, March 2020
- Harper, Fenner; Roy, Rahul; Rudner, Mark S.
- Annual Review of Condensed Matter Physics, Vol. 11, Issue 1
Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators
journal, January 2021
- Nathan, Frederik; Abanin, Dmitry; Lindner, Netanel
- SciPost Physics, Vol. 10, Issue 6
Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels
journal, December 2011
- Kitagawa, Takuya; Oka, Takashi; Brataas, Arne
- Physical Review B, Vol. 84, Issue 23
Classification of Interacting Topological Floquet Phases in One Dimension
journal, October 2016
- Potter, Andrew C.; Morimoto, Takahiro; Vishwanath, Ashvin
- Physical Review X, Vol. 6, Issue 4
Floquet Majorana fermions and parafermions in driven Rashba nanowires
journal, April 2017
- Thakurathi, Manisha; Loss, Daniel; Klinovaja, Jelena
- Physical Review B, Vol. 95, Issue 15
Interaction-stabilized steady states in the driven model
journal, May 2016
- Chandran, Anushya; Sondhi, S. L.
- Physical Review B, Vol. 93, Issue 17
Dynamically enriched topological orders in driven two-dimensional systems
journal, April 2017
- Potter, Andrew C.; Morimoto, Takahiro
- Physical Review B, Vol. 95, Issue 15
Floquet quantum criticality
journal, August 2018
- Berdanier, William; Kolodrubetz, Michael; Parameswaran, S. A.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 38
Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases
journal, June 2016
- von Keyserlingk, C. W.; Sondhi, S. L.
- Physical Review B, Vol. 93, Issue 24
Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases
journal, June 2016
- von Keyserlingk, C. W.; Sondhi, S. L.
- Physical Review B, Vol. 93, Issue 24