Nepal Banerjee | University of Seoul (original) (raw)

Drafts by Nepal Banerjee

Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner th... more Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an order state could developed in 2D spin system in presence of short range isotropic interaction.Very recent discovery of several van der waals magnet revised and redefined our understanding on 2D Heisenberg magnet and its ground state properties.After a rigorous and careful study of several 2D magnetic material we have realized from both experimentally and numerically that the finite size of a 2D system has great impact on the ground state symmetry breaking.Because of that finite size effect more often an anisotropic residual magnetic moment is generated and trigger the spontaneous symmetry breaking at finite temperature (T) and even only presence of short-range interaction we observed the phase transition of that Heisenberg spin system.In this present work we have shown the basic role of finite size,anisotropy during the symmetry breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless transition using classical Monte-carlo simulation and study the effect of anisotropy during the phase transition.We presented the behaviour of different thermodynamic properties of 2D XY spin model system during the Kosterlitz-Thouless (KT) transition.The generic characteristic of KT transition which make it distinct from other critical phenomena is that the peak of heat capacity is not diverging with increase of system size rather peak is decreasing with the increasing of system size near at transition temperature.Here we are observing that behaviour in our present simulation and that specific behaviour help us for classifying the present transition as Kosterlitz-Thouless (KT) transition.

Recent discovery of several van der waals magnetic material introduce to us an extremely challeng... more Recent discovery of several van der waals magnetic material introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material[1][2][3][4][5].More often the simplest spin models which is based on inter-atomic exchange and spin-orbit coupling(SOC) potentially able to capture and explain the critical phenomena of extremely complicated correlated magnetic material[6][7][8][9].In this present work we have attempted to simulate 3D Heisenberg magnet using classical Monte Carlo simulation[10, 11, 12, 13].Our goal is to established a new and simplest spin simulation technique which can help us to understand those van der waals magnet from the microscopic length scale.Here we have been proposing a completely new methodology of classical Monte Carlo simulation of Heisenberg spin which is based on single spin ipping Metropolis algorithm[14].Our state of art simulation technique potentially able to study the phase transition of isotropic XY(O(2)) and XYZ(O(3))spin model very eciently.With this simulation technique we overcome the barrier of critical slowing down during the phase transition in a eective way[15][16][17][18][19][20][21].

Papers by Nepal Banerjee

Nano Letters, Feb 18, 2021

We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with w... more We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak inter-layer versus intra-layer exchange coupling have strong magnetoelectric response that can be detected in dual gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature dependent magnetoelectric response in bilayer CrI 3 at charge neutrality by calculating the gate voltage dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data, and present a simple model for electrical control of magnetism by electrostatic doping.

arXiv (Cornell University), Jun 22, 2015

We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict... more We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict the condition for non-topological phase to the topological phase transition conditions for three different model Hamiltonians in cavity QED lattice. We study these topological quantum phase transition through winding number, which is a topological invariant quantity. We argue that the appearance of topological phase in these systems where the discrete Z 2 symmetry broken. We show that the non-topological state is the vacuum state of the system where each cavity contains fermionic type excitations from light-matter interaction whereas the topological state of system contains Majorana modes of excitations at the end cavity of the lattice.

arXiv (Cornell University), Jun 4, 2023

Recent discovery of several van der waals magnetic material and moire magnet introduce to us an e... more Recent discovery of several van der waals magnetic material and moire magnet introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material[

Norbert Wiener and Claude Shannon introduced information theory independently in 1948. Shannon in... more Norbert Wiener and Claude Shannon introduced information theory independently in 1948. Shannon introduced it to quantify the amount of data that can be transmitted by communication devices. It causes considerable confusion when it was applied to biological system. This theory deals with the capacity of the system to transmit information, not with the meaning or content of the transmitted information. Here, in this paper, we make a critical analysis regarding the applicability of this information theory in molecular biology, gene and specificity and the origin of life. It raises the controversy between the reductionist and non-reductionist in the context of use of information theory in living organism.

Journal of the Physical Society of Japan, 2016

We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict... more We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict the condition for non-topological phase to the topological phase transition conditions for three different model Hamiltonians in cavity QED lattice. We study these topological quantum phase transition through winding number, which is a topological invariant quantity. We argue that the appearance of topological phase in these systems where the discrete Z 2 symmetry broken. We show that the non-topological state is the vacuum state of the system where each cavity contains fermionic type excitations from light-matter interaction whereas the topological state of system contains Majorana modes of excitations at the end cavity of the lattice.

Physical Review B, 2021

Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge ... more Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the topological invariants − giving a symmetry classification table. Here we consider various topological phases protected by different symmetries, and examine how the corresponding topological invariants evolve once the protecting symmetry is spontaneously lost. To our surprise, we find that the topological invariants and edge states can sometimes be robust to symmetry breaking quantum orders. This topological robustness persists as long as the mean-field Hamiltonian in a symmetry breaking ordered phase maintains its adiabatic continuity to the non-interacting Hamiltonian. For example, for a time-reversal symmetric topological phase in 2+1D, we show that the Z2 time-reversal polarization continues to be a good topological invariant even after including distinct time-reversal breaking order parameters. Similar conclusions are drawn for various other symmetry breaking cases. Finally, we discuss that the change in the internal symmetry associated with the spontaneous symmetry breaking has to be accounted for to reinstate the topological invariants into the expected classification table.

Physical Review B, 2020

We present a density functional theory study of the carrier-density and strain dependence of magn... more We present a density functional theory study of the carrier-density and strain dependence of magnetic order in two-dimensional (2D) MAX 3 (M= V, Cr, Mn, Fe, Co, Ni; A= Si, Ge, Sn, and X= S, Se, Te) transition metal trichalcogenides. Our ab initio calculations show that this class of compounds includes wide and narrow gap semiconductors, metals, and half-metals, and that most of these compounds are magnetic. Although antiferromagnetic order is most common, ferromagnetism is predicted in MSiSe 3 for M= Mn, Ni, in MSiTe 3 for M= V, Ni, in MnGeSe 3 , in MGeTe 3 for M=Cr, Mn, Ni, in FeSnS 3 , and in MSnTe 3 for M= V, Mn, Fe. Among these compounds CrGeTe 3 , VSnTe 3 , CrSnTe 3 are ferromagnetic semiconductors. Our calculations suggest that the competition between antiferromagnetic and ferromagnetic order can be substantially altered by strain engineering, and in the semiconductor case also by gating. The associated critical temperatures can be enhanced by means of carrier doping and strains.

Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner th... more Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an order state could developed in 2D spin system in presence of short range isotropic interaction.Very recent discovery of several van der waals magnet revised and redefined our understanding on 2D Heisenberg magnet and its ground state properties.After a rigorous and careful study of several 2D magnetic material we have realized from both experimentally and numerically that the finite size of a 2D system has great impact on the ground state symmetry breaking.Because of that finite size effect more often an anisotropic residual magnetic moment is generated and trigger the spontaneous symmetry breaking at finite temperature (T) and even only presence of short-range interaction we observed the phase transition of that Heisenberg spin system.In this present work we have shown the basic role of finite size,anisotropy during the symmetry breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless transition using classical Monte-carlo simulation and study the effect of anisotropy during the phase transition.We presented the behaviour of different thermodynamic properties of 2D XY spin model system during the Kosterlitz-Thouless (KT) transition.The generic characteristic of KT transition which make it distinct from other critical phenomena is that the peak of heat capacity is not diverging with increase of system size rather peak is decreasing with the increasing of system size near at transition temperature.Here we are observing that behaviour in our present simulation and that specific behaviour help us for classifying the present transition as Kosterlitz-Thouless (KT) transition.

Recent discovery of several van der waals magnetic material introduce to us an extremely challeng... more Recent discovery of several van der waals magnetic material introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material[1][2][3][4][5].More often the simplest spin models which is based on inter-atomic exchange and spin-orbit coupling(SOC) potentially able to capture and explain the critical phenomena of extremely complicated correlated magnetic material[6][7][8][9].In this present work we have attempted to simulate 3D Heisenberg magnet using classical Monte Carlo simulation[10, 11, 12, 13].Our goal is to established a new and simplest spin simulation technique which can help us to understand those van der waals magnet from the microscopic length scale.Here we have been proposing a completely new methodology of classical Monte Carlo simulation of Heisenberg spin which is based on single spin ipping Metropolis algorithm[14].Our state of art simulation technique potentially able to study the phase transition of isotropic XY(O(2)) and XYZ(O(3))spin model very eciently.With this simulation technique we overcome the barrier of critical slowing down during the phase transition in a eective way[15][16][17][18][19][20][21].

Nano Letters, Feb 18, 2021

We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with w... more We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak inter-layer versus intra-layer exchange coupling have strong magnetoelectric response that can be detected in dual gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature dependent magnetoelectric response in bilayer CrI 3 at charge neutrality by calculating the gate voltage dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data, and present a simple model for electrical control of magnetism by electrostatic doping.

arXiv (Cornell University), Jun 22, 2015

We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict... more We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict the condition for non-topological phase to the topological phase transition conditions for three different model Hamiltonians in cavity QED lattice. We study these topological quantum phase transition through winding number, which is a topological invariant quantity. We argue that the appearance of topological phase in these systems where the discrete Z 2 symmetry broken. We show that the non-topological state is the vacuum state of the system where each cavity contains fermionic type excitations from light-matter interaction whereas the topological state of system contains Majorana modes of excitations at the end cavity of the lattice.

arXiv (Cornell University), Jun 4, 2023

Recent discovery of several van der waals magnetic material and moire magnet introduce to us an e... more Recent discovery of several van der waals magnetic material and moire magnet introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material[

Norbert Wiener and Claude Shannon introduced information theory independently in 1948. Shannon in... more Norbert Wiener and Claude Shannon introduced information theory independently in 1948. Shannon introduced it to quantify the amount of data that can be transmitted by communication devices. It causes considerable confusion when it was applied to biological system. This theory deals with the capacity of the system to transmit information, not with the meaning or content of the transmitted information. Here, in this paper, we make a critical analysis regarding the applicability of this information theory in molecular biology, gene and specificity and the origin of life. It raises the controversy between the reductionist and non-reductionist in the context of use of information theory in living organism.

Journal of the Physical Society of Japan, 2016

We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict... more We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict the condition for non-topological phase to the topological phase transition conditions for three different model Hamiltonians in cavity QED lattice. We study these topological quantum phase transition through winding number, which is a topological invariant quantity. We argue that the appearance of topological phase in these systems where the discrete Z 2 symmetry broken. We show that the non-topological state is the vacuum state of the system where each cavity contains fermionic type excitations from light-matter interaction whereas the topological state of system contains Majorana modes of excitations at the end cavity of the lattice.

Physical Review B, 2021

Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge ... more Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the topological invariants − giving a symmetry classification table. Here we consider various topological phases protected by different symmetries, and examine how the corresponding topological invariants evolve once the protecting symmetry is spontaneously lost. To our surprise, we find that the topological invariants and edge states can sometimes be robust to symmetry breaking quantum orders. This topological robustness persists as long as the mean-field Hamiltonian in a symmetry breaking ordered phase maintains its adiabatic continuity to the non-interacting Hamiltonian. For example, for a time-reversal symmetric topological phase in 2+1D, we show that the Z2 time-reversal polarization continues to be a good topological invariant even after including distinct time-reversal breaking order parameters. Similar conclusions are drawn for various other symmetry breaking cases. Finally, we discuss that the change in the internal symmetry associated with the spontaneous symmetry breaking has to be accounted for to reinstate the topological invariants into the expected classification table.

Physical Review B, 2020

We present a density functional theory study of the carrier-density and strain dependence of magn... more We present a density functional theory study of the carrier-density and strain dependence of magnetic order in two-dimensional (2D) MAX 3 (M= V, Cr, Mn, Fe, Co, Ni; A= Si, Ge, Sn, and X= S, Se, Te) transition metal trichalcogenides. Our ab initio calculations show that this class of compounds includes wide and narrow gap semiconductors, metals, and half-metals, and that most of these compounds are magnetic. Although antiferromagnetic order is most common, ferromagnetism is predicted in MSiSe 3 for M= Mn, Ni, in MSiTe 3 for M= V, Ni, in MnGeSe 3 , in MGeTe 3 for M=Cr, Mn, Ni, in FeSnS 3 , and in MSnTe 3 for M= V, Mn, Fe. Among these compounds CrGeTe 3 , VSnTe 3 , CrSnTe 3 are ferromagnetic semiconductors. Our calculations suggest that the competition between antiferromagnetic and ferromagnetic order can be substantially altered by strain engineering, and in the semiconductor case also by gating. The associated critical temperatures can be enhanced by means of carrier doping and strains.