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Topic of Interest 1

Topic of Interest 2

Topic of Interest 3

Topic of Interest 4

The topics below indicate my interests thus far. In the future, I hope to explore also some new directions.

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What's New

a) A recent paper presents a numerical simulation of quantum Hall transport in the doubly connected "anti Hall bar within a Hall bar" configuration, which is a rectangular frame-shaped 2D electron system that is simultaneously excited by two current sources in order to realize two simultaneous ordinary and quantized Hall effects in a single specimen. The questions of interest are: how does the current flow in the sample? And, how is it possible to realize two Hall effects at once? The details appear in:

Voltage and current distribution in a doubly connected two-dimensional quantum Hall system, M. Oswald, J. Oswald, and R. G. Mani, Phys. Rev. B 72, 035334 (2005), (Get PDF) [*].


b) Are the microwave- and Terahertz- radiation-induced zero-resistance states destroyed by a small (< 0.5 Tesla) applied magnetic field that lies in the plane of the two-dimensional electron system? This is an interesting problem that could provide new insight into the origin of radiation-induced zero-resistance states. It looks like the zero-resistance states do disappear when the magnetic field appears mostly in the plane of the 2D electron system. However, our tilted magnetic field studies, which provide for an inplane B-component, suggest that the decay of the radiation-induced magnetoresistance with increasing tilt angle can be mostly understood as a consequence of reduced photon flux on the specimen. The details can be found in:

Radiation-induced oscillatory magnetoresistance in a tilted magnetic field in GaAs/AlGaAs devices, R. G. Mani, Phys. Rev. B 72, 075327 (2005), (Get PDF) [*].

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1. Radiation induced zero-resistance states

The detection of a zero-resistance state in a metal introduced superconductivity. More recently, the discovery of quantum Hall effects (QHE) stemmed from studies of zero-resistance states at low temperatures, T, and high magnetic fields, B, in the 2-Dimensional Electron System (2DES).

Quantum Hall effect and superconductivity have shown that a complex electronic system can exhibit instantly-recognizable physical phenomena. They have also demonstrated that observations of vanishing resistance in unusual settings can be a harbinger of new physics.

Recently, novel vanishing resistance states have been reported in an unexpected setting - the ultra high mobility 2DES irradiated by low energy photons, at low temperatures, in the low magnetic field, large filling factor limit. Our experiments indicated that GaAs/AlGaAs heterostructures including a 2DES exhibit vanishing diagonal resistance about B = (4/5) B_{f} and B = (4/9) B_{f}, where B_{f} = 2 \pi f m*/e, m* is an effective mass, e is the electron charge, and f is the radiation frequency. Remarkably, in this instance, vanishing resistance in the 2DES did not produce plateaus in the Hall resistance, although the diagonal resistance exhibited activated transport and zero-resistance states, similar to QHE.

This phenomena has generated theoretical interest in identfying the underlying physical mechanism. Our ongoing experimental studies aim to examine some of the outstanding questions in this area. Further information relating to the phenomenology in this effect may be obtained by following the references given below.

References: 

Zero-resistance states induced by electromagnetic-wave excitation in GaAs/AlGaAs heterostructures, R. G. Mani, J. H. Smet, K. von Klitzing, V. Narayanamurti, W. B. Johnson, and V. Umansky, Nature (London) 420, 646 (2002) (Get PDF).[Copyright: Nature Publishing Group]

Microwaves induce vanishng resistance in two-dimensional electron systems, R. Fitzgerald, Physics Today 56 (4), 24 (2003). (Get Pdf). [Copyright: American Institute of Physics]

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2. Spin manipulation for quantum information processing

The interest in spintronics and spin-basedsemiconductor quantum computing has increased the regard for the spin degree of freedom, and especially semiconductor systems that allow for the control of spin. Low Dimensional Electronic Systems[LDES] have consequently drawn special attention because, at low temperatures, they include properties, which make possible relatively simple electrical detection- and radio-frequency (rf) / microwave control- of nuclear- and electronic- spins. For example, microwave-induced Electron Spin Resonance (ESR) can be resistively detected in the quantum Hall regime, the ESR can be utilized to build up nuclear polarization via the flip-flop interaction, and the nuclear spin state can be subsequently characterized, also using an electrical measurement, by examining the back action of the nuclear magnetic field on the ESR. Such electrical characterization techniques are valuable because they can potentially help to characterize the spin state over microscopic length scales.

Our studies have examined the above-mentioned approach towards the initialization, control, and readout of the nuclear spin polarization in spin domains within the LDES, with a view towards spintronic and quantum computing applications. The goals have been to develop the capability to measure and control a spin domain, to scale down its size to reduce the number of spins per domain, and to finally realize the capacity to simultaneously handle, i.e., measure and control, a multiplicity of domains on a single chip. Further information relating to this project may be obtained by following the reference given below.

Reference: Nuclear spin based quantum information processing at high magnetic fields, R. G. Mani, W. B. Johnson, and V. Narayanamurti, Nanotechnology 14, 515 (2003) (Get PDF).[Copyright: Institute of Physics Publishing]

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3. "Anti Hall bar within a Hall bar "and dual simultaneous Hall effects

Multiply connected specimens have long enjoyed a special role in the understanding of quantum Hall effects. Yet, paradoxically, in experiment, the Hall measurement is widely carried out in the simply connected Hall bar configuration - a geometry that typically does not include holes. A problem of interest has been, therefore, to examine and generalize the Hall effect measurement to multiply connected specimens. That is, to answer the question: how should the experimenter develop and measure Hall's effect in a multiply connected sample?

Our experimental investigation of this problem identified an elementary multiply-connected "dual" of the Hall bar, called the "anti Hall bar," which can help to realize a Hall effect within the interior boundary of a doubly connected specimen, when current is injected via contacts lying on the interior boundary. Further, our studies also indicated that configuration superposition is possible in experiment, meaning that the "anti Hall bar" configuration can be placed within the Hall bar configuration, and two currents can be simultaneously be applied to the specimen. Surprisingly, this "anti Hall bar within a Hall bar" configuration helps to realize two simultaneous Hall effects in a single specimen.

This basic advance in Hall effect measurement technology seems to make possible new experimental configurations which appear to be very useful in examining the current distribution and the role of topology under quantum Hall conditions. Further, such configurations seem to provide for further flexibility in Hall effect device engineering, in the search for an improved magnetic field sensor. Additional information relating on this topic may be obtained by following the references given below.

References:

Hall effect under null current conditions, R. G. Mani and K. von Klitzing, Appl. Phys. Lett. 64, 1262 (1994) (Get PDF).[Copyright: American Institute of Physics]

Dual ordinary, integral quantum, and fractional quantum Hall effects in partially gated doubly connected GaAs/AlGaAs heterostructure devices, R. G. Mani, Phys. Rev. B 55, 15838 (1998) (Get PDF).[Copyright: American Physical Society]

Hall effect device with current and Hall voltage connection points, R. G. Mani et al., U. S. Patent No. 5,646,527 (1997) (Get PDF)

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4. Self-similarity in quantized Hall effect

Imagine electrons living in flatland, i.e., electrons distributed on- and confined to- a two dimensional plane. Imagine further that (a) there is a strong magnetic field applied perpendicular to the plane to quench the kinetic energy, (b) the temperature is sufficiently low, and (c) the disorder potential due to impurities is weak. Experiment has shown that this regime can exhibit so-called fractional quantized Hall effect.

In the situation envisaged above, an examination of the two-dimensional potential landscape from the perspective obtained upon sitting atop an individual electron suggests that the effective potential experienced by an electron, in a single particle picture, might consist of the usual confining term in the z-direction, plus a plane periodic potential resulting from the Coulomb interaction with neighboring electrons. Then, this problem appears to resemble the Hofstader butterfly problem, with the difference that the periodic potential in this case orginates from the presence of the neighboring electrons. In such a situation, one expects to observe self-similarity in the electronic spectrum, and perhaps a manifestation of this self-similarity in the experimentally measured transport characteristics. In the reference given below, we demonstrate fractal characteristics in fractional quantized Hall effect and suggest that the observed self similarity provides evidence for the picture described above.

Reference: Fractional quantum Hall effects as an example of fractal geometry in nature, R. G. Mani and K. von Klitzing, Z. Phys. B 100, 635 (1996) (Get PDF).[Copyright: Springer Verlag]

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