Research Highlights

My research spans a broad spectrum, from foundational topics like quantum information and entanglement to applied pursuits such as discovering new quantum materials and designing systems for topological quantum computing. Below, I outline four key research areas, with the full list of publications available at the bottom of the page.

External links:

https://pcts.princeton.edu/events/2024/new-twists-quantum-geometry

Entanglement and quantum geometry

My current research centers on the fascinating world of quantum geometry and how it shapes measurable physical properties. I explore deep connections between quantum entanglement and geometry, and how quantum Fisher information relies on quantum-geometric structures, and develop innovative ways to detect these hidden features through quantum transport experiments.

Research highlights:

Alexander Kruchkov and Shinsei Ryu, Entanglement entropy in lattice models with quantum metric, arXiv 2408.10314 (2024), under review in PRL

Alexander Kruchkov and Shinsei Ryu, Spectral sum rules reflect topological and quantum-geometric invariants (28 Dec 2023), submitted to PRX.

Alexander Kruchkov and Shinsei Ryu, Measure of an ultranarrow topological gap via quantum noise, Letter in PRB ,Phys. Rev. B 110, L041118, (2024).

A. Kruchkov, Quantum transport anomalies in dispersionless electronic bands, Letter in Physical Review B, 107, L241102 (2023).

Quantum matter with strong interactions

Certain strongly interacting phases of matter - such as SYK phase - can be understood from a gravity perspective. Can we prepare and measure this quantum phase in a direct experiment ?

Towards SYK experiment: Theory and modeling

M. Brzezinska, Y. Guan, O. V. Yazyev, S. Sachdev, A. Kruchkov, Engineering SYK interactions in disordered graphene flakes under realistic experimental conditions, Phys Rev Lett (2023).

A. Kruchkov, A. Patel, P. Kim, S. Sachdev, Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments, Phys. Rev. B 101, 205148 (2020).

(Editor's suggestion)

First experiment:

Laurel E. Anderson, Antti Laitinen, Andrew Zimmerman, Thomas Werkmeister, Henry Shackleton, Alexander Kruchkov, Takashi Taniguchi, Kenji Watanabe, Subir Sachdev, and Philip Kim, Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations, Phys. Rev. Lett. 132, 246502, (2024)

(Editors' suggestion)

External links (outreach)

https://www.lindau-nobel.org/blog-designing-black-holes-in-the-lab/

Topological quantum materials

One of my favorite research areas is developing new quantum materials with nearly flat, topological electronic bands. This includes systems like twisted bilayer and multilayer graphene, which we had predicted with colleagues at Harvard. More recently, this field took an exciting turn with twisted transition metal dichalcogenides, which host even more robust flat bands—an essential ingredient for realizing exotic states of matter such as anyon-hosting Fractional Chern insulators.

External links:

https://www.quantamagazine.org/whats-the-magic-behind-graphenes-magic-angle-20190528/

https://physicsworld.com/a/researchers-solve-magic-angle-mystery/

https://www.quantamagazine.org/a-new-twist-reveals-superconductivitys-secrets-20210316/

https://news.mit.edu/2021/physicists-create-tunable-superconductivity-twisted-graphene-nanosandwich-0201

https://www.azonano.com/news.aspx?newsID=39391

Research highlights:

G. Tarnopolsky, A. J. Kruchkov, A. Vishwanath, Origin of Magic Angles in Twisted Bilayer Graphene, Physical Review Letters 122, 106405 (2019).

S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020).

F. Haddadi, Q. Wu, A. J. Kruchkov, O.V. Yazyev, Moiré Flat Bands in Twisted Double Bilayer Graphene, Nano Letters (2020).

Y. Guan, O.V. Yazyev, A. Kruchkov, Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes, Physical Review B (Letter), 106, L121115 (2022).

Y. Guan, O.V. Yazyev, A. Kruchkov, Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices, Nano Letters (2023)

Materials for topological quantum computing

This research explores a cutting-edge direction in quantum materials—topological phases that emerge without the need for external magnetic fields. These phases hold groundbreaking potential for advancing topological quantum computing by enabling the manipulation of anyons within flat electronic bands. The focus is on uncovering the entanglement and geometric properties of strongly correlated flat-band phases, with particular attention to the Fractional Chern Insulator (FCI) phase in new-generation quantum materials. A key objective is to identify conditions under which FCIs can host non-Abelian anyons—exotic particles crucial for fault-tolerant quantum computing. Recent experimental discoveries of FCIs (2023/2024) have sparked significant interest, but major questions remain open, particularly around the role of quantum geometry in stabilizing nontrivial FCIs with non-Abelian anyonic excitations. This research aims to bridge that gap by combining insights from topological materials, quantum geometry, and advanced numerical methods, helping guide experimental efforts in this rapidly evolving field.

We have secured grant funding "Quantum materials and entangled phases for topological quantum computing" with Titus Neupert and Shinsei Ryu, to start sometime in 2025.

External links:

https://data.snf.ch/grants/grant/225225

Publications

Publications summary: h-index 16 (Google Scholar), >2500 citations, 11 Letters: 4 Nano Letters, 4 Physical Review Letters, 3 Physical Review B Letters, several single-author papers, 4 published Letters as PI [Carr...Kruchkov, Nano Lett, 2020], [Guan, Yazyev, Kruchkov, Phys Rev B Lett 2022], [Guan, Yazyev, Kruchkov, Nano Lett 2023], [Brzezinska,Guan, Yazyev, Sachdev, Kruchkov, Phys Rev Lett 2023].

***NEW PAPER***Alexander Kruchkov and Shinsei Ryu, Entanglement entropy in lattice models with quantum metric, arXiv 2408.10314 (2024), under review in PRL (Jan 2025)

Selected papers:

[1] A. Kruchkov, Quantum transport anomalies in dispersionless electronic bands, Letter in Physical Review B (2023).

[2] A. Kruchkov, "Quantum geometry, flat Chern bands, and Wannier orbital quantization", Letter in Physical Review B 105, L241102 (2022).

[3] A. Kruchkov, A. Patel, P. Kim, S. Sachdev, Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments, Phys. Rev. B 101, 205148 (2020).

Outreach: Lindau Nobel Laureate Meeting release.

Related experiment: [2401.08050] Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

[4] G. Tarnopolsky, A. J. Kruchkov, A. Vishwanath, Origin of Magic Angles in Twisted Bilayer Graphene, Physical Review Letters 122, 106405 (2019).

Press release: Quanta Magazine (2019) and Quanta Magazine (2021).

[5] A. Kruchkov, One-dimensional Bose-Einstein condensation of photons in a microtube , Phys. Rev. A 93, 043817 (2016).Related experiment: Nature Physics 14, 1173 (2018).

[6] S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020).

Remark: The theoretical paper which lead to experiments Nature 590, 249 (2021) and Science 371, 6534, 1133 (2021). See also comment by Mike Zaletel.

Letters as PI:

[1] M. Brzezinska, Y. Guan, O. V. Yazyev, S. Sachdev, A. Kruchkov, Engineering SYK interactions in disordered graphene flakes under realistic experimental conditions, Phys Rev Lett (2023).

[2] Y. Guan, O.V. Yazyev, A. Kruchkov, Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices, Nano Letters (2023)

[3] Y. Guan, O.V. Yazyev, A. Kruchkov, Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes, Physical Review B (Letter), 106, L121115 (2022).

[4] S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020).

[5] I. Lukin, A. Sotnikov, A. Kruchkov, Unconventional superfluidity and quantum geometry of topological bosons (July 2023)

Full List

[29] Alexander Kruchkov and Shinsei Ryu, Entanglement entropy in lattice models with quantum metric, arXiv 2408.10314 (2024), under review in PRL

[28] Laurel E. Anderson, Antti Laitinen, Andrew Zimmerman, Thomas Werkmeister, Henry Shackleton, Alexander Kruchkov, Takashi Taniguchi, Kenji Watanabe, Subir Sachdev, and Philip Kim, Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations, Phys. Rev. Lett. 132, 246502, (2024)

[27] Alexander Kruchkov and Shinsei Ryu, Spectral sum rules reflect topological and quantum-geometric invariants (28 Dec 2023), submitted to PRX.

[26] Alexander Kruchkov and Shinsei Ryu, Measure of an ultranarrow topological gap via quantum noise, Letter in PRB ,Phys. Rev. B 110, L041118, (2024).

[25] Alexander Kruchkov, Anomalous conductivity of PT-symmetric Fermi liquids (27 May 2023), submitted, under reviw.

[24] I. Lukin, A. Sotnikov, A. Kruchkov, Unconventional superfluidity and quantum geometry of topological bosons (July 2023)

[23] A. Kruchkov, Quantum transport anomalies in dispersionless electronic bands, Letter in Physical Review B, 107, L241102 (2023).

[22] M. Brzezinska, Y. Guan, O. V. Yazyev, S. Sachdev, A. Kruchkov, Engineering SYK interactions in disordered graphene flakes under realistic experimental conditions, Physical Review Letters, 131, 036503 (2023).

[21] Y. Guan, O.V. Yazyev, A. Kruchkov, Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes, Physical Review B (Letter), 106, L121115 (2022).

[20] Y. Guan, O.V. Yazyev, A. Kruchkov, Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices, Nano Letters (2023)

[19] [Letter] A. Kruchkov, Origin of band flatness and constraints of higher Chern numbers (2021), published as Letter "Quantum geometry, flat Chern bands, and Wannier orbital quantization" in Physical Review B 105, L241102 (2022).

[18] [Editors' Suggestion] A. Kruchkov, A. Patel, P. Kim, S. Sachdev, Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments, Phys. Rev. B 101, 205148 (2020).

[17] S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020).

[16] F. Haddadi, Q. Wu, A. J. Kruchkov, O.V. Yazyev, Moiré Flat Bands in Twisted Double Bilayer Graphene, Nano Letters (2020).

[15] D.S. Borgnia, A.J. Kruchkov and R.-J. Slager, Non-Hermitian Boundary Modes, Phys. Rev. Lett. 124, 056802 (2020).

[14] [Editors' Suggestion] E. Khalaf, A. J. Kruchkov, G. Tarnopolsky, A. Vishwanath, Magic Angle Hierarchy in Twisted Graphene Multilayers, Phys. Rev. B 100, 085109 (2019).

[13] [Editors' Suggestion] G. Tarnopolsky, A. J. Kruchkov, A. Vishwanath, Origin of Magic Angles in Twisted Bilayer Graphene, Physical Review Letters 122, 106405 (2019)

[12] J. S. White, I. Živković, A. J. Kruchkov, M. Bartkowiak, A. Magrez, and H. M. Rønnow, Electric-Field-Driven Topological Phase Switching and Skyrmion-Lattice Metastability in Magnetoelectric Cu2OSeO3. Phys. Rev. Apllied, 10, 014021 (2018).

[11] A. J. Kruchkov, J. S. White, M. Bartkowiak, I. Zivcovic, A. Magrez, H.M. Rønnow, Direct control of the skyrmion phase stability by electric field in a magnetoelectric insulator. Scientific Reports, 8, 10466 (2018).

[10] P.Huang, M. Cantoni, A. Kruchkov, R. Jayaraman, A. Magrez, F. Carbone, H.M. Rønnow, In situ Electric Field Skyrmion Creation in Magnetoelectric Cu2OSeO3. Nano Letters, 2018, 18 (8), pp 5167–5171.

[9] A. J. Kruchkov and H.M. Rønnow, Skyrmion Lattices in Electric Fields. Preprint: arXiv 1702.08863. Submitted to Phys.Rev. B

[8] A. Kruchkov, One-dimensional Bose-Einstein condensation of photons in a microtube , Phys. Rev. A 93, 043817 (2016).

[7] [Editors' Suggestion] G. Berruto, I. Madan, Y. Murooka, E. Pomarico, G. M. Vanacore, J. Rajeswari, R. Lamb, P. Huang, A.J. Kruchkov, Y. Togawa, T. LaGrange, D. McGrouther, H. M. Rønnow and F. Carbone, Laser-induced Skyrmion writing and erasing in an ultrafast cryo-Lorentz transmission electron microscope, Phys. Rev. Lett., 120 (2018)

[6] I. Levatic, P. Popcevic, V. Surija, A. Kruchkov, H. Berger, A. Magrez, J. S. White, H. M. Rønnow & I. Zivkovic, Dramatic pressure-driven enhancement of bulk skyrmion stability, Scientific Reports 6, 21347 (2016).

[5] A. Kruchkov, Radiation spectrum of systems with condensed light. Preprint: arXiv:1404.2561

[4] A. Kruchkov, Bose-Einstein condensation of light in a cavity, Phys. Rev. A 89, 033862 (2014).

[3] A. Kruchkov, Y. Slyusarenko, Bose-Einstein condensation of photons in an ideal atomic gas, Phys. Rev. A 88, 013615 (2013).

[2] Y. Slyusarenko, A. Kruchkov, Mechanism of collisionless sound damping in dilute Bose gas with condensate , Cond.Mat.Phys., vol. 16, No. 2, 23004, (2013).

[1] A. Kruchkov, Reflections on the 66th Lindau Nobel Laureate Meeting, Condens. Matter, 1(1), 13 (2016) doi: 10.3390/condmat1010013.