Topological Quantum Matter in Motion

Topology, correlations, and transport in and out of equilibrium.

Topology provides a language for describing quantum matter through quantities that remain unchanged under smooth deformations. In physics these ideas often appear through geometric phases and Berry curvature. The Aharonov-Bohm effect and Pancharatnam phase already show that a quantum wavefunction can remember the geometry of a path. The quantum Hall effect made this principle spectacularly measurable: a geometric property of electronic bands appears as an exactly quantized Hall conductance. Its fractional version revealed that topology can survive, and become even richer, in interacting many-body systems.

Graphene and related two-dimensional materials made this physics especially concrete. They provide clean platforms for Dirac electrons, spin-orbit effects, valley degrees of freedom, superconducting proximity effects, and moiré superlattices. The same broad ideas now shape the study of quantum spin Hall systems, Weyl semimetals, topological superconductors, cold atoms, driven systems, and quantum devices. In many of these platforms, topology is not only a classification principle: it becomes visible through currents, conductance, Hall response, Josephson effects, spectroscopy, and non-local transport.

Mathematically, topology classifies objects by invariants. A cup and a doughnut, for example, are equivalent because both have one hole; a sphere is not. For a closed surface the integral of Gaussian curvature gives an integer set by the genus, $$\oint_{\rm surface} k_g \frac{dS}{2\pi} = 2-2g.$$ In a crystal, the Brillouin zone plays an analogous role. The Berry curvature of electronic bands can have an integer integral, and in two dimensions this integer controls the quantized Hall conductance, $$ \oint_{\rm Brillouin~zone} F_{xy} \frac{dk_x dk_y}{2\pi} = \sigma_{xy}. $$ Because the result is an integer, it is stable against many microscopic changes as long as the relevant gap does not close.

Quantum transport is one of the sharpest probes of this stability. Currents, conductance, noise, Josephson response, Hall signals, and non-local transport can reveal protected edge modes, Fermi arcs, Majorana bound states, Berry-curvature effects, and non-equilibrium topology.

In the quantum Hall effect, topology forces $\sigma_{xy}$ to be quantized, so $\rho_{xy}=1/\sigma_{xy}$ appears in inverse-integer steps. More generally, our work asks how topological and correlated quantum matter moves, responds, and reorganizes in equilibrium and out of equilibrium. This is the organizing theme of our group: quantum matter in motion.

Research.

Our research focuses on quantum phases, phase transitions, and transport in topological, correlated, and driven systems. We use analytical and numerical tools including scattering theory, Floquet theory, bosonization, mean-field methods, and equilibrium and non-equilibrium Green's functions. A common thread is the interplay of topology, interactions, superconductivity, disorder, and external driving, with an emphasis on experimentally visible signatures. The listed publications reflect this strategy: start from a concrete platform, identify the relevant topology or correlation effect, and connect it to a measurable response.

Twisted and moiré quantum matter

Twisted van der Waals heterostructures create moiré bands in which correlation, topology, and superconductivity are strongly tunable. Our recent work includes theoretical support for experiments on superconducting magic-angle twisted trilayer graphene with competing magnetic order and moiré inhomogeneities, Josephson junctions in minimally twisted bilayer graphene, skyrmion stripe phases in twisted double bilayer graphene, and umklapp-enhanced interlayer valley drag in moiré bilayers.

These projects connect microscopic band structure, symmetry breaking, and transport response in graphene-based moiré systems. We are also studying van der Waals Josephson junctions and twisted high-$T_c$ SQUIDs as probes of interfacial order in twisted cuprates, where superconducting devices become sensitive probes of emergent quantum order.

Floquet systems and non-equilibrium physics

Periodically driven quantum systems are a long-standing theme of our work. For a Hamiltonian with $H(t+T)=H(t)$, quasienergy replaces energy, and the drive supplies an additional compact direction for defining topological invariants, $$ \oint F(k_x,k_y,t) \frac{dk_xdk_ydt}{2\pi} = {\rm integer}. $$ This allows topological phases with no equilibrium counterpart and makes driven systems a controlled setting for engineering band topology.

We have developed effective theories of Floquet topological transitions, proposed Floquet-engineered valleytronics in Dirac systems, and studied disorder-enhanced transport in the anomalous Floquet-Anderson insulator. A second line concerns Floquet Majorana bound states, from early transport proposals in driven topological superconductors to recent Josephson-current signatures of unpaired Floquet Majoranas.

We also study the long-time steady states of driven systems, including time-resolved ARPES, optical transport in irradiated twisted bilayer graphene, and valley filtering in irradiated pristine graphene. These studies address how a periodically driven band structure becomes visible in spectroscopy, dc transport, and superconducting response, and how heating or bath coupling determines the observable steady state.

Correlated and interacting topological systems

Interactions reshape topological phases by producing collective modes, symmetry breaking, and new transport responses. Using bosonization, we have studied chiral Luttinger liquids in irradiated graphene, the two-channel Kondo effect in coupled helical liquids, and non-Hermitian Luttinger liquids after quantum quenches.

In frustrated magnets, we use Schwinger-boson mean-field theory and quantum kinetic approaches to study spin liquids, thermal Hall signatures, and nonlinear magnon transport. These works ask how Berry curvature and many-body correlations combine in magnetic and electronic systems, especially when the relevant carriers are magnons, helical edge modes, or surface states. At Weyl-semimetal interfaces, we showed how Coulomb interactions between Fermi arcs can generate competing excitonic orders, linking topology, surface states, and broken symmetry.

Transport in topological systems

Weyl semimetals provide a natural platform where topology, surface states, and transport meet. We have studied Josephson junctions of Weyl semimetals, predicting $0$-$\pi$ transitions, chiral oscillations, and Fermi-arc mediated transport as signatures of Weyl nodes and surface arcs.

We have also investigated collective responses in topological semimetals, including dipolar optical plasmons in thin-film Weyl semimetals, plasmons in nonsymmorphic Dirac semimetals, and RKKY interactions in Weyl thin films. More broadly, we use transport to identify the fingerprints of topological band structure in realistic geometries, including finite samples, interfaces, and superconducting hybrids.

Other directions

Related directions include graphene-superconductor heterostructures, topological-insulator thin films, quantum dots, spin-dependent Andreev reflection, topological electrical circuits, engineered defect networks, and links between condensed matter physics and high-energy ideas such as Carroll symmetry at phase boundaries. These projects expand the same core questions into new materials, devices, and theoretical settings.

People.

Group postdoc:

Group PhD students:

Past postdoc:

Krashna Mohan Tripathi

Graduated PhD students:

Present BS/MS/MSc/MTech students:

Aman Cheema

Aseem Chandra Pathak

Sarvottam Singh

Past BS/MS/MSc/MTech students:

Vidhi

Ayush Rana

Sandipan

Subhradeep

Ishita Agarwal

Arpan Das

Siddhartha

Subhadeep Pal

Neraimathi P.K

Prajwal Samal

Siddharth Jain

Yatharth Shivhare

Manoj Kumar Yadav

Rohit Mukherjee

Sreemayee Aditya

Tarun Maity

Vikas Soni

Keshav Pareek

Srujan Sapkal

Nivedita

Smriti Pradhan

Jay Deshmukh

Active collaborators:

Past collaborators:

Prof. Gopal Dixit, IITB

Prof. Udit Khanna, PRL

Dr. Dibya Kanti Mukherjee

Prof. Arijit Saha, IOP, Bhubaneswar

Prof. Tarun Kanti Ghosh, IIT Kanpur

Prof. Netanel Lindner, Technion, Israel

Prof. Reinhold Egger, HHU, Düsseldorf, Germany. My PhD Supervisor!

Prof. Alfredo Levy Yeyati, UAM, Madrid, Spain

Prof. Thierry Martin, AMU, Marseille, France

Present Grants:

ANRF funded ARG with Prof. Mandar Deshmukh: 2026-2029, ~2 Cr

MATRICS: 2026-2030

Past Grants:

Initiation grant (IIT Kanpur): 2017-19, 17 Lakh

Early Career Research Award (SERB, DST): 2019-22, 24.6 Lakh

SPARC (MHRD) along with A. Polkovnikov, A. Dutta, H.A. Fertig and A De Martino: 2019-21, 35 Lakh

Young Scientist’s Research Award (BRNS, DAE): 2019-22, 17.7 Lakh

Publications.

50. "Non-Bloch band theory of boundary-controlled magnon edge modes in an antiferromagnetic chain"
Suman Debnath, Sonu Verma, Rohit Mukherjee, Arijit Kundu
arXiv:2606.09267

49. "New frontiers in quantum science and technology using van der Waals Josephson junctions"
Joydip Sarkar, Ayshi Mukherjee, Amit Basu, Ritajit Kundu, Arijit Kundu, Mandar M. Deshmukh
arXiv:2604.15276

48. "Emergent topological phase from a one-dimensional network of defects"
Rahul Singh, Ritajit Kundu, Arijit Kundu, Adhip Agarwala
arXiv:2604.13532

47. "Umklapp-Enhanced Interlayer Valley Drag in Moiré Bilayers"
Ritajit Kundu, Mandar M. Deshmukh, Herbert A. Fertig, Arijit Kundu
arXiv:2603.15520

46. "Quantum interference in a twisted high-T$_c$ SQUID senses emergent interfacial order"
Amit Basu, Samrat Ash, Ritajit Kundu, Neha Bhatia, Sakshi Nema, Tejaswini Gawade, Khushabu Agrawal, Abhishek Das, Joydip Sarkar, Amit Shah, Ruta Kulkarni, Digambar A. Jangade, Arijit Kundu, A. Thamizhavel, Mandar M. Deshmukh
arXiv:2603.12092

45. "Index-theoretic route to the subgap Andreev bands and topological response in Josephson junctions"
Sinchan Ghosh, Srinjoy Ghosh, Arijit Kundu, K. Sengupta
arXiv:2512.07701

44. "Skyrmion stripes in twisted double bilayer graphene"
Debasmita Giri, Dibya Kanti Mukherjee, H.A. Fertig, Arijit Kundu
Phys. Rev. B (Letters) 112, L081406 (2025) (arXiv:2310.01185)

43. "Time-resolved ARPES and optical transport properties of irradiated twisted bilayer graphene in a steady state"
Ashutosh Dubey, Ritajit Kundu, and Arijit Kundu
Phys. Rev. B 111, 035431 (2025)

42. "Superconducting magic-angle twisted trilayer graphene with competing magnetic order and moiré inhomogeneities"
Ayshi Mukherjee, Surat Layek, Subhajit Sinha, Ritajit Kundu, Alisha H. Marchawala, Mahesh Hingankar, Joydip Sarkar, L. D. Varma Sangani, Heena Agarwal, Sanat Ghosh, Aya Batoul Tazi, Kenji Watanabe, Takashi Taniguchi, Abhay N. Pasupathy, Arijit Kundu & Mandar M. Deshmukh
Nature Materials 24(9), 1400-1406 (2025)

41. "Valley filtering and valley valves in irradiated pristine graphene"
Rekha Kumari, Gopal Dixit, and Arijit Kundu
Phys. Rev. B 111, 155421 (2025)

40. "Carroll at Phase Separation"
Sourav Biswas, Ashutosh Dubey, Saikat Mondal, Aritra Banerjee, Arijit Kundu, Arjun Bagchi
arXiv:2501.16426

39. "Josephson junction of minimally twisted bilayer graphene"
Ritajit Kundu and Arijit Kundu
Phys. Rev. B 110, 085422 (2024)

38. "The two-channel Kondo effect in coupled interacting helical liquids"
Sourav Biswas, Alessandro De Martino, Sumathi Rao, Arijit Kundu
Phys. Rev. B 109, 155119 (2024)

37. "Josephson-Current Signatures of Unpaired Floquet Majorana Bound States"
Rekha Kumari, Babak Seradjeh, Arijit Kundu
Physical Review Letters 133, 196601 (2024) (arXiv:2301.07707)

36. "Fermi-arcs mediated transport in surface Josephson junctions of Weyl semimetal"
Rekha Kumari, Dibya Kanti Mukherjee, Arijit Kundu
arXiv:2401.14956

35. "Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach"
Harsh Varshney, Rohit Mukherjee, Arijit Kundu, Amit Agarwal
Phys. Rev. B 108, 165412 (2023) (arXiv:2305.18127)

34. "Operator correlations in a quenched non-Hermitian Luttinger liquid"
Ashutosh Dubey, Sourav Biswas, Arijit Kundu
Phys. Rev. B 108, 085433 (2023) (arXiv:2304.00881)

33. "Non-linear magnon transport in a bilayer van der Waals antiferromagnets"
Rohit Mukherjee, Sonu Verma, Arijit Kundu
Phys. Rev. B 107, 245426 (2023) (arXiv:2303.15426)

32. "Broken symmetry and competing orders in Weyl semimetal interfaces"
Ritajit Kundu, H.A. Fertig, Arijit Kundu
Phys. Rev. B 107, L041402 (2023) (arXiv:2205.13254)

31. "Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi}$ model in honeycomb lattice: thermal Hall signature"
Rohit Mukherjee, Ritajit Kundu, Avinash Singh, Arijit Kundu
Phys. Rev. B 107, 155122 (2023) (arXiv:2108.08801)

30. "Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands"
Pratap Chandra Adak, Debasmita Giri, L. D. Varma Sangani, Kenji Watanabe, Takashi Taniguchi, H.A. Fertig, Arijit Kundu, Mandar M. Deshmukh
Nature Communications 13, 7781 (2022) (arXiv:2212.09690)

29. "Dipolar optical plasmon in thin-film Weyl semimetals"
Debasmita Giri, Dibya Kanti Mukherjee, Sonu Verma, H.A. Fertig, Arijit Kundu
Phys. Rev. B 105, 075426 (2022) (arXiv:2011.06862)

28. "Observation of Fermi liquid phase with broken symmetry in a single crystalline nanorod of Pr$_2$Ir$_2$O$_7$"
Bikash Ghosh, Abhishek Juyal, Sourav Biswas, R. Rawat, Arijit Kundu, Soumik Mukhopadhyay
arXiv:2208.08811

27. "Plasmon in Nonsymmorphic Dirac semimetals"
Debasmita Giri, Arijit Kundu
arXiv:2108.07782

26. "Dynamical polarization and plasmons in noncentrosymmetric metals"
Sonu Verma, Arijit Kundu, Tarun Kanti Ghosh
Phys. Rev. B 102, 195208 (2020) (arXiv:2009.13105)

25. "Chiral Luttinger liquids in graphene tuned by irradiation"
Sourav Biswas, Tridev Mishra, Sumathi Rao, Arijit Kundu
Phys. Rev. B 102, 155428 (2020) (arXiv:2003.09160)

24. "Bulk-edge correspondence and new topological phases in periodically driven spin-orbit coupled materials in the low frequency limit"
Ruchi Saxena, Sumathi Rao, Arijit Kundu
J. Phys. Commun., 4, 075019 (2020) (arXiv:1712.05916)

23. "RKKY coupling in Weyl semimetal thin films"
Sonu Verma, Debasmita Giri, H.A. Fertig, Arijit Kundu
Phys. Rev. B 101, 085419 (2020) (arXiv:1908.04554)

22. "Quantized large-bias current in the anomalous Floquet-Anderson insulator"
Arijit Kundu, Mark Rudner, Erez Berg, Netanel H. Lindner
Phys. Rev. B 101, 041403(R) (2020) (arXiv:1708.05023)

21. "Non-local control of spin-spin correlation in finite geometry helical edge"
Sonu Verma, Arijit Kundu
Phys. Rev. B 99, 121409(R) (2019) (arXiv:1805.00739)

20. "RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems"
Sonu Verma, Arijit Kundu, Tarun Kanti Ghosh
Journal of Applied Physics 125, 233903 (2019) (arXiv:1807.01967)

19. "Quantum transport simulation of non-local response in Weyl semimetals"
Keshav Pareek, Arijit Kundu
arXiv:1812.05504

18. "Spin Response and Collective Modes in Simple Metal Dichalcogenides"
Dibya Kanti Mukherjee, Arijit Kundu, H. A. Fertig
Phys. Rev. B 98, 184413 (2018) (arXiv:1805.08223)

17. "Spin-dependent Andreev reflection in spin-orbit coupled systems by breaking time-reversal symmetry"
Dibya Kanti Mukherjee, Joanna Hutchinson, Arijit Kundu
Phys. Rev. B 98, 125424 (2018) (arXiv:1708.06773)

16. "Transport through Andreev bound states in a Weyl semimetal quantum dot"
Dibya Kanti Mukherjee, Sumathi Rao and Arijit Kundu
Phys. Rev. B 96, 161408 (Rapid Comm.) (2017) (arXiv:1708.01707)

15. "$0$-$\pi$ transitions in a Josephson junction of irradiated Weyl semimetal"
Udit Khanna, Sumathi Rao and Arijit Kundu
Phys. Rev. B 95, 201115 (Rapid Comm.) (2017) (arXiv:1703.01312)

14. "Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials"
Priyanka Mohan, Ruchi Saxena, Arijit Kundu, Sumathi Rao
Phys. Rev. B 94, 235419 (2016) (arXiv:1609.06504)

13. "Chiral nodes and oscillations in the Josephson current in Weyl semimetals"
Udit Khanna, Dibya Kanti Mukherjee, Arijit Kundu, Sumathi Rao
Phys. Rev. B 93, 121409 (Rapid Comm.) (2016) (arXiv:1509.03166)

12. "Floquet-Engineered Valleytronics in Dirac Systems"
Arijit Kundu, H.A. Fertig, Babak Seradjeh
Phys. Rev. Lett. 116, 016802 (2016) (arXiv:1505.03818)

11. "Effective Theory of Floquet Topological Transitions"
Arijit Kundu, H.A. Fertig, Babak Seradjeh
Phys. Rev. Lett. 113, 236803 (2014) (arXiv:1406.1490)

10. "Proximity induced superconductivity in Weyl semi-metals"
Udit Khanna, Arijit Kundu, Saurabh Pradhan, Sumathi Rao
Phys. Rev. B 90, 195430 (2014) (arXiv:1407.7515)

9. "Tunable Floquet Majorana Fermions in Driven Coupled Quantum Dots"
Yantao Li, Arijit Kundu, Fan Zhong, Babak Seradjeh
Phys. Rev. B 90, 121401 (Rapid Comm.) (2014) (arXiv:1402.7353)

8. "Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots"
A. Brunetti, A. Zazunov, A. Kundu, R. Egger
Phys. Rev. B 88, 144515 (2013) (arXiv:1305.3816)

7. "Transport signatures of Floquet Majorana fermions in driven topological superconductors"
Arijit Kundu, Babak Seradjeh
Phys. Rev. Lett. 111, 136402 (2013) (arXiv:1301.4433)

6. "Electron-phonon scattering in topological insulator thin films"
Sébastien Giraud, Arijit Kundu, Reinhold Egger
Phys. Rev. B 85, 035441 (2012) (arXiv:1111.4063)

5. "Energy spectrum and broken spin-surface locking in topological insulator quantum dots"
A. Kundu, A. Zazunov, A. Levy Yeyati, T. Martin, R. Egger
Phys. Rev. B 83, 125429 (2011) (arXiv:1102.4437)

4. "Quantum charge pumping through a superconducting double barrier structure in graphene"
Arijit Kundu, Sumathi Rao and Arijit Saha
Phys. Rev. B 83, 165451 (2011) (arXiv:1102.1447)

3. "Magnetic scattering of Dirac fermions in topological insulators and graphene"
A. Zazunov, A. Kundu, A. Hütten, R. Egger
Phys. Rev. B 82, 155431 (2010) (arXiv:1007.5398)

2. "Resonant tunneling through superconducting double barrier structures in graphene"
Arijit Kundu, Sumathi Rao and Arijit Saha
Phys. Rev. B 82, 155441 (2010) (arXiv:1007.3716)

1. "Resonant spin transport through a superconducting double barrier Structure"
Arijit Kundu, Sumathi Rao and Arijit Saha
EPL (Europhys. Lett.) 88, 57003 (2009) (arXiv:0906.3679)

Teaching.

Contact.

Department of Physics,
Indian Institute of Technology - Kanpur
Kanpur, 206018, India

Email: kundua AT iitk.ac.in
Phone: +91 512 259 7065