Fetching the paper…

Reading the bibliography…

2021

Bound on resistivity in flat-band materials due to the quantum metric

Mitscherling, Johannes, Holder, Tobias

Original
PDF
Post on X

Understand

The quantum metric is a central quantity of band theory but has so far not been related to many response coefficients due to its nonclassical origin.

However, within a newly developed Kubo formalism for fast relaxation, the decomposition of the dc electrical conductivity into both classical (intraband) and quantum (interband) contributions recently revealed that the interband part is proportional to the quantum metric.
Here, we show that interband effects due to the quantum metric can be significantly enhanced and even dominate the conductivity for semimetals at charge neutrality and for systems with highly quenched bandwidth.
This is true in particular for topological flat-band materials of nonzero Chern number, where for intermediate relaxation rates an upper bound exists for the resistivity due to the common geometrical origin of quantum metric and Berry curvature.

Bound on resistivity in flat-band materials due to the quantum metric · Around

Built on

A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. A. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science 365
Original
1901
Earlier work this paper cites.
Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigorda, K. Watanabe, T. Taniguchi, T. Senthil, and P. Jarillo-Herrero, Strange Metal in Magic-Angle Graphene with near Planckian Dissipation, Phys. Rev. Lett. 124
Original
1901
Earlier work this paper cites.
X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A. H. MacDonald, and D. K. Efetov, Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature 574
Original
1903
Earlier work this paper cites.
G. Chen, A. L. Sharpe, E. J. Fox, Y.-H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, Z. Shi, T. Senthil, D. Goldhaber-Gordon, Y. Zhang, and F. Wang, Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice, Nature 579
Original
1905
Earlier work this paper cites.
A. A. Patel and S. Sachdev, Theory of a Planckian Metal, Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
X. Hu, T. Hyart, D. I. Pikulin, and E. Rossi, Geometric and Conventional Contribution to the Superfluid Weight in Twisted Bilayer Graphene, Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
A. Julku, T. J. Peltonen, L. Liang, T. T. Heikkilä, and P. Törmä, Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene, Phys. Rev. B 101
Original
1906
Earlier work this paper cites.
L. Wang, E.-M. Shih, A. Ghiotto, L. Xian, D. A. Rhodes, C. Tan, M. Claassen, D. M. Kennes, Y. Bai, B. Kim, K. Watanabe, T. Taniguchi, X. Zhu, J. Hone, A. Rubio, A. Pasupathy, and C. R. Dean, Correlated electronic phases in twisted bilayer transition metal dichalcogenides, Nat. Mater. 19
Original
1910
Earlier work this paper cites.
Z. Zhang, Y. Wang, K. Watanabe, T. Taniguchi, K. Ueno, E. Tutuc, and B. J. LeRoy, Flat bands in twisted bilayer transition metal dichalcogenides, Nat. Phys. 16
Original
1910
Earlier work this paper cites.
T. Holder, D. Kaplan, and B. Yan, Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion, Phys. Rev. Research 2
Original
1911
Earlier work this paper cites.
U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, A. Stern, E. Berg, P. Jarillo-Herrero, and S. Ilani, Cascade of phase transitions and Dirac revivals in magic-angle graphene, Nature 582
Original
1912
Earlier work this paper cites.
J. S. Hofmann, E. Berg, and D. Chowdhury, Superconductivity, pseudogap, and phase separation in topological flat bands, Phys. Rev. B 102
Original
1912
Earlier work this paper cites.
N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976)
1976
Earlier work this paper cites.
D. R. Nelson and J. M. Kosterlitz, Universal Jump in the Superfluid Density of Two-Dimensional Superfluids, Phys. Rev. Lett. 39
1977
Earlier work this paper cites.
J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76
1980
Earlier work this paper cites.
N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56
1997
Earlier work this paper cites.
P. M. Bonetti, J. Mitscherling, D. Vilardi, and W. Metzner, Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model, Phys. Rev. B 101
Original
2002
Earlier work this paper cites.
D. Kaplan, T. Holder, and B. Yan, Nonvanishing Subgap Photocurrent as a Probe of Lifetime Effects, Phys. Rev. Lett. 125
Original
2003
Earlier work this paper cites.
Z. Wang, G. Chaudhary, Q. Chen, and K. Levin, Quantum geometric contributions to the BKT transition: Beyond mean field theory, Phys. Rev. B 102
Original
2007
Earlier work this paper cites.

Similar

N. A. Sinitsyn, A. H. MacDonald, T. Jungwirth, V. K. Dugaev, and J. Sinova, Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach, Phys. Rev. B 75
2007
Cited alongside, same era.
J. Mitscherling, Longitudinal and anomalous Hall conductivity of a general two-band model, Phys. Rev. B 102
Original
2008
Cited alongside, same era.
M. Koshino and E. McCann, Trigonal warping and berry’s phase n π n\pi in ABC-stacked multilayer graphene, Phys. Rev. B 80
2009
Cited alongside, same era.
A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81
Original
2009
Cited alongside, same era.
F. Zhang, B. Sahu, H. Min, and A. H. MacDonald, Band structure of ABC-stacked graphene trilayers, Phys. Rev. B 82

Then

S. A. Hartnoll, Theory of universal incoherent metallic transport, Nat. Phys. 11
Original
2015
Later among the works it cites.
L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. Törmä, Band geometry, Berry curvature, and superfluid weight, Phys. Rev. B 95
Original
2017
Later among the works it cites.
M. Kolodrubetz, D. Sels, P. Mehta, and A. Polkovnikov, Geometry and non-adiabatic response in quantum and classical systems, Phys. Rep. 697
Original
2017
Later among the works it cites.
A. Lucas and S. A. Hartnoll, Resistivity bound for hydrodynamic bad metals, PNAS 114
Original
2017
Later among the works it cites.
T. Hartman, S. A. Hartnoll, and R. Mahajan, Upper Bound on Diffusivity, Phys. Rev. Lett. 119

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2010

Cited alongside, same era.

M. Koshino, Interlayer screening effect in graphene multilayers with ABA and ABC stacking, Phys. Rev. B 81

2010

Cited alongside, same era.

K. F. Mak, J. Shan, and T. F. Heinz, Electronic structure of few-layer graphene: Experimental demonstration of strong dependence on stacking sequence, Phys. Rev. Lett. 104

2010

Cited alongside, same era.

S. Matsuura and S. Ryu, Momentum space metric, nonlocal operator, and topological insulators, Phys. Rev. B 82

2010

Cited alongside, same era.

N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82

2010

Cited alongside, same era.

R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, PNAS 108

Original

2011

Cited alongside, same era.

R. Resta, The insulating state of matter: a geometrical theory, Euro. Phys. J. B 79

2011

Cited alongside, same era.

Z. Hao, A. M. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene, Science 371

2012

Cited alongside, same era.

2017

Later among the works it cites.

J. Mitscherling and W. Metzner, Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order, Phys. Rev. B 98

2018

Later among the works it cites.

M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363

2019

Later among the works it cites.

H. Polshyn, M. Yankowitz, S. Chen, Y. Zhang, K. Watanabe, T. Taniguchi, C. R. Dean, and A. F. Young, Large linear-in-temperature resistivity in twisted bilayer graphene, Nat. Phys. 15

2019

Later among the works it cites.

Y. Gao and D. Xiao, Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole, Phys. Rev. Lett. 122

2019

Later among the works it cites.

X. Liu, Z. Hao, E. Khalaf, J. Y. Lee, Y. Ronen, H. Yoo, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, et al. , Tunable spin-polarized correlated states in twisted double bilayer graphene, Nature 583

2020

Later among the works it cites.

J. Park, O. Golan, Y. Vinkler-Aviv, and A. Rosch, Thermal Hall response: violation of gravitational analogues and Einstein relations, arXiv , arXiv:2108.06162 (2021), arXiv:2108.06162 [cond-mat.mes-hall]

2021

Closest in time.

A. Ghiotto, E.-M. Shih, G. S. S. G. Pereira, D. A. Rhodes, B. Kim, J. Zang, A. J. Millis, K. Watanabe, T. Taniguchi, J. C. Hone, L. Wang, C. R. Dean, and A. N. Pasupathy, Quantum criticality in twisted transition metal dichalcogenides, Nature 597

2021

Closest in time.

J. Ahn, G.-Y. Guo, N. Nagaosa, and A. Vishwanath, Riemannian Geometry of Resonant Optical Responses, Nat. Phys. 10.1038/s41567-021-01465-z (2021), arXiv:2103.01241 [cond-mat.mes-hall]

2021

Closest in time.

T. Holder, D. Kaplan, R. Ilan, and B. Yan, Mixed axial-gravitational anomaly from emergent curved spacetime in nonlinear charge transport, arXiv , arXiv:2111.07780 (2021), arXiv:2111.07780 [cond-mat.mes-hall]

2021

Closest in time.

T. Holder, Electrons flow like falling cats: Deformations and emergent gravity in quantum transport, arXiv , arXiv:2111.07782 (2021), arXiv:2111.07782 [cond-mat.mes-hall]

2021

Closest in time.

T. Ozawa and B. Mera, Relations between topology and the quantum metric for Chern insulators, Phys. Rev. B 104

2021

Closest in time.

D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82

2021

Closest in time.

J. Herzog-Arbeitman, V. Peri, F. Schindler, S. D. Huber, and B. A. Bernevig, Superfluid weight bounds from symmetry and quantum geometry in flat bands, arXiv , arXiv:2110.14663 (2021), arXiv:2110.14663 [cond-mat.mes-hall]

2021

Closest in time.