arXiv subjects

A. Srinivasan

Publications and source records attributed to A. Srinivasan.

At least 19 recordsLinked to original sources

arXiv2025

A classification of Markoff-Fibonacci m-triples

We classify all solution triples with Fibonacci components to the equation $a^2+b^2+c^2=3abc+m,$ for positive $m$. We show that for $m=2$ they are precisely $(1,F(b),F(b+2))$, with even $b$; for $m=21$, there exist exactly two Fibonacci solutions $(1,2,8)$ and $(2,2,13)$ and for any other $m$ there exists at most one Fibonacci solution, which, in case it exists, is always minimal (i.e. it is a root of a Markoff tree). Moreover, we show that there is an infinite number of values of $m$ admitting exactly one such solution.

math.NT↗

arXiv2025

Probing Fermi surface parity with spin resolved transverse magnetic focussing

Measurements of the Fermi surface are a fundamental technique for determining the electrical and magnetic properties of solids. In 2D systems, the area and diameter of the Fermi surface is typically measured using Shubnikov-de Haas oscillations and commensurability oscillations respectively. However, these techniques are unable to detect changes in the parity of the Fermi surface (i.e. when +k $\neq$ -k). Here, we show that transverse magnetic focussing can be used to detect such changes, because focussing only measures a well defined section of the Fermi surface and does not average over +k and -k. Furthermore, our results show that focussing is an order of magnitude more sensitive to changes in the Fermi surface than other 2D techniques, and could be used to investigate similar Fermi surface changes in other 2D systems.

cond-mat.mes-hall↗

arXiv2024

Markoff $m$-triples with $k$-Fibonacci components

We classify all solution triples with $k$-Fibonacci components to the equation $x^2+y^2+z^2=3xyz+m,$ where $m$ is a positive integer and $k\geq 2$. As a result, for $m=8$, we have the Markoff triples with Pell components $(F_2(2), F_2(2n), F_2(2n+2))$, for $n\geq 1$. For all other $m$ there exists at most one such ordered triple, except when $k=3,$ $a$ is odd, $b$ is even and $b\geq a+3$, where $(F_3(a),F_3(b),F_3(a+b))$ and $(F_3(a+1),F_3(b-1),F_3(a+b))$ share the same $m$.

math.GM↗

arXiv2023

Minimal triples for a generalized Markoff equation

For a positive integer $m>1$, if the generalized Markoff equation $a^2+b^2+c^2=3abc+m$ has a solution triple, then it has infinitely many solutions. We show that all positive solution triples are generated by a finite set of triples that we call minimal triples. We exhibit a correspondence between the set of minimal triples with first or second element equal to $a$, and the set of fundamental solutions of $m-a^2$ by the form $x^2-3axy+y^2$. This gives us a formula for the number of minimal triples in terms of fundamental solutions, and thus a way to calculate minimal triples using composition and reduction of binary quadratic forms, for which there are efficient algorithms. Additionally, using the above correspondence we also give a criterion for the existence of minimal triples of the form $(1, b, c)$, and present a formula for the number of such minimal triples.

math.NT↗

arXiv2022

Intrinsic Fano factor of nuclear recoils for dark matter searches

Nuclear recoils in germanium and silicon are shown to have much larger variance in electron-hole production than their electron-recoil counterparts for recoil energies between 10 and 200\,keV. This effect--owing primarily to deviations in the amount of energy given to the crystal lattice in response to a nuclear recoil of a given energy--has been predicted by the Lindhard model. We parameterize the variance in terms of an intrinsic nuclear recoil Fano factor which is 24.3$\pm$0.2 and 26$\pm$8 at around 25\,keV for silicon and germanium respectively. The variance has important effects on the expected signal shapes for experiments utilizing low-energy nuclear recoils such as direct dark matter searches and coherent neutrino-nucleus scattering measurements.

physics.ins-det↗

arXiv2022

Spin polarisation and spin dependent scattering of holes in transverse magnetic focussing

In 2D systems with a spin-orbit interaction, magnetic focussing can be used to create a spatial separation of particles with different spin. Here we measure hole magnetic focussing for two different magnitudes of the Rashba spin-orbit interaction. We find that when the Rashba spin-orbit magnitude is large there is significant attenuation of one of the focussing peaks, which is conventionally associated with a change in the spin polarisation. We instead show that in hole systems with a $k^3$ spin-orbit interaction, this peak suppression is due to a change in the scattering of one spin state, not a change in spin polarisation. We also show that the change in scattering length extracted from magnetic focussing is consistent with results obtained from measurements of Shubnikov-de Haas oscillations. This result suggests that scattering must be considered when relating focussing peak amplitude to spin polarisation in hole systems

cond-mat.mes-hall↗

arXiv2022

Gate voltage dependent Rashba spin splitting in hole transverse magnetic focussing

Magnetic focussing of charge carriers in two-dimensional systems provides a solid state version of a mass spectrometer. In the presence of a spin-orbit interaction, the first focussing peak splits into two spin dependent peaks, allowing focussing to be used to measure spin polarisation and the strength of the spin-orbit interaction. In hole systems, the k^3 dependence of the Rashba spin-orbit term allows the spatial separation of spins to be changed in-situ using a voltage applied to an overall top gate. Here we demonstrate that this can be used to control the splitting of the magnetic focussing peaks. Additionally, we compare the focussing peak splitting to that predicted by Shubnikov-de Haas oscillations and k.p bandstructure calculations. We find that the focussing peak splitting is consistently larger than expected, suggesting further work is needed on understanding spin dependent magnetic focussing.

cond-mat.mes-hall↗

arXiv2020

Improving reproducibility of quantum devices with completely undoped architectures

The reproducible operation of quantum electronic devices is a key requirement for future quantum information processing and spintronics applications. Traditionally quantum devices have been fabricated from modulation doped heterostructures, where there is an intrinsic lack of reproducibility due to the random potential from ionized donors. Here we show that we can greatly improve reproducibility over modulation doped devices by using a completely undoped architecture, with superior uniformity in the confinement potential and more consistent operating voltages for both electron and hole devices. Our results demonstrate that undoped heterostructures have significant advantages over modulation doping for reproducible manufacturing of quantum devices.

cond-mat.mes-hall↗

arXiv2020

Non-linear spin filter for non-magnetic materials at zero magnetic field

The ability to convert spin accumulation to charge currents is essential for applications in spintronics. In semiconductors, spin-to-charge conversion is typically achieved using the inverse spin Hall effect or using a large magnetic field. Here we demonstrate a general method that exploits the non-linear interactions between spin and charge currents to perform all-electrical, rapid and non-invasive detection of spin accumulation without the need for a magnetic field. We demonstrate the operation of this technique with ballistic GaAs holes as a model system with strong spin-orbit coupling, in which a quantum point contact provides the non-linear energy filter. This approach is generally applicable to electron and hole systems with strong spin orbit coupling.

cond-mat.mes-hall↗

arXiv2020

From Bad to Worse: Airline Boarding Changes in Response to COVID-19

Airlines have introduced a back-to-front boarding process in response to the COVID-19 pandemic. It is motivated by the desire to reduce passengers' likelihood of passing close to seated passengers when they take their seats. However, our prior work on the risk of Ebola spread in airplanes suggested that the driving force for increased exposure to infection transmission risk is the clustering of passengers while waiting for others to stow their luggage and take their seats. In this work, we examine whether the new boarding processes lead to increased or decreased risk of infection spread. We also study the reasons behind the risk differences associated with different boarding processes. We accomplish this by simulating the new boarding processes using pedestrian dynamics and compare them against alternatives. Our results show that back-to-front boarding roughly doubles the infection exposure compared with random boarding. It also increases exposure by around 50% compared to a typical boarding process prior to the outbreak of COVID-19. While keeping middle seats empty yields a substantial reduction in exposure, our results show that the different boarding processes have similar relative strengths in this case as with middle seats occupied. We show that the increased exposure arises from the proximity between passengers moving in the aisle and while seated. Our results suggest that airlines either revert to their earlier boarding process or adopt the better random process.

physics.soc-ph↗

arXiv2017

Mechanisms for strong anisotropy of in-plane g-factors in hole based quantum point contacts

In-plane hole g-factors measured in quantum point contacts based on p-type heterostructures strongly depend on the orientation of the magnetic field with respect to the electric current. This effect, first reported a decade ago and confirmed in a number of publications, has remained an open problem. In this work, we present systematic experimental studies to disentangle different mechanisms contributing to the effect and develop the theory which describes it successfully. We show that there is a new mechanism for the anisotropy related to the existence of an additional $B_+k_-^4σ_+$ effective Zeeman interaction for holes, which is kinematically different from the standard single Zeeman term $B_-k_-^2σ_+$ considered until now.

cond-mat.mes-hall↗

arXiv2017

Detection and control of spin-orbit interactions in a GaAs hole quantum point contact

We investigate the relationship between the Zeeman interaction and the inversion asymmetry induced spin orbit interactions (Rashba and Dresselhaus SOIs) in GaAs hole quantum point contacts. The presence of a strong SOI results in crossing and anti-crossing of adjacent spin-split hole subbands in a magnetic field. We demonstrate theoretically and experimentally that the anti-crossing energy gap depends on the interplay between the SOI terms and the highly anisotropic hole g tensor, and that this interplay can be tuned by selecting the crystal axis along which the current and magnetic field are aligned. Our results constitute independent detection and control of the Dresselhaus and Rashba SOIs in hole systems, which could be of importance for spintronics and quantum information applications.

cond-mat.mes-hall↗

arXiv2017

Electrical control of the sign of the g-factor in a GaAs hole quantum point contact

Zeeman splitting of 1D hole subbands is investigated in quantum point contacts (QPCs) fabricated on a (311) oriented GaAs-AlGaAs heterostructure. Transport measurements can determine the magnitude of the g-factor, but cannot usually determine the sign. Here we use a combination of tilted fields and a unique off-diagonal element in the hole g-tensor to directly detect the sign of g*. We are able to tune not only the magnitude, but also the sign of the g-factor by electrical means, which is of interest for spintronics applications. Furthermore, we show theoretically that the resulting behavior of g* can be explained by the momentum dependence of the spin-orbit interaction.

cond-mat.mes-hall↗

arXiv2016

$T^3$-interferometer for atoms

The quantum mechanical propagator of a massive particle in a linear gravitational potential derived already in 1927 by Earle H. Kennard \cite{Kennard,Kennard2} contains a phase that scales with the third power of the time $T$ during which the particle experiences the corresponding force. Since in conventional atom interferometers the internal atomic states are all exposed to the same acceleration $a$, this $T^3$-phase cancels out and the interferometer phase scales as $T^2$. In contrast, by applying an external magnetic field we prepare two different accelerations $a_1$ and $a_2$ for two internal states of the atom, which translate themselves into two different cubic phases and the resulting interferometer phase scales as $T^3$. We present the theoretical background for, and summarize our progress towards experimentally realizing such a novel atom interferometer.

quant-ph↗

arXiv2016

Manifestation of a non-abelian gauge field in a p-type semiconductor system

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms and many others. However, the non-abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In the present paper we report the first observation of a non-abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-abelian gauge field was controlled by the components of the magnetic field in the 2D plane.

cond-mat.mes-hall↗

arXiv2016

Self-Propelled Pedestrian Dynamics Model: Application to Passenger Movement and Infection Propagation in Airplanes

Reducing the number of contacts between passengers on an airplane can potentially curb the spread of infectious diseases. In this paper, a social force based pedestrian movement model is formulated and applied to evaluate the movement and contacts among passengers during boarding and deplaning of an airplane. Within the social force modeling framework, we introduce location dependence on the self-propelling momentum of pedestrian particles. The model parameters are varied over a large design space and the results are compared with experimental observations to validate the model. This model is then used to assess the different approaches to minimize passenger contacts during boarding and deplaning of airplanes. We find that smaller aircrafts are effective in reducing the contacts between passengers. Column wise deplaning and random boarding are found to be two strategies that reduced the number of contacts during passenger movement, and can potentially lower the likelihood of infection spread.

physics.soc-ph↗

arXiv2013

Using a tunable quantum wire to measure the large out-of-plane spin splitting of quasi two-dimensional holes in a GaAs nanostructure

The out-of-plane g-factor g_perp for quasi-2D holes in a (100) GaAs heterostructure is studied using a variable width quantum wire. A direct measurement of the Zeeman splitting is performed in a magnetic field applied perpendicular to the 2D plane. We measure an out-of-plane g-factor up to g_perp = 5, which is larger than previous optical studies of g_perp, and is approaching the long predicted but never experimentally verified out-of-plane g-factor of 7.2 for heavy holes.

cond-mat.mes-hall↗

arXiv2010

Piezoelectric rotator for studying quantum effects in semiconductor nanostructures at high magnetic fields and low temperatures

We report the design and development of a piezoelectric sample rotation system, and its integration into an Oxford Instruments Kelvinox 100 dilution refrigerator, for orientation-dependent studies of quantum transport in semiconductor nanodevices at millikelvin temperatures in magnetic fields up to 10T. Our apparatus allows for continuous in situ rotation of a device through >100deg in two possible configurations. The first enables rotation of the field within the plane of the device, and the second allows the field to be rotated from in-plane to perpendicular to the device plane. An integrated angle sensor coupled with a closed-loop feedback system allows the device orientation to be known to within +/-0.03deg whilst maintaining the sample temperature below 100mK.

cond-mat.mes-hall↗