The majority of my work is in the field of quantum condensed matter physics. Most of it deals with the interplay between the two dominant energy scales at the quantum scale: the quantum kinetic energy and the Coulomb interaction. A major theme is describing strongly-correlated electronic systems, which cannot be adequately described using conventional theories of either solid or gaseous states of matter.

Read on for a few particular examples.

**Using 2D materials to engineer unusual quasiparticles**

The experimental isolation of graphene one decade ago ushered in a revolution in physics and materials science, because it allowed us to think about assembling materials one atomic layer at a time. This revolution continues today, bolstered by developments in other two-dimensional (2D) materials, including bilayer graphene, BN, MoS_{2}, and TaS_{2}, and a variety of others Importantly, these materials span the full spectrum of electronic behaviors, from metals to semimetals to insulators. This diverse palette allows us to dream about engineering layered materials with completely customizable electronic properties.

At a more basic level, the ability to layer different materials raises the possibility of making custom-tailored quasiparticles. Indeed, by coupling electronic excitations in one layer to very different excitations in adjacent layers, one can potentially create unusual quasiparticles whose properties are distinct from those in either layer separately. Such quasiparticles can also, in general, have properties that respond in unusual ways to applied fields.

Some specific current projects involve hyperbolic polaritons in boron nitride, and making interlayer excitons using materials with "Mexican-hat" shaped dispersion relation.

Relevant past publications:

*"Interlayer excitons with tunable dispersion relation"*, BS, Phys. Rev. B**93**, 235110 (2016)*"Chemical potential and compressibility of quantum Hall bilayer excitons"*, BS, Phys. Rev. B**93**, 085436 (2016)*"Hydrogen atom with a Mexican hat"*, BS, B. I. Shklovskii, and M. B. Voloshin, Phys. Rev. B**89**, 041405(R) (2014)

**Long-ranged disorder and nonlinear screening in exotic materials**

In solid state systems, disorder is usually described in terms of impurities that scatter electrons moving through the material, and thereby decrease the conductivity. But when the disorder comes from poorly screened charged impurities, its effect can be much more dramatic, and its effects counterintuitive. This is particularly the case for materials with vanishing density of states, such as insulators and semimetals, which have no intrinsic ability to screen charged impurities. In such materials screening happens only in a nonlinear way that involves significant band bending and the formation of electron/hole puddles.

Part of my research involves working out the consequence of these kinds of effects for the behavior of exotic new materials. A range of new insulators and semimetals have been proposed recently, arising from our growing understanding of topological features in electron band structure. But the robustness of these features against the presence of charged impurities is not always clear, and the standard arguments designed for short-ranged disorder often fail to describe them. I have been particularly interested in describing the effects of charged impurities on the conductivity in topological insulators, Weyl semimetals, and node line semimetals.

Relevant past publications:

*Coulomb disorder in 3D Dirac systems,*BS, Phys. Rev. B**90**, 060202(R)*Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators*, BS, T. Chen, and B. I. Shklovskii, JETP**117**, 579 (2013).*Theory of the random potential and conductivity at the surface of a topological insulator*, BS and B.I. Shklovskii, Phys. Rev. B**87**, 075454 (2013).*Why is the bulk resistivity of topological insulators so small?*, BS, T. Chen, and B. I. Shklovskii, Phys. Rev. Lett.**109**, 176801 (2012).

**"Negative compressibility" through strong correlations**

Negative compressibility is a phenomenon in which a system lowers its energy with increasing density. While this would seemingly imply that the system is unstable and must collapse, there is an interesting manifestation of negative compressibility in (stable) systems of correlated electrons. In particular, in situations when electron-electron repulsion is much stronger than the Fermi energy, electrons adopt a strongly-correlated arrangement that is reminiscent of an electron crystal. This almost-crystal is much more easily compressible then a uniform electron gas, and this can lead to an apparent "negative" compressibility.

The effect becomes particularly noticeable in capacitance measurements of low-dimensional electron gases. My work has focused on trying to understand these compressibility effects, including their manifestation in graphene, Quantum Hall systems, and carbon nanotubes. Understanding its strength and nature allows one to use capacitance measurements as a probe of electron-electron correlations.

Relevant past publications:

*Correlation effects in the capacitance of a gated carbon nanotube*, H. Fu, B. I. Shklovskii, and BS, Phys. Rev. B**91**, 155118 (2015).*Effect of dielectric response on the quantum capacitance of graphene in a strong magnetic field*, BS, G. L. Yu, A. V. Kretinin, A. K. Geim, K. S. Novoselov, and B. I. Shklovskii, Phys. Rev. B**88**, 155417 (2013).*Universal behavior of repulsive two-dimensional fermions in the vicinity of the quantum freezing point*, M. Babadi, BS, M. M. Fogler, and E Demler, Europhysics Letters 103, 16002 (2013).*Giant capacitance of a plane capacitor with a two-dimensional electron gas in a magnetic field*, BS and B. I. Shklovskii, Phys. Rev. B**87**, 035409 (2013).*Simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions*, BS and M. M. Fogler, Phys. Rev. B**82**, 201306(R) (2010).*Anomalously large capacitance of a plane capacitor with a two-dimensional electron gas*, BS and B. I. Shklovskii, Phys. Rev. B**82**, 155111 (2010).

**Electron conduction in nanocrystal-based metamaterials**

In the traditional view of crystalline materials, each "site" (usually, an atomic orbital) within the crystal is characterized by a particular electronic energy level, and is coupled to other sites by quantum tunneling. The electronic properties of the material arise from a combination of the distribution of energy levels between sites and the strength of the tunneling. But the question now arises: what if each site were characterized not by a single energy level but by a completely tunable spectrum of energy levels? Could we get from the superlattice any kind of electronic/optical behavior that we wanted?

Such is the promise of nanocrystal (NC)-based supercrystals, in which the tunable spectrum of quantum dots is combined with the collective effects of a superlattice to create novel electronic properties. The experimental study of NCs is entering a mature phase, in which the size, shape, and composition of synthesized NCs can be chosen with tremendous precision, and nearly defect-free superlattices of such NCs can be created over macroscopic length scales. My own work has adapted classic theories of hopping conduction to examine how the electron transport through these arrays can be tailored using semiconductor bandgaps, magnetism, and superconductivity.

Relevant past publications:

*Carrier Transport in Films of Alkyl-Ligand-Terminated Silicon Nanocrystals*, T. Chen, BS, W. Xie, B. I. Shklovskii, and U. R. Kortshagen, J. Phys Chem C 118, 19580 (2014).*Electrostatic tuning of the properties of disordered indium-oxide films near the superconductor-insulator transition*, Yeonbae Lee, Aviad Frydman, Tianran Chen, BS, and A. M. Goldman, Phys. Rev. B 88, 024509 (2013).*Coulomb gap triptychs, √2 effective charge, and hopping transport in periodic arrays of superconductor grains*, T. Chen, BS, and B. I. Shklovskii, Phys. Rev. B**86**, 045135 (2012).*Coulomb Gap Triptych in a Periodic Array of Metal Nanocrystals*, T. Chen, BS, and B. I. Shklovskii, Phys. Rev. Lett.**109**, 126805 (2012).*Theory of hopping conduction in arrays of doped semiconductor nanocrystals*, BS, T. Chen, and B. I. Shklovskii, Phys. Rev. B**85**, 205316 (2012).