Probing electrons with microwaves

Contact Rupini Kamat and Sandesh Kalantre for more details.

 

What do the words used to describe condensed matter phenomena such as superconductivity,  quantum Hall effect and topological insulators have in common? They are all named after a distinguishing property measured in transport. Needless to say, our understanding of electronic properties of materials has been primarily derived from some kind of transport measurements. However, it would be unfair to say that such measurements can foretell the entire microscopic picture of a material. 

While transport measurements such as the longitudinal and Hall resistance of a material can yield a surprising amount of information about the basic physics, they do have certain limitations. Transport measurements occur at frequencies much lower than any energy scale intrinsic to the material. They essentially probe off-resonant interactions with phonons and other electrons in the material. Finally, we are limited to probing the equilibrium properties of the Fermi surface. However, a better understanding  can be obtained by some kind of resonant coupling to an external degree of freedom that is easy to produce, manipulate and measure. Microwaves, typically referred to frequencies in the GHz range, can resonantly couple to electronic spins. Such techniques, collectively referred to as electron spin resonance (ESR), are a powerful probe of electronic properties. We are developing these techniques in the group to broadly understand van-der Waals materials, doped Si near its metal insulator transition and quantum spin liquids. 

Resistively-detected ESR in van-der Waals materials

Moire heterostructures of two-dimensional van der Waals materials and their associated nearly flat electronic minibands have been shown to produce novel correlated electron states, including superconductivity^[1] and orbital ferromagnetism^[2][3].  While conventional electron transport measurements are a powerful tool to identify and probe novel electronic states in moire materials, these measurements alone are insufficient to fully understand these states.  In ferromagnetic TBG for example, transport measurements can identify the existence of a ferromagnetic state and provide preliminary characterization of the corresponding critical field and temperature, but they cannot quantify the magnetization of the material, nor can they identify the valley and spin properties of the sample throughout the material’s phase diagram. Typical approaches to determine magnetic order, such as neutron scattering or inelastic x-ray scattering, are also not feasible given that graphene is atomically thin and the magnetic scattering cross-section is much too small. Resistively detected electron spin resonance (RD ESR) measurements may be capable of filling this gap in our understanding of magnetic TBG. 

ESR is a technique in which the energy cost of disturbing a material’s magnetic order is directly measured. Microwaves are transmitted to the material, and when the energy of the microwaves exactly matches this energy cost, the material will absorb the microwaves. In traditional ESR measurements, this is detected optically via the absorption spectrum of the material, but this requires sample sizes significantly larger than the TBG samples we’re currently able to fabricate. Instead, we can measure this resonance electrically, using the fact that the increased absorption of microwaves at resonance perturbs the electronic ground state of the material, which can be observed via a corresponding change in resistance. This technique for measuring electron spin resonance was pioneered in GaAs heterostructures^[4], and has been since extended to several other materials systems, including CVD graphene^[5][6] but has yet to be successfully realized in exfoliated graphene heterostructures with strongly correlated electron states.

[1] Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

[2] Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

[3]  Serlin, M., et al. "Intrinsic quantized anomalous Hall effect in a moiré heterostructure." Science 367.6480 (2020): 900-903.

[4] Stein, D., K. V. Klitzing, and G. Weimann. "Electron Spin Resonance on G a A s− Al x Ga 1− x As Heterostructures." Physical review letters 51.2 (1983): 130.

[5] Sichau, J. et al. Intrinsic spin-orbit coupling gap and the evidence of a topological state in graphene. Phys. Rev. Lett. 122, 046403 (2019).

[6] Mani, R. G., Hankinson, J., Berger, C. & de Heer, W. A. Observation of resistively detected hole spin resonance and zero-field pseudo-spin splitting in epitaxial graphene. Nature Communications 3, 996 (2012)

Spin Resonance with Superconducting Resonators 

In the past two decades, considerable progress has been made in the development of high-quality superconducting microwave resonators [1]. A microwave analog of a Fabry-Perot cavity, a superconducting resonator, confines electro-magnetic (EM) fields that can then couple to electric or magnetic dipole moments in materials. The confinement effectively leads to stronger fields in the resonator. In the planar version of superconducting resonators, coplanar waveguides, the resonator is much smaller in transverse dimensions than the wavelength. Hence, a further enhancement of EM fields results from this confinement which can lead to coherent coupling of microwave photons to appropriate dipole moments in the resonator. In fact, the field of circuit quantum electrodynamics rests on this simple idea, and coherent coupling of a single photon and a superconducting qubit has been demonstrated [2]. 

The first step is fabrication and measurement of resonators with superconductors such as NbTiN and TiN that can survive magnetic fields necessary for spin resonance. Examples of such devices are shown below : 

 

Quality factors on the order of 1E5 to 1E6 at thsingle photon level can be obtained when fabricated on Si, which is a metric on the sensitivity of superconducting resonators. 

 

Such devices are well-suited for the study for thin-film materials by virtue of their two-dimensional nature. One of the goals is a better understanding of the metal-insulator transition (MIT) in phosphorus doped Si. In these devices, dopants are placed in a thin layer with a doping density close to the MIT critical density. Near the critical density, the electron spins are interacting strongly because of their proximity to each other, and novel many-body physics can occur [3]. We are working on measurement of energy and spin relaxation times measured that can shed light on the many-body dynamics of spins in this system. A parallel effort is to use ESR with high-quality resonators to understand spin dynamics in thin-film candidates for quantum spin liquids. 

[1] : McRae, Corey Rae Harrington, et al. "Materials loss measurements using superconducting microwave resonators." Review of Scientific Instruments 91.9 (2020): 091101.

[2] : Blais, Alexandre, Steven M. Girvin, and William D. Oliver. "Quantum information processing and quantum optics with circuit quantum electrodynamics." Nature Physics 16.3 (2020): 247-256.

[3] : Potter, Andrew C., et al. "Quantum spin liquids and the metal-insulator transition in doped semiconductors." Physical Review Letters 109.7 (2012): 077205.

[4] : Clark, Lucy, et al. "Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO3." Nature Physics 15.3 (2019): 262-268.