Research overview

Our group conducts research in condensed-matter theory. We study semiconductors, nanostructures, graphene, and other two-dimensional crystals. We are interested in electronic, excitonic, photonic, and plasmonic properties of such materials.

Publications

All known superfluid and superconducting states of condensed matter are enabled by composite bosons (atoms, molecules and Cooper pairs) made of an even number of fermions. Temperatures where such macroscopic quantum phenomena occur are limited by the lesser of the binding energy and the degeneracy temperature of the bosons. High-critical temperature cuprate superconductors set the present record of~ 100 K. Here we propose a design for artificially structured materials to rival this record. The main elements of the structure are two monolayers of a transition metal dichalcogenide separated by an atomically thin spacer. Electrons and holes generated in the system would accumulate in the opposite monolayers and form bosonic bound states—the indirect excitons. The resultant degenerate Bose gas of indirect excitons would exhibit macroscopic occupation of a … Link

M.M. Fogler, L.V. Butov, and K.S. Novoselov. Nature communications 5, 4555

If bosonic particles are cooled down below the temperature of quantum degeneracy, they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis of a number of fundamental phenomena in physics, including superconductivity, superfluidity and Bose– Einstein condensation 1, 2. Spontaneous coherence is the key characteristic of condensation in momentum space 3. Excitons—bound pairs of electrons and holes—form a model system to explore the quantum physics of cold bosons in solids 4, 5. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy owing to their long lifetimes 6. Here we report measurements of spontaneous coherence in a gas of indirect excitons. We found that … Link

Alexander A High, Jason R Leonard, Aaron T Hammack, Michael M Fogler, Leonid V Butov, Alexey V Kavokin, Kenneth L Campman, and Arthur C Gossard. Nature 483 (7391), 584

We report on the observation of the Pancharatnam-Berry phase in a condensate of indirect excitons realized in a GaAs coupled quantum well structure. Our measurements indicate long range coherent spin transport … The Pancharatnam-Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian gov- erning the evolution of the system. It was discovered by Pancharatnam in studies of polarized light and introduced by Berry as a topological phase for matter wave functions. Excitons are matter waves that directly transform to photons inheriting their coherence … Link

J.R. Leonard, A.A. High, A.T. Hammack, M.M. Fogler, L.V. Butov, K.L. Campman, and A.C. Gossard. CLEO: QELS_Fundamental Science, FM3H. 3


Graphene and other 2D materials

Graphene has many superlative properties such as enormous mechanical strength, excellent electrical and heat conductivity, and strong interaction with light. Our theoretical work on graphene includes investigation of electron interaction and transport, nanomechanics, plasmonic and polaritonic characteristics, ultrafast optical response, solid-state hydrodynamics, etc. Graphene is a member of a large family of 2D and quasi-2D physical systems known as van der Waals (vdW) materials. We also study multi-component vdW systems or heterostructures composed of graphene, hexagonal boron nitride, and transition metal dichalcogenides. Such heterostructures can exhibit emergent phenomena not found in its individual components. 


Selected publications

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing, topological protection, anddipole-forbidden absorption. A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes. Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale... Link

G.X. Ni, A.S. McLeod, Z. Sun, L. Wang, L. Xiong, K.W. Post, S.S. Sunku, B-Y Jiang, J. Hone, C.R. Dean, M.M. Fogler, and D.N. Basov. Nature 557, 530–533 (2018)

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory. Link

Zhiyuan Sun, Dmitri N Basov, and Michael M Fogler. PNAS 115, 3285-3289 (2018)

We theoretically investigate charged collective modes in a two-dimensional conductor with hot electrons where the instantaneous mode frequencies gradually increase or decrease with time. We show that the loss compensation or even amplification of the modes may occur. We apply our theory to two types of collective modes in graphene, the plasmons and the energy waves, which can be probed in optical pump-probe experiments. Link

Zhiyuan Sun, D. N. Basov, and M. M. Fogler. Physical Review Letters 117, 076805 (2016)


Nano Optics

Our interest in near-field optics has been stimulated by imaging experiments that probe material properties with nanoscale spatial resolution, beating the diffraction limit by many orders of magnitude. We have investigated fundamental theory as well as applications of nano-optics to a wide range of systems including van der Waals materials, correlated electron systems, superconductors, and topological insulators.


Selected publications

Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves... Link

B.-Y. Jiang, L. M. Zhang, A. H. Castro Neto, D. N. Basov, and M. M. Fogler. Journal of Applied Physics 119, 054305 (2016)

We present a comprehensive study of the reflection of normally incident plasmon waves from a low-conductivity 1D junction in a 2D conductive sheet. Rigorous analytical results are derived in the limits of wide and narrow junctions. Two types of phenomena determine the reflectance, the cavity resonances within the junction and the capacitive coupling between the leads. The resonances give rise to alternating strong and weak reflection but are vulnerable to plasmonic damping. The capacitive coupling, which is immune to damping, induces a near perfect plasmon reflection in junctions narrower than 1/10 of the plasmon wavelength. Our results are important for infrared 2D plasmonic circuits utilizing slot antennas, split gates or nanowire gates. They are also relevant for the implementation of nanoscale terahertz detectors, where optimal light absorption coincides with the maximal junction reflectance. Link

Bor-Yuan Jiang, Eugene J. Mele, and Michael M. Fogler. Optics Express 26, 17209-17226 (2018)

Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and surface-confined polaritons are computed for spheroidal nanogranules of hexagonal boron nitride, a natural hyperbolic crystal. The field distribution created by polaritons excited by an external dipole source is predicted to exhibit raylike patterns due to classical periodic orbits. Near-field infrared imaging and Purcell-factor measurements are suggested to test these predictions. Link

Zhiyuan Sun, Á. Gutiérrez-Rubio, D.N. Basov, and M.M. Fogler. Nano letters 15, 4455-4460 (2015)


Excitons

An exciton is a bound state of an electron and a hole in a semiconductor. It is a composite bosonic quasiparticle that can transport energy and spin. Our research focuses on excitons in 2D systems, including quantum wells in bulk semiconductors and atomically thin van der Waals materials. We are especially interested in indirect (aka charge transfer) excitons that possess a permanent dipole moment. We explore both fundamental physics and device application of such excitons. We are a part of the UCSD Center for Excitonic Devices supported by the NSF and by the NERC, a subsidiary of SRC.


Selected publications

All known superfluid and superconducting states of condensed matter are enabled by composite bosons (atoms, molecules and Cooper pairs) made of an even number of fermions. Temperatures where such macroscopic quantum phenomena occur are limited by the lesser of the binding energy and the degeneracy temperature of the bosons. High-critical temperature cuprate superconductors set the present record of~ 100 K. Here we propose a design for artificially structured materials to rival this record. The main elements of the structure are two monolayers of a transition metal dichalcogenide separated by an atomically thin spacer. Electrons and holes generated in the system would accumulate in the opposite monolayers and form bosonic bound states—the indirect excitons. The resultant degenerate Bose gas of indirect excitons would exhibit macroscopic occupation of a … Link

M.M. Fogler, L.V. Butov, and K.S. Novoselov. Nature Communications 5, 4555 (2014)

The Pancharatnam–Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian governing the evolution of the system. Here, we report on the observation of the Pancharatnam–Berry phase in a condensate of indirect excitons (IXs) in a GaAs-coupled quantum well structure. The Pancharatnam–Berry phase is directly measured by detecting phase shifts of interference fringes in IX interference patterns. Correlations are found between the phase shifts, polarization pattern of IX emission, and onset of IX spontaneous coherence. The evolving Pancharatnam–Berry phase is acquired due to coherent spin precession in IX condensate and is observed with no decay over lengths exceeding 10 μm indicating long-range coherent spin transport. Link

J.R. Leonard, A.A. High, A.T. Hammack, M.M. Fogler, L.V. Butov, K.L. Campman, and A.C. Gossard. Nature Communications 9, 2158 (2018)

If bosonic particles are cooled down below the temperature of quantum degeneracy, they can spontaneously form a coherent state in which individual matter waves synchronize and combine. Spontaneous coherence of matter waves forms the basis of a number of fundamental phenomena in physics, including superconductivity, superfluidity and Bose– Einstein condensation.. Spontaneous coherence is the key characteristic of condensation in momentum space. Excitons—bound pairs of electrons and holes—form a model system to explore the quantum physics of cold bosons in solids. Cold exciton gases can be realized in a system of indirect excitons, which can cool down below the temperature of quantum degeneracy owing to their long lifetimes. Here we report measurements of spontaneous coherence in a gas of indirect excitons. We found that … Link

A. A. High, J. R. Leonard, A. T. Hammack, M. M. Fogler, L. V. Butov, A. V. Kavokin, K. L. Campman, and A. C. Gossard. Nature 483, 584–588 (2012)


Other Work On Low-Dimensional Systems

Low dimensional systems are a fertile ground for investigating quantum, interaction, and disorder effects. Our early work in this area included investigation of 2D electron gases under the conditions of the quantum Hall effect, predicting the formation of bubble and stripe phases in the ground state at high Landau levels. We have also studied electron correlations and transport in 1D conductors.

Selected publications

We consider a clean two-dimensional electron liquid in a weak magnetic field where N≫1 lower Landau levels are completely filled, while the upper level is only partially filled. Due to a screening by the lower Landau levels, the repulsive interaction between any two electrons at the upper level as a function of the separation between the guiding centers of their cyclotron orbits abruptly drops at the distance of two cyclotron radii. Such a ‘‘box-like’’ component in the interaction potential makes the uniform distribution of the electron density at the upper Landau level unstable, and domains with filling factor equal to one and zero are formed. The shape of domains is studied both analytically and numerically... Link

M.M. Fogler, A.A. Koulakov, and B.I. Shklovskii. Physical Review B 54, 1853 (1996)

The ground-state energy and the density correlation function of the electron liquid in a thin one-dimensional wire are computed. The calculation is based on an approximate mapping of the problem with a realistic Coulomb interaction law onto exactly solvable models of mathematical physics. This approach becomes asymptotically exact in the limit of a small wire radius but remains numerically accurate even for modestly thin wires. Link

Michael M. Fogler. Physical Review Letters 94, 056405 (2005)

The dependence of hopping conductance on temperature and voltage for an ensemble of modestly long one-dimensional wires is studied numerically using the shortest-path algorithm. In a wide range of parameters this dependence can be approximated by a power law rather than the usual stretched-exponential form. The relation to recent experiments and prior analytical theory is discussed. Link

A. S. Rodin and M. M. Fogler. Physicial Review Letters 105, 106801 (2010)