Field-induced excitonic insulator in graphite

In graphite, electrons and holes are confined to their lowest Landau levels when magnetic field exceeds 10 T. Between 22 T and 70 T, two insulating states emerge, with critical temperatures each displaying a distinct dome-like field dependence [1]. The summit of the first dome corresponds to a critical temperature of 9.2 K and a critical magnetic field of 47 T. At this critical field, hole and electron Landau sub-bands simultaneously cross the Fermi level allowing exciton formation with infintesimal Coulomb attraction. Quantifying the effective mass and the spatial separation of the excitons in the basal plane, we found that the expected degeneracy temperature of the excitonic fluid is close to the experimentally measured critical temperature. This supports the picture of a metal-insulator transition driven by the Bose-Einstein Condensation (BEC) of excitons [2]. The evolution of this dome under hydrostatic pressure documents an original case of BCS-BEC crossover, which is tunable by both magnetic field and pressure, but its summit remains locked at a fixed temperature [3].

References:

1. Benoît Fauqué et al. Two phase transitions induced by a magnetic field in graphite. Phys. Rev. Lett. 110, 266601 (2013).
2. Jinhua Wang et al. Critical point for Bose-Einstein condensation of excitons in graphite. Proc. Natl. Acad. Sci. 117, 30215 (2020).
3. Yuhao Ye et al. Tuning the BCS-BEC crossover of electron-hole pairing with pressure, Nature Communications 15:9794 (2024)

Indirect excitons

Spatially indirect excitons (IXs), also known as interlayer excitons, are formed by electrons and holes in separated layers in a heterostructure (HS). Due to the layer separation, the IX lifetimes are orders of magnitude longer than lifetimes of spatially direct excitons. The long lifetimes allow IXs to cool below the temperature of quantum degeneracy and form quantum bosonic states. We present recent results in quantum IX systems. In GaAs HS: Cooper-pair-like excitons [1], excitonic Bose polarons [2], and the Mott transition in excitonic Bose polarons [3]. In van der Waals HS: long-distance IX transport [4], IX mediated long- distance spin transport [5], and efficient IX transport with anomalously high diffusivity, orders of magnitude higher than for regular diffusive exciton transport in van der Waals heterostructures, agreeing with long-range ballistic transport [6].

Acknowledgements: The PL and PLE studies were supported by DOE Award DE-FG02- 07ER46449, the device fabrication by NSF Grant 1905478, the GaAs heterostructure growth by Gordon and Betty Moore Foundation Grant GBMF9615 and NSF Grant DMR 2011750.

References:

1. Z. Zhou, W. J. Brunner, E. A. Szwed, H. Henstridge, L. H. Fowler-Gerace, L. V. Butov, Efficient transport of indirect excitons in a van der Waals heterostructure, arXiv:2507.04556 (2025).
2. D. J. Choksy, E. A. Szwed, L. V. Butov, K. W. Baldwin, L. N. Pfeiffer, Fermi edge singularity in neutral electron-hole system, Nat. Phys. 19, 1275 (2023).
3. E. A. Szwed, B. Vermilyea, D. J. Choksy, Z. Zhou, M. M. Fogler, L.V. Butov, D.K. Efimkin, K.W. Baldwin, L.N. Pfeiffer, Excitonic Bose-polarons in electron-hole bilayers, Nano Lett. 24, 13219 (2024).
4. E.A.Szwed,B.Vermilyea,D.J.Choksy,Z.Zhou,M.M.Fogler,L.V.Butov,K.W.Baldwin, L. N. Pfeiffer, Mott transition in excitonic Bose polarons, arXiv:2504.07227 (2025).
5. L. H. Fowler-Gerace, Zhiwen Zhou, E. A. Szwed, D. J. Choksy, L. V. Butov, Transport and localization of indirect excitons in a van der Waals heterostructure, Nat. Photon. 18, 823 (2024).
6. Z. Zhou, E. A. Szwed, D. J. Choksy, L. H. Fowler-Gerace, L. V. Butov, Long-distance decay- less spin transport in indirect excitons in a van der Waals heterostructure, Nat. Commun. 15, 9454 (2024).

Optical and cavity engineering of driven excitonic condensates

Bilayer materials hosting interlayer excitons—comprising electrons in one layer and holes in the other—are a promising experimental platform for realising high-temperature condensates and studying their dynamical properties. Imposing a chemical potential bias through optical pumping or electrical contacts drives exciton condensates into distinct dynamical regimes. We investigate how these regimes manifest in emitted light and how they are influenced by placing the material within an optical cavity.

We show that in a bilayer system where the charge can tunnel between the layers, the chemical potential bias means that an exciton condensate is in the dynamical regime of the Josephson effect. By increasing the bias voltage, the system undergoes a transition from the phase- trapped to phase-delocalized dynamical condensation. Optical spectroscopy can identify these phases, with a strong response to weak fields near the transition due to the instability in the order parameter dynamics [1].

If such a system is placed in an optical cavity within the phase-trapped regime, coupling to photons favours a superradiant state. The phenomenon allows the device to convert DC currents into coherent photons at tunable frequencies determined by the bias and material thickness. These findings highlight mechanisms to control and harness excitonic condensates for optoelectronic applications [2].

References:

1. Alexander Osterkorn, Yuta Murakami, Tatsuya Kaneko, Zhiyuan Sun, Andrew J Millis, Denis Golež, arXiv:2410.22116.
2. Zhiyuan Sun, Yuta Murakami, Fengyuan Xuan, Tatsuya Kaneko, Denis Golež and Andrew J. Millis PRL 133, 217002 (2024).

Manipulating Topological Phases and Correlated States in HfTe₅

Controlling topological phases in quantum materials offers a route to explore emergent quantum states and develop devices with topologically protected carriers. Yet, few materials allow both efficient tunability and in situ electronic measurements. Here, we present our work on HfTe₅, a prototypical van der Waals material with exceptional topological tunability. First, we apply a large, controllable uniaxial strain to induce a topological phase transition from a weak topological insulator (WTI) to a strong topological insulator (STI). This transition leads to a dramatic increase in resistivity of over 190,000% and results in surface-state-dominated transport at cryogenic temperatures. Second, we find that the WTI phase of HfTe5 supports zeroth Landau level physics at moderate magnetic fields. Fields above 10 T drive transitions to 1D Weyl modes and, under low carrier density, stabilize a spin-triplet excitonic insulator phase, enabled by strong electronic instabilities in quasi-1D systems. Notably, in the STI phase, this excitonic phase emerges at even lower fields. Third, we explore thin HfTe₅ devices (<100 nm), where enhanced surface-to-bulk transport and correlated phenomena appear. These observations highlight HfTe₅ as a versatile platform for studying topological transitions and emergent correlated states. Together, these results position HfTe₅ as a key material for advancing quantum device applications, from spintronics to fault-tolerant topological quantum computing.

Counterflow excitonic plasmons on a chip

A defining feature of exciton condensates is the emergence of a Goldstone mode associated with spontaneous interlayer phase coherence, which enables dissipationless counterflow of electrons and holes – analogous to superfluidity in a Bose-Einstein condensate (BEC). In BECs, such superfluid behavior results from the spontaneous breaking of a continuous symmetry (typically global U(1) charge conservation). In contrast, in excitonic insulators, this symmetry is often explicitly broken by coupling to the lattice, leading to a gapped pseudo-Goldstone mode and frequently accompanied by lattice distortions. This complicates both the identification of a true excitonic condensate and the interpretation of spectroscopic signatures. Moreover, the pseudo- Goldstone mode is optically silent in the far field, making its detection especially challenging.

In this talk I will present a theoretical framework demonstrating that on-chip terahertz (THz) spectroscopy provides a direct and linear probe of the pseudo-Goldstone mode in two-dimensional excitonic insulators. This mode—referred to here as a counterflow excitonic plasmon—involves in-phase oscillations of electrons and holes. Although these oscillations produce no net dipole moment and thus evade far-field optical detection, they can couple efficiently to near-field THz pulses guided along on-chip metallic transmission lines. I will show how this coupling enables the excitation and detection of counterflow excitonic plasmons, and discuss the potential of this technique to address long standing questions in this field.

Green’s function zeros in Mott quantum magnets

Even deep in strongly correlated Mott insulating phases, the free, non-interacting energy- momentum relation plays a crucial role for the analytic structure of the single- particle Green’s function G [1]. In particular, the momentum structure of the zero eigenvalues of G is given by an appropriately renormalized form of the bare electronic dispersion, despite the presence of a hard gap which prevents from a straightforward spectroscopic access. After exploring topological classification schemes based on Green’s function zeros and their connection with low-energy excitations in spin liquids [2], I will present setups that have been put forward for an experimental detection [3,4]. In the second part of the talk, I will extend the notion of zeros of G to long-range ordered magnetic phases [5] and discuss the role of temperature. If time allows, I will discuss other types of symmetry breaking and connect to altermagnets with interlayer excitonic order [6].

References:

1. L. Del Re. et al. in preparation
2. N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. König, T. Schäfer, D. Di Sante, J. Cano, A. J. Millis, A. Georges and G. Sangiovanni, Nat. Commun. 14, 7531 (2023).
3. N. Wagner, D. Guerci, A. J. Millis and G. Sangiovanni, Phys. Rev. Lett. 133, 126504 (2024).
4. E. Stepanov, M. Chatzieleftheriou, N. Wagner and G. Sangiovanni, Phys. Rev. B 110,L161106 (2024).
5. C. Lehmann, L. Crippa, G. Sangiovanni and J. Budich, arXiv:2502.19479
6. F. Valerio Servilio, et al., in preparation

Signatures of Collective Ordering and Ferroelectric Phases of Moiré Excitons

In this talk, I will present our recent observation of many-body interaction-induced ferroelectric ordering of moiré excitons in H-stacked WSe₂/WS₂ heterobilayer. Strong exciton-exciton repulsion leads to an excitonic Mott state with a large on-site energy U_xx ~35 meV. Due to the interplay of anisotropic nature of dipolar interactions, large U_xx, and spatially indirect in-plane excitons in H-stacking, we observe signatures of ferroelectric ordering of moiré excitons in time-resolved photoluminescence spectra. In particular, we find a reduction in emission lifetime consistent with this ordering, which can be thought of as a novel cooperative phenomenon. Our observations open new avenues to explore a system of correlated moiré electrons and excitons as a rich platform to study and create quantum matter in a driven-dissipative setting and also a many-body quantum open system simulator to uncover novel cooperative phenomena.

Ab initio calculations of excitons in complex 2D van der Waals Heterostructures

I will describe a number of recently developed computational methods to predict the optical properties of van der Waals heterostructures containing hundreds of atoms in a unit cell. To obtain the single-particle band structure, we employ a layer-projected scissors (LAPS) operator that incorporates short and long-range electron self-energy effects and ensures a proper description of the band alignment at the interface [1]. I will show that the LAPS method yields an accuracy comparable to the many-body GW approximation, but at the cost of a standard density functional theory (DFT) calculation. To compute the optical excitations, we solve the Bethe-Salpeter Equation (BSE) using a minimal basis for the electron-hole states. The screened Coulomb interaction is calculated using a mixed quantum-classical electrostatic model – an extension of the previously published QEH model. By using a hierarchical basis comprising dielectric eigenstates of the individual monolayers, we can converge the BSE calculations using only a handful of basis functions. Combining these methods, we perform a high-throughput screening to identify vdW heterobilayers with interesting excitonic properties. The calculated data is made available in the open heterostructure database HetDB [2,3], which is integrated with the C2DB monolayer database [4].

References:

1. Dario A. Leon et al., arXiv:2505.17292 (2025) 2. https://hetdb.fysik.dtu.dk
3. M. O. Sauer et al. arXiv:2504.05754
4. https://c2db.fysik.dtu.dk

Electromagnetic responses of Excitonic Insulators

In this seminar, I will first introduce the main concepts of bilayer exciton insulator, a new type of charge neutral quantum liquid recently realized in 2D materials. Then I will mostly focus on the electromagnetic responses of bilayer excitonic insulators (EIs) and identify two distinct collective modes: (1) Two gapped plasmon modes couple to the layer symmetric gauge field. The transverse mode is nearly dispersionless in the long wavelength limit, while the longitudinal mode, accounting for total charge fluctuations, has a linear dispersion with velocity proportional to 2D electrical polarizability. (2) A gapless phase (Goldstone) mode and a gapped amplitude mode, associated with the fluctuations of EI order parameter, couple to the layer antisymmetric gauge field. In the long wavelength and low frequency limit, the phase mode behaves like an acoustic phonon with speed inversely proportional to the square root of exciton compressibility. Significantly, its linear dispersion yields a cubic frequency dependence of the real admittance in microwave impedance microscopy (MIM), providing a method to detect the Goldstone mode directly.

Light-Induced Electron Pairing in Laser-Excited Semiconductor-Metal Heterostructures

Laser excited quasi-2D heterostructures of transition metal dichalcogenides (TMDCs) have been shown to allow for quite a few higher order excitonic bound states such as trions (charged excitons), biexcitons (excitonic molecules), charged biexcitons, and more [1-5]. Such a large variety of coupled electron-hole quasiparticle excitations opens the door to a variety of new laser- driven phenomena in these systems, including metal-insulator transitions and Wigner crystallization, Bose-Einstein condensation (BEC), and even unconventional superconductivity [6-10]. Recently [5,10], an atom-like excitonic complex was reported experimentally in laser excited bilayer TMDCs in accord with theory predictions – the quaternion, the tightly bound complex of a free charge carrier in the top layer coupled to a like-charge trion in the bottom layer – provided that the entire heterostructure is placed close to a metallic surface to screen the excessive repulsive interaction in the system. Since such quaternions carry two net charges and are also bosonic, BEC of these quasiparticles would be a superfluid and therefore also a Schafroth superconductor [11]. Here, we develop a theoretical framework to explain the latest experimental observations of the Zeeman effect for quaternion complexes in perpendicular magnetostatic field [10]. Our theory is based on group theoretical analysis and spin-Hamiltonian formalism. We show that, contrary to the linear Zeeman shift known for excitons and trions in TMDC monolayers [12], the quaternion ground state is the spin-triplet to exhibit a quadratic magnetic field shift similar to that known for hydrogen-like atoms (whose ground state is singlet). In addition to prospective laser-driven BEC and superconductivity, another fascinating possibility for quaternions is that, as these bound four- particle doubly charged complexes repel each other, they could form a bosonic Wigner crystal. Such a light-induced quasiparticle crystal would be an atom-like supersolid inside of the crystalline material. The process of Wigner crystallization is controlled by the ratio of the Coulomb repulsion energy to the average single-particle kinetic energy of a statistical ensemble of charge carriers [13,14]. Due to the double charge and quadruple mass as compared to electrons, this ratio is at least 10 times greater for quaternions, suggesting higher crystallization temperature than that of the order of 10 K reported for quasi-2D electrons in TMDC nanostructures [15].

Acknowledgements: This research is supported by the U.S. Army Research Office grant No. W911NF-24-1-0237.

References:

1. I.V.Bondarev and M.R. Vladimirova, Phys. Rev. B 97, 165419 (2018).
2. E.Liu, et al., Nat. Commun. 12, 6131 (2021).
3. I.V.Bondarev, O.L.Berman, R.Ya.Kezerashvili, and Yu.E.Lozovik, Commun. Phys. (Nature) 4, 134 (2021).
4. X.Sun, et al., Nature 610, 478 (2022).
5. Z.Sun, et al., Nano Lett. 21, 7669 (2021).
6. Y.N.Joglekar, A.V.Balatsky, and S.Das Sarma, Phys. Rev. B 74, 233302 (2006).
7. L.Ma, et al., Nature 598, 585 (2021).
8. I.V.Bondarev and Yu.E.Lozovik, Commun. Phys. (Nature) 5, 315 (2022).
9. D.Erkensten, S.Brem, R.Perea-Causin, and E.Malic, Phys. Rev. B 110, 155132 (2024).
10. Q.Wan, et al., arXiv:2412.06941 (12 Dec 2024).
11. M.Schafroth, Phys. Rev. 96, 1442 (1954).
12. D.MacNeill, et al., Phys. Rev. Lett. 114, 037401 (2015).
13. P.M.Platzman and H.Fukuyama, Rev. B 10, 3150 (1974).
14. I.V.Bondarev, A.Boltasseva, J.B.Khurgin, and V.M.Shalaev, arXiv:2503.05165 (7 Mar 2025).
15. T.Smolen ́ski, et al., Nature 595, 53 (2021); Y. Zhou, et al., ibid. 595, 48 (2021).

From Dirac Altermagnets to Excitonic Spin Transport in Correlated Bilayers

Altermagnetism – a phase where antiferromagnetic order coexists with non-relativistic spin split- ting – has recently emerged as a fertile ground for novel spintronic and optical functionalities. In this talk, I first present results on a two-dimensional Hubbard model that hosts interaction-driven altermagnetic states with emergent Dirac cones. Using dynamical mean-field theory, we show that strong correlations lead to a re-emergence of high-energy Dirac features near the Mott transition, even when absent in static mean-field theory. These spectral signatures produce spin-selective optical responses, including a double-peak structure and photon-energy-dependent spin activation, revealing new routes for optical manipulation of spin degrees of freedom in correlated altermagnets.

Building on this, I explore a bilayer generalization of the same model, where the inclusion of a layer degree of freedom gives rise to richer symmetry-breaking patterns that intertwine spin and interlayer coherence. In this regime, the system realizes a correlated altermagnetic phase with features akin to an interlayer excitonic insulator. I show that applying an in-plane electric field with opposite signs across the layers induces a polarisation current that drives a highly anisotropic and tunable spin current, whose sign can be reversed by varying the photon energy. This coupling between interlayer coherence and spin transport opens the door to electrically controlled spintronic responses in Mott bilayers, and highlights the role of excitonic correlations in shaping the dynamics of layered altermagnets.

Unconventional excitonic insulators in two-dimensional topological materials

We theoretically studied the excitonic insulator in a pair of recently proposed two-dimensional candidate materials with nontrivial band topology. Contrary to previous works, we included interaction channels that violate the individual electron and hole number conservations. These are on equal footing with the number-conserving processes due to the substantial overlap of Wannier orbitals of different bands, which cannot be exponentially localized due to the nontrivial Chern numbers of the latter. Their inclusion is crucial to determine the symmetry of the electron- hole pairing and, by performing mean-field calculations at nonzero temperatures, we found that the order parameter in these systems is a chiral d-wave. In this talk I will discuss the nontrivial topology of this unconventional state as well as some properties of the associated Berezinskii-Kosterlitz-Thouless transition. In particular, I will argue that here it becomes a smooth crossover, for which we estimated an associated temperature lying between 50 and 75 K on realistic substrates. This is over an order of magnitude larger than in the number-conserving approximation where s-wave pairing is favored. I will also propose an experimental setup which leverages the topological properties to indirectly probe the presence of this phase. Our results highlight the interplay between topology at the single-particle level and long-range interactions, motivating further research in systems where both phenomena coexist.

References:

1. L. Maisel Licerán and H. Stoof, Phys. Rev. B 111, 245102 (2025)

Magnetic tuning of coupled excitonic-structural transitions

The search for excitonic coherence in quantum materials is hindered by the fact that excitonic orders often couples to other types of symmetry breaking. The candidate material Ta₂NiS₅ represents a paradigmatic example in which the excitonic order parameter couples linear with structural distortion giving rise to a structural distortion whose origin stimulated an intense debate in recent years [1,2]. In this seminar, I will discuss strategies for tuning coupled excitonic- structural transitions by exploiting time-reversal symmetry breaking realizations of the excitonic instability. I will introduce the general mechanism for a toy model [3]. Eventually, I will show the explicit application in the case of Ta₂NiSe₅ in perpendicular field [4].

References:

1. G. Mazza et. al, Nature of Symmetry breaking at the excitonic insulator transition: Ta₂NiS₅, Phys. Rev. Lett. 124, 197601 (2020).
2. L. Windgaetter et. al, Common microscopic origin of the phase transitions in Ta₂NiS₅ and the excitonic insulator candidate Ta2NiSe5, npj Quantum Materials 7, 210 (2021).
3. G. Mazza and M. Polini, Hidden excitonic quantum phases with broken time-reversal sym- metry, Phys. Rev. B 108, L241107 (2023)
4. G. Mazza in prep. (2025).

Control of phonon modes through the collective modes in excitonic insulators

Electron-hole bound pairs, interacting by Coulomb force, are common excitations in semicon- ductors. Spontaneous condensation of excitons is expected to occur if the binding energy of the excitons overcomes the small band gap of the semiconductor, giving rise to a new insulating ground state, the so-called excitonic insulator (EI). The excitonic condensate is not directly observable in EI candidates. However, the phonon excitations couple to the electrons in such a way that may affect the excitonic condensate. For instance, a strong Raman anomaly has been observed for the EI candidate, Ta₂NiSe₅, across the transition[1, 2]. In this work we aim at theoretically studying the phonon modes screened by the excitonic order parameter fluctuations. We show the excitonic condensate play an important role in renormalizing the phonon spectral densities. Using the dressed phonon Green’s functions, we could map out some regions in the MF phase diagram where the phonon modes spectral density behave different. More importantly, we found that phonon mode becomes soft in the band insulator phase and disappear by falling into the zero energy at strong electron-phonon couplings. While it exist as a hybridized mode, as an effect of the EI phase mode, in the EI phase at even strong electron-phonon couplings. Our calculated results will help elucidate the origin of the phase transitions in EI candidates with strong elecron-phonon coupling.

References:

1. Kwangrae. Kim, Hoon. Kim, Jonghwan. Kim, Changil. Kwon, Jun. Sung. Kim, and B. J. Kim, Nature Communications 12, 1969 (2021).
2. A. Pavel Volkov, Mai. Ye, Himanshu. Lohani, Irena. Feldman, Amit. Kanigel, and Girsh. Blumberg, Phys. Rev. B. 104, L241103 (2021).