Research Overview
I work on the microscopic theory of transport and optical phenomena in quantum materials, with a particular focus on the role of quantum geometry. While the electronic band structure determines the energy spectrum of a crystal, the geometry of its Bloch wavefunctions provides an additional layer of information that governs many measurable responses to electric, magnetic, and optical fields. My research seeks to understand how geometric quantities, such as the Berry curvature, quantum metric, and orbital and spin magnetic moments, and, more recently, higher-order quantum geometric objects, manifest themselves in experimentally observable phenomena.
Rather than studying quantum geometry in isolation, I am interested in identifying physical responses that reveal it. A typical project begins by asking whether a particular electrical, optical, or spin response is permitted by symmetry, develops a microscopic theory for its geometric origin, identifies realistic material platforms where it should be observable, and proposes experimental signatures. My work has explored a broad range of quantum geometric phenomena, including nonlinear Hall and spin transport, magnetotransport, optical responses, transport in topological materials, and altermagnetic switching. More recently, I have been investigating the role of higher-order quantum geometry in generating nonlinear optical and transport phenomena beyond the conventional Berry curvature and quantum metric paradigm. Unconventional spin and orbital responses in altermagnets, and their spin-space-group symmetry restrictions, are another frontier I am working on.
Methodologically, I combine semiclassical Boltzmann transport theory, quantum kinetic (density-matrix) theory, and Wannier-based numerical calculations to bridge fundamental theory with experimentally relevant predictions. Several of my works have been carried out in close collaboration with experimental groups, and a number of the theoretical predictions have subsequently been verified experimentally.
Ongoing and Future Directions
The broad directions I am currently pursuing and would like to develop further.
Higher-order quantum geometry driven nonlinear transport and optics
Most quantum geometric responses studied so far are governed by the Berry curvature and the quantum metric. These are only the leading geometric quantities, however, and a richer set of higher-order objects becomes relevant once one goes beyond linear order in the applied fields. Quantities such as the Berry connection polarizability, and higher moments of the quantum geometric tensor, enter the intrinsic nonlinear conductivities, second-harmonic generation, and photocurrent responses, and they remain comparatively unexplored. I am interested in developing a systematic understanding of which geometric object governs which nonlinear response, what symmetry conditions make it observable, and how it can be tuned in practice. Multilayer and moiré platforms, where gating, twist angle, and displacement field offer direct control over the wavefunctions, seem to me natural settings in which to pursue this.
Correlated quantum geometry and superconducting transport
Much of the quantum geometric framework has been developed for weakly interacting systems. In flat-band and moiré materials, where interactions dominate and the band velocity is small, geometric contributions become essential, and they enter quantities such as the superfluid stiffness that have no simple semiclassical counterpart. I would like to extend the response theory I have worked with to this regime, and to understand how quantum geometry shapes superconducting transport, including Josephson coupling and nonreciprocal responses such as the superconducting diode effect. A question I find particularly interesting is how the symmetry framework that organizes normal-state responses carries over to the superconducting state, and what it implies for identifying geometric contributions experimentally.
Spin, orbital, and altermagnetic responses
Beyond charge transport, spin and orbital angular momentum responses are central to low-dissipation device concepts, and their geometric origins are less well understood than their charge counterparts. Altermagnets are a particularly interesting platform in this context, since they combine momentum-dependent spin splitting with vanishing net magnetization, and their symmetry is described by spin space groups rather than the conventional magnetic point groups. I am working on the unconventional spin and orbital responses these materials support, the restrictions that spin-space-group symmetry places on them, and the switching mechanisms that follow. The broader aim is to connect such responses to measurable transport signatures and to realistic device geometries.
Completed Research Themes
Published work, grouped into six themes.
Chiral anomalies and magnetotransport in Weyl systems
The chiral anomaly refers to the non-conservation of chiral charge and energy between Weyl nodes. Using the Boltzmann framework with Landau levels, we showed that inversion-symmetry-broken tilted Weyl semimetals have a finite longitudinal nonlinear magnetoconductivity, which vanishes when the tilt is absent. Because it depends on the tilt orientation, second-harmonic measurements can be used to determine the tilt direction. We then showed that chiral anomalies also occur in three-dimensional spin-orbit coupled (Kramers-Weyl) metals, where the electrical, thermal, and gravitational anomalies transfer chiral charge between two Fermi surfaces attached to a single node with opposite Berry curvature flux, with consequences for the spin Nernst effect. In work with an experimental group, we found that disorder-driven Kondo interactions in the type-II Weyl semimetal WTe2 pin the Fermi level near the Weyl nodes. This enhances Berry-curvature-driven responses and produces a zero-field spontaneous Hall effect together with a second-harmonic Hall signal that scales quadratically with current.
Layer-space band geometry and Hall responses in multilayered materials
In a strictly two-dimensional system the planar Hall effect is forbidden, because the out-of-plane Berry curvature does not couple to the in-plane band velocity. We showed that quasi-two-dimensional materials still support a planar Hall effect, since interlayer tunneling generates in-plane components of the Berry curvature and the orbital magnetic moment. We listed the planar band-geometric contributions, worked out their crystalline symmetry restrictions, and showed that in gated bilayer graphene the effect is also sensitive to Lifshitz transitions. Applying the same reasoning to out-of-plane fields, we found that electric and magnetic fields together couple layer polarization to the orbital moment, which produces a mixed layer-orbital geometry in field-dressed Bloch states. This gives an intrinsic magnetoelectric Hall effect that is bilinear in E and B, independent of the scattering time, finite inside the band gap, and possible in nonmagnetic systems without spin-orbit coupling. We estimated its magnitude in rhombohedral pentalayer graphene.
Odd-parity magnetoresistance as a probe of time-reversal symmetry breaking
Intrinsic time-reversal symmetry breaking is difficult to detect in materials whose crystal symmetries forbid the anomalous Hall effect. With an experimental group, we measured a large, gate-tunable, room-temperature odd-parity magnetoresistance in a bilayer graphene/Cr2Ge2Te6 heterostructure, and attributed it to the coupling of the out-of-plane Berry curvature and orbital magnetic moment to the applied field. We then worked out the general theory. Onsager reciprocity forbids a longitudinal magnetoconductivity linear in B when time-reversal symmetry is present, so a finite B-linear longitudinal response indicates that the symmetry is broken intrinsically. This provides a transport measurement that can be used in cases where the anomalous Hall effect is not available.
Generalized Onsager quantization and aperiodic quantum oscillations
Quantum oscillation measurements are interpreted using Onsager's semiclassical quantization rule, which gives oscillations periodic in 1/B and a linear Landau fan diagram. We showed that higher-order magnetic susceptibility corrections to the free energy modify this rule and produce a nonlinear Landau fan, a field-dependent oscillation frequency, and a field-dependent cyclotron mass. We derived the field-dependent frequency and a generalized Lifshitz-Kosevich formula for three-dimensional systems, and identified the conditions under which these corrections become observable. In parallel work with experiment, the same features were seen at the LaVO3/KTaO3 and EuO/KTaO3 interfaces, where the Fermi surfaces are small and the susceptibility corrections are correspondingly larger, giving evidence for field-induced Fermi surface expansion.
Quantum-geometric spin responses and energy-efficient spintronics
One aim in spintronics is to transport spin angular momentum without a net charge current. We described an intrinsic nonlinear pure spin Hall effect, in which the linear and second-order charge Hall currents vanish while the second-order spin transport remains finite. A symmetry analysis identified the 39 magnetic point groups that allow it, and first-principles calculations gave a sizeable effect in the Kramers-Weyl metal RhGe at room temperature. We also showed that light-induced nonlinear spin magnetization is the leading magnetization response in centrosymmetric materials, separated its quantum-geometric contributions, and predicted a helicity-dependent response in the antiferromagnet CuMnAs. In a related study we found that collinear altermagnets have unequal sublattice spin torques, unlike conventional antiferromagnets. This allows field-free 180° Néel vector switching on picosecond timescales in centrosymmetric systems with weak spin-orbit coupling, where the Néel spin-orbit torque mechanism does not operate.
Valley physics and strain-engineered gauge fields in graphene
Nonuniform strain in graphene acts as a valley-dependent gauge field and produces pseudomagnetic fields, while the global time-reversal symmetry is preserved. Such fields had been imaged locally, but were difficult to quantify in a transport measurement. With an experimental group, we showed that high-mobility graphene shows beating in the Shubnikov-de Haas oscillations because the two valleys are quantized under different effective fields, and that the scaling of the node carrier density and filling factor with the applied field allows pseudomagnetic fields of a few millitesla to be extracted. We have since extended this into a diagnostic method. Strain, valley imbalance, valley-dependent energy shifts, spin-orbit splitting, and Kekulé distortion each give a different scaling of the beating nodes with carrier density and field, so the beating pattern indicates which mechanism is present. I also contributed to a Roadmap article on valleytronics in two-dimensional materials.