Alexander Punnoose

Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems

We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase, which is stabilized by electronic interactions, from the insulating phase, where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interactions and disorder can explain the observed transport properties and the anomalous enhancement of the spin susceptibility near the metal-insulator transition.

Dilute electron gas near the metal-insulator transition: Role of valleys in silicon inversion layers

Dilute electron gas near the metal-insulator transition in two dimensions.

Flow diagram of the metal–insulator transition in two dimensions

The discovery of the metal–insulator transition (MIT) in two-dimensional electron systems1 challenged the veracity of one of the most influential conjectures2 in the physics of disordered electrons, which states that ‘in two dimensions, there is no true metallic behaviour’; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here, we investigate the interplay between the electron–electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data, we construct a resistance–interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory3. The metallic side of this diagram is accurately described by the renormalization-group theory4 without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches γ2≈0.45—a value in remarkable agreement with the one predicted by theory4.

Fundamental Limits on Wavelength, Efficiency and Yield of the Charge Separation Triad

In an attempt to optimize a high yield, high efficiency artificial photosynthetic protein we have discovered unique energy and spatial architecture limits which apply to all light-activated photosynthetic systems. We have generated an analytical solution for the time behavior of the core three cofactor charge separation element in photosynthesis, the photosynthetic cofactor triad, and explored the functional consequences of its makeup including its architecture, the reduction potentials of its components, and the absorption energy of the light absorbing primary-donor cofactor. Our primary findings are two: First, that a high efficiency, high yield triad will have an absorption frequency more than twice the reorganization energy of the first electron transfer, and second, that the relative distance of the acceptor and the donor from the primary-donor plays an important role in determining the yields, with the highest efficiency, highest yield architecture having the light absorbing cofactor closest to the acceptor. Surprisingly, despite the increased complexity found in natural solar energy conversion proteins, we find that the construction of this central triad in natural systems matches these predictions. Our analysis thus not only suggests explanations for some aspects of the makeup of natural photosynthetic systems, it also provides specific design criteria necessary to create high efficiency, high yield artificial protein-based triads.

Test of the scaling theory in two dimensions in the presence of valley splitting and intervalley scattering in Si-MOSFETs

We show that once the effects of valley splitting and intervalley scattering are incorporated, renormalization group theory consistently describes the metallic phase in silicon metal-oxide-semiconductor field-effect transistors down to the lowest accessible temperatures.

Temperature-induced spontaneous time-reversal symmetry breaking on the honeycomb lattice.

Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is raised in a region where the ground state is a trivial metal.

Renormalization group study of a two-valley system with spin splitting

Renormalization group equations in a two-valley system with valley-splitting and intervalley scattering are derived in the presence of spin-splitting induced by a parallel magnetic field. The relevant amplitudes in different regimes set by the relative strengths of the spin and valley splittings and the intervalley scattering rate are identified. The range of applicability of the standard formula for the magnetoconductance is discussed.

Renormalization group study of intervalley scattering and valley splitting in a two-valley system

Renormalization group equations are derived for the case when both valley splitting and intervalley scattering are present in a two-valley system. A third scaling parameter is shown to be relevant when the two bands are split but otherwise distinct. The existence of this parameter changes the quantitative behavior at finite temperatures, but the qualitative conclusions of the two-parameter theory are shown to be unaffected for realistic choice of parameters.

Quantum theory of structured monochromatic light

Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom that the photons inherit from the classical wave solutions are orthogonal. To test this critical assumption, we quantize the beam-like solutions of the vector Helmholtz equation from first principles to delineate its elementary quantum mechanical degrees of freedom. We show that although the beam-photon operators do not in general satisfy the canonical commutation relations, implying that the photon states they create are not orthogonal, the states are nevertheless bona fide eigenstates of the number and Hamiltonian operators. The explicit representation for the photon operators presented in this work forms a natural basis to study light-matter interactions and quantum information processing at the single photon level.

Role of intervalley scattering in silicon inversion layers near the metal–insulator transition

In recent years systematic experimental studies of the temperature dependence of the resistivity in a variety of dilute, ultra-clean two dimensional electron/hole systems have revived the fundamental question of localization or, alternatively, the existence of a metal–insulator transition in the presence of strong electron–electron interactions in two dimensions. We argue that under the extreme conditions of ultra-clean systems not only is the electron–electron interaction very strong but the role of other system specific properties are also enhanced. In particular, we emphasize the role of valleys in determining the transport properties of the dilute electron gas in silicon inversion layers (Si-MOSFETs). It is shown that for a high quality sample the temperature behavior of the resistivity in the region close to the critical region of the metal–insulator transition is well described by a renormalization group analysis of the interplay of interaction and disorder if the electron band is assumed to have two distinct valleys. The decrease in the resistivity up to five times has been captured in the correct temperature interval by this analysis, without involving any adjustable parameters. The considerable variance in the data obtained from different Si-MOSFET samples is attributed to the sample dependent scattering rate across the two valleys, presenting thereby with a possible explanation for the absence of universal behavior in Si-MOSFET samples of different quality.