Zeng, Y. & MacDonald, A. H. Electrically controlled two-dimensional electron-hole fluids. Phys. Rev. B 102, 085154 (2020).

CAS 

Google Scholar
 

Wu, F.-C., Xue, F. & MacDonald, A. H. Theory of two-dimensional spatially indirect equilibrium exciton condensates. Phys. Rev. B 92, 165121 (2015).


Google Scholar
 

Qi, R. et al. Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures. Nat. Commun. 14, 8264 (2023).

PubMed 
PubMed Central 
CAS 

Google Scholar
 

Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021).

PubMed 
CAS 

Google Scholar
 

De Palo, S., Rapisarda, F. & Senatore, G. Excitonic condensation in a symmetric electron-hole bilayer. Phys. Rev. Lett. 88, 206401 (2002).

PubMed 

Google Scholar
 

Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).

PubMed 
CAS 

Google Scholar
 

Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).

CAS 

Google Scholar
 

Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

PubMed 
CAS 

Google Scholar
 

Zhu, X., Littlewood, P. B., Hybertsen, M. S. & Rice, T. M. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633–1636 (1995).

PubMed 
CAS 

Google Scholar
 

Maezono, R., López Ríos, P., Ogawa, T. & Needs, R. J. Excitons and biexcitons in symmetric electron-hole bilayers. Phys. Rev. Lett. 110, 216407 (2013).

PubMed 

Google Scholar
 

Dai, D. D. & Fu, L. Strong-coupling phases of trions and excitons in electron-hole bilayers at commensurate densities. Phys. Rev. Lett. 132, 196202 (2024).

PubMed 
CAS 

Google Scholar
 

Qi, R. et al. Electrically controlled interlayer trion fluid in electron-hole bilayers. Preprint at https://arxiv.org/abs/2312.03251 (2023).

Nguyen, P. X. et al. A degenerate trion liquid in atomic double layers. Preprint at https://arxiv.org/abs/2312.12571 (2023).

Nguyen, P. X. et al. Perfect Coulomb drag in a dipolar excitonic insulator. Science 388, 274–278 (2025).

PubMed 
CAS 

Google Scholar
 

Qi, R. et al. Perfect Coulomb drag and exciton transport in an excitonic insulator. Science 388, 278–283 (2025).

PubMed 
CAS 

Google Scholar
 

Liu, X. et al. Crossover between strongly coupled and weakly coupled exciton superfluids. Science 375, 205–209 (2022).

PubMed 
CAS 

Google Scholar
 

Eisenstein, J. P. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159–181 (2014).

CAS 

Google Scholar
 

Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).

CAS 

Google Scholar
 

Croxall, A. F. et al. Anomalous Coulomb drag in electron-hole bilayers. Phys. Rev. Lett. 101, 246801 (2008).

PubMed 
CAS 

Google Scholar
 

Du, L. et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat. Commun. 8, 1971 (2017).

PubMed 
PubMed Central 

Google Scholar
 

Wang, R., Sedrakyan, T. A., Wang, B., Du, L. & Du, R.-R. Excitonic topological order in imbalanced electron–hole bilayers. Nature 619, 57–62 (2023).

PubMed 
CAS 

Google Scholar
 

Han, Z., Li, T., Zhang, L., Sullivan, G. & Du, R.-R. Anomalous conductance oscillations in the hybridization gap of InAs/GaSb quantum wells. Phys. Rev. Lett. 123, 126803 (2019).

PubMed 
CAS 

Google Scholar
 

Xiao, D., Liu, C.-X., Samarth, N. & Hu, L.-H. Anomalous quantum oscillations of interacting electron-hole gases in inverted type-II InAs/GaSb quantum wells. Phys. Rev. Lett. 122, 186802 (2019).

PubMed 
CAS 

Google Scholar
 

Shao, Y. & Dai, X. Quantum oscillations in an excitonic insulating electron-hole bilayer. Phys. Rev. B 109, 155107 (2024).

CAS 

Google Scholar
 

Zou, B., Zeng, Y., MacDonald, A. H. & Strashko, A. Electrical control of two-dimensional electron-hole fluids in the quantum Hall regime. Phys. Rev. B 109, 085416 (2024).

CAS 

Google Scholar
 

Li, L., Sun, K., Kurdak, C. & Allen, J. W. Emergent mystery in the Kondo insulator samarium hexaboride. Nat. Rev. Phys. 2, 463–479 (2020).

CAS 

Google Scholar
 

Pirie, H. et al. Visualizing the atomic-scale origin of metallic behavior in Kondo insulators. Science 379, 1214–1218 (2023).

PubMed 
CAS 

Google Scholar
 

Shen, H. & Fu, L. Quantum oscillation from in-gap states and a non-Hermitian Landau level problem. Phys. Rev. Lett. 121, 026403 (2018).

PubMed 
CAS 

Google Scholar
 

Zhang, L., Song, X.-Y. & Wang, F. Quantum oscillation in narrow-gap topological insulators. Phys. Rev. Lett. 116, 046404 (2016).

PubMed 

Google Scholar
 

Knolle, J. & Cooper, N. R. Quantum oscillations without a Fermi surface and the anomalous de Haas-van Alphen effect. Phys. Rev. Lett. 115, 146401 (2015).

PubMed 

Google Scholar
 

Knolle, J. & Cooper, N. R. Excitons in topological Kondo insulators: theory of thermodynamic and transport anomalies in SmB6. Phys. Rev. Lett. 118, 096604 (2017).

PubMed 

Google Scholar
 

Erten, O., Chang, P.-Y., Coleman, P. & Tsvelik, A. M. Skyrme insulators: insulators at the brink of superconductivity. Phys. Rev. Lett. 119, 057603 (2017).

PubMed 

Google Scholar
 

Lee, P. A. Quantum oscillations in the activated conductivity in excitonic insulators: possible application to monolayer WTe2. Phys. Rev. B 103, L041101 (2021).

CAS 

Google Scholar
 

He, W.-Y. & Lee, P. A. Quantum oscillation of thermally activated conductivity in a monolayer WTe2-like excitonic insulator. Phys. Rev. B 104, L041110 (2021).

CAS 

Google Scholar
 

Chowdhury, D., Sodemann, I. & Senthil, T. Mixed-valence insulators with neutral Fermi surfaces. Nat. Commun. 9, 1766 (2018).

PubMed 
PubMed Central 

Google Scholar
 

Sodemann, I., Chowdhury, D. & Senthil, T. Quantum oscillations in insulators with neutral Fermi surfaces. Phys. Rev. B 97, 045152 (2018).

CAS 

Google Scholar
 

Li, G. et al. Two-dimensional Fermi surfaces in Kondo insulator SmB6. Science 346, 1208–1212 (2014).

PubMed 
CAS 

Google Scholar
 

Tan, B. S. et al. Unconventional Fermi surface in an insulating state. Science 349, 287–290 (2015).

PubMed 
CAS 

Google Scholar
 

Wang, P. et al. Landau quantization and highly mobile fermions in an insulator. Nature 589, 225–229 (2021).

PubMed 
CAS 

Google Scholar
 

Xiang, Z. et al. Quantum oscillations of electrical resistivity in an insulator. Science 362, 65–69 (2018).

PubMed 
CAS 

Google Scholar
 

Rikken, G. L. J. A. et al. Two-terminal resistance of quantum Hall devices. Phys. Rev. B 37, 6181–6186 (1988).

CAS 

Google Scholar
 

Moon, K. et al. Spontaneous interlayer coherence in double-layer quantum Hall systems: charged vortices and Kosterlitz-Thouless phase transitions. Phys. Rev. B 51, 5138–5170 (1995).

CAS 

Google Scholar
 

Jungwirth, T., Shukla, S. P., Smrčka, L., Shayegan, M. & MacDonald, A. H. Magnetic anisotropy in quantum Hall ferromagnets. Phys. Rev. Lett. 81, 2328–2331 (1998).

CAS 

Google Scholar
 

Shi, Q. et al. Odd- and even-denominator fractional quantum Hall states in monolayer WSe2. Nat. Nanotechnol. 15, 569–573 (2020).

PubMed 
CAS 

Google Scholar
 

Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97, 201407 (2018).

CAS 

Google Scholar
 

Fenton, E. W. Excitonic insulator in a magnetic field. Phys. Rev. 170, 816–821 (1968).


Google Scholar
 

Shoenberg D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 2009).

Zhu, J., Li, T., Young, A. F., Shan, J. & Mak, K. F. Quantum oscillations in two-dimensional insulators induced by graphite gates. Phys. Rev. Lett. 127, 247702 (2021).

PubMed 
CAS 

Google Scholar
 

Zou, B. & MacDonald, A. H. Vortex lattice states of bilayer electron-hole fluids in quantizing magnetic fields. Preprint at https://arxiv.org/abs/2411.08810 (2024).

Li, H. et al. Electrode-free anodic oxidation nanolithography of low-dimensional materials. Nano Lett. 18, 8011–8015 (2018).

PubMed 
CAS 

Google Scholar