Quantum Materials Theory and Mesoscopics
We are a group interested in elucidating the inner workings and responses of new quantum and topological materials.
Below are some directions our group are actively engaged in.
Electronic & opto-electronic responses in quantum materials
Charge carriers in materials are often described as particles similar to free electrons but characterized by effective quantities such as an effective mass. However, electrons in new quantum materials, such as van der Waals heterostructures, can possess new properties that defy this description.
One particularly striking example is Berry curvature, a quantum mechanical property of Bloch wavefunctions in certain crystals which radically alters the dynamics of quasiparticles. Much as a spinning baseball allows a pitcher to start a wide variety of plays - e.g., fastballs, curveballs, changeups - Berry curvature (a kind angular momentum that is engineered into a crystal) may yield a plethora of non-intuitive electronic behavior. Many of these new phenomena can be useful. For example, in gapped Dirac systems found in van der Waals materials, Berry curvature enables the easy manipulation of the valley index - an internal degree of freedom akin to spin; such materials include graphene on hexagonal Boron Nitride (G/hBN) as well as dual gated bilayer graphene (BLG), and transition metal dichalcogenides. The new electronic action may enable new low-dissipation methods of manipulating information and other degrees of freedom. This forms part of an emerging sub-field called Valleytronics.
Our group is interested in elucidating how new electronic as well as opto-electronic responses can arise in quantum materials (e.g. van der Waals heterostructures), some of which are host possess unconventional winding of Bloch wavefunctions.
Related articles:
Detecting Topological Currents in Graphene Superlattices
Roman V. Gorbachev†, Justin C.W. Song†, Ge Liang Yu, A. V. Kretinin, F. Withers, Y. Cao, A. Mishchenko, K. S. Novoselov, K. Watanabe, T. Taniguchi, L. Levitov, A. K. Geim
-->This work was reported in popular level commentaries:
Science magazine perspective - "Harnessing Chirality for Valleytronics".
MIT news - "Physicists find a new way to push electrons around".
IEEE Spectrum - "Weird New Graphene Effect Makes Electrons Scoot Sideways".
Condensed Matter Journal Club - "Topological features and gauge fields in graphene superlattices"
Topological Valley Currents in Gapped Dirac Materials
Yuri L. Lensky, Justin C. W. Song, Polnop Samutpraphoot, Leonid S. Levitov
Phys. Rev. Lett. 114, 256601 (2015).
Constructing Topological Bands in Generic Materials
Justin C. W. Song, Polnop Samutpraphoot, & Leonid S. Levitov
Interactions and collective phenomena in topological materials
In a crystal, the “twisting” of electronic wave functions in momentum space – as encoded in the Bloch band Berry curvature or band topology – gives rise to a wealth of interesting “anomalous” behaviors that typify the newly discovered topological materials. Going beyond the paradigm of single-particle dynamics, electron-electron interactions have the potential of working hand-in-hand with band topology to unveil rich new vistas of novel and potentially useful electronic phenomena.
Our group is interested in understanding the interplay of electron interactions and band topology. In particular we are interested in how it can affect various collective and transport behavior. Our approach complements the current efforts of enumerating the array of exotic strongly interacting topological phases that may exist in-principle.
Recently, we showed that the combined action of Berry curvature and interactions dramatically alters the collective behavior of electron liquids, with striking consequences for readily available experimental systems; these include materials of intense current interest, including magnetically-doped topological insulators, and gapped Dirac materials such as transition metal dichalcogenides, and graphene heterostructures. The novel behavior is manifested as the chiral propagation of plasmonic modes, which are confined to system boundaries, even in the absence of magnetic field and are the first example of new class of collective modes which emerge in interacting electronic systems with Berry curvature. Strikingly, it manifests edge behavior for fundamentally different reasons than the familiar single particle edge states of topological insulators.
The above is an example of a new vista that our group is interested in where electron interactions as well as Bloch band Berry curvature conspire to produce unexpected phenomena.
Related articles:
Chiral Plasmons without Magnetic Field
Justin C. W. Song, Mark S. Rudner
Three dimensional Dirac and Weyl semimetals
Once the exclusive purview of high-energy accelerators, solid state systems have recently become a venue of choice to discover exotic quasiparticles. This has grown out of the unprecedented ability to synthesize new crystals, enabling solid state systems to become a simulacrum for quasiparticles that have been difficult to directly observe, e.g. Dirac, Majorana, and Weyl fermions.
3D Dirac and Weyl Semimetals are a particularly exciting example. Their gapless nodes in crystal momentum space (called Weyl points) can be thought of as sources (and sinks) of Berry curvature. As a result, the Weyl quasiparticles close to these points can mediate a variety of bulk, as well as surface phenomena. These include the chiral anomaly, chiral magnetic effect, and Fermi arc surface states. The first of which (chiral anomaly) has a particularly interesting history arising from particle motion deep in the bands.
A second reason why these materials have garnered intense interest is its strong magneto-transport response. One striking phenomena is giant, linear, and non-saturating (transverse) magneto-resistance that seemed to be a generic feature of 3D Dirac materials, appearing in TiBiSSe, Cd3As2, Na3Bi, and TaAs, appearing in semi-classically large fields. Magnetoresistance of any kind is surprising since it vanishes in a single carrier Drude treatment. Recently, we explained this mystery as a consequence of squeezed trajectories of semi-classical guiding centers that manifest generically in 3D metals but are emphasized in 3D Dirac materials due several of its material properties working in concert.
Our group is interested in uncovering new quantum mechanical phenomena that include transport, interacting phenomena, as well as semi-classical phenomena in 3D Dirac and Weyl systems.
Related article:
Linear magnetoresistance in metals: Guiding center diffusion in a smooth random potential
Justin C. W. Song, Gil Refael, Patrick A. Lee
Phys. Rev. B 92 180204(R) (2015)
---> Featured as an Editor's Suggestion. Popular level commentary:
Designer responses from out-of-equilibrium and driven systems
The linear response of a system to an external perturbation can be thought of as a means to measure its equilibrium ground state. As a result, these responses are constrained in a number of different ways. For example, a Hall current only arises if the instantaneous Hamiltonian breaks time reversal symmetry. Since the responses derive from the equilibrium ground state, an often trodden route to discover new responses is to construct novel ground states.
An alternative is to study out-of-equilibrium systems which can host phenomena that transcend the usual strictures of equilibrium systems. Our group is interested in discovering new types of responses that out-of-equilibrium states enable as well as uncovering how to control their (quantum coherent) dynamics. The ability to dress electron wavefunctions (for e.g. via periodic driving including via light irradiation) opens up a whole new set of tools with which to create designer responses.
One example of unconventional behavior occur in out-of-equilibrium systems prepared via quantum quenches. Recently, we showed that such systems allow a new type of Hall response that occurs even if the instantaneous Hamiltonian preserves time reversal symmetry. Surprisingly, it exhibits a Hall current that persists long after an electric field pulse is applied. This persistent Hall effect arises from processes beyond those captured by linear response, and is a signature of the novel dynamics in out-of-equilibrium systems. Importantly, these can be probed in Dirac-type quenches found in readily available cold-atomic optical lattice experiments/setups.
Related article:
Persistent Hall effect in a Quantum Quench
Justin H. Wilson, Justin C. W. Song, Gil Refael
Pre-print, arXiv:1603.1621 (2016).
