HOME

TheInfoList



OR:

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which electrons bind magnetic flux lines to make new
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exa ...
s, and excitations have a fractional
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
and possibly also fractional statistics. The 1998
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
was awarded to
Robert Laughlin Robert Betts Laughlin (born November 1, 1950) is the Anne T. and Robert M. Bass Professor of Physics and Applied Physics at Stanford University. Along with Horst L. Störmer of Columbia University and Daniel C. Tsui of Princeton Universi ...
,
Horst Störmer Horst may refer to: Science * Horst (geology), a raised fault block bounded by normal faults or graben People * Horst (given name) * Horst (surname) * ter Horst, Dutch surname * van der Horst, Dutch surname Places Settlements Germany * Hor ...
, and
Daniel Tsui Daniel Chee Tsui (, born February 28, 1939) is a Chinese-born American physicist, Nobel laureate, and the Arthur Legrand Doty Professor of Electrical Engineering, Emeritus, at Princeton University. Tsui's areas of research include electrical prop ...
"for their discovery of a new form of quantum fluid with fractionally charged excitations" Laughlin's explanation only applies to fillings \nu = 1/m where m is an odd integer. The microscopic origin of the FQHE is a major research topic in condensed matter physics.


Introduction

The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the
electron gas An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. T ...
condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. As in the integer
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
, the Hall resistance undergoes certain
quantum Hall transitions Quantum Hall transitions are the quantum phase transitions that occur between different robustly quantized electronic phases of the quantum Hall effect. The robust quantization of these electronic phases is due to strong localization of electron ...
to form a series of plateaus. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) :\nu = p/q,\ where p and q are integers with no common factors. Here ''q'' turns out to be an odd number with the exception of two filling factors 5/2 and 7/2. The principal series of such fractions are :, , , \mbox and :, , , \mbox There were several major steps in the theory of the FQHE. *Laughlin states and fractionally-charged
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exa ...
s: this theory, proposed by Laughlin, is based on accurate trial wave functions for the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
at fraction 1/q as well as its quasiparticle and quasihole excitations. The excitations have fractional charge of magnitude e^*=. *Fractional exchange statistics of
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exa ...
s: Bertrand Halperin conjectured, and Daniel Arovas, J. R. Schrieffer, and
Frank Wilczek Frank Anthony Wilczek (; born May 15, 1951) is an American theoretical physicist, mathematician and Nobel laureate. He is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Direc ...
demonstrated, that the fractionally charged quasiparticle excitations of the Laughlin states are
anyon In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
s with fractional statistical angle \theta = ; the wave function acquires phase factor of e^ (together with an Aharonov-Bohm phase factor) when identical quasiparticles are exchanged in a counterclockwise sense. A recent experiment seems to give a clear demonstration of this effect. *Hierarchy states: this theory was proposed by Duncan Haldane, and further clarified by Halperin, to explain the observed filling fractions not occurring at the Laughlin states' \nu = 1/q. Starting with the Laughlin states, new states at different fillings can be formed by condensing quasiparticles into their own Laughlin states. The new states and their fillings are constrained by the fractional statistics of the quasiparticles, producing e.g. \nu = 2/5 and 2/7 states from the Laughlin \nu = 1/3 state. Similarly constructing another set of new states by condensing quasiparticles of the first set of new states, and so on, produces a hierarchy of states covering all the odd-denominator filling fractions. This idea has been validated quantitatively, and brings out the observed fractions in a natural order. Laughlin's original plasma model was extended to the hierarchy states by MacDonald and others. Using methods introduced by Moore and Read, based on
conformal field theory A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes ...
explicit wave functions can be constructed for all hierarchy states. *
Composite fermions A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions we ...
: this theory was proposed by
Jain Jainism ( ), also known as Jain Dharma, is an Indian religion. Jainism traces its spiritual ideas and history through the succession of twenty-four tirthankaras (supreme preachers of ''Dharma''), with the first in the current time cycle being ...
, and further extended by Halperin, Lee and Read. The basic idea of this theory is that as a result of the repulsive interactions, two (or, in general, an even number of) vortices are captured by each electron, forming integer-charged quasiparticles called composite fermions. The fractional states of the electrons are understood as the integer QHE of composite fermions. For example, this makes electrons at filling factors 1/3, 2/5, 3/7, etc. behave in the same way as at filling factor 1, 2, 3, etc. Composite fermions have been observed, and the theory has been verified by experiment and computer calculations. Composite fermions are valid even beyond the fractional quantum Hall effect; for example, the filling factor 1/2 corresponds to zero magnetic field for composite fermions, resulting in their Fermi sea. The FQHE was experimentally discovered in 1982 by
Daniel Tsui Daniel Chee Tsui (, born February 28, 1939) is a Chinese-born American physicist, Nobel laureate, and the Arthur Legrand Doty Professor of Electrical Engineering, Emeritus, at Princeton University. Tsui's areas of research include electrical prop ...
and
Horst Störmer Horst may refer to: Science * Horst (geology), a raised fault block bounded by normal faults or graben People * Horst (given name) * Horst (surname) * ter Horst, Dutch surname * van der Horst, Dutch surname Places Settlements Germany * Hor ...
, in experiments performed on
gallium arsenide Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a Zincblende (crystal structure), zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monoli ...
heterostructure A heterojunction is an interface between two layers or regions of dissimilar semiconductors. These semiconducting materials have unequal band gaps as opposed to a homojunction. It is often advantageous to engineer the electronic energy bands in m ...
s developed by Arthur Gossard. Tsui, Störmer, and Laughlin were awarded the 1998 Nobel Prize for their work. Fractionally charged quasiparticles are neither
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
s nor
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
s and exhibit
anyon In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
ic statistics. The fractional quantum Hall effect continues to be influential in theories about
topological order In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian ...
. Certain fractional quantum Hall phases appear to have the right properties for building a
topological quantum computer A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to for ...
.


Evidence for fractionally-charged quasiparticles

Experiments have reported results that specifically support the understanding that there are fractionally-charged quasiparticles in an electron gas under FQHE conditions. In 1995, the fractional charge of Laughlin quasiparticles was measured directly in a quantum antidot electrometer at
Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...
, New York. In 1997, two groups of physicists at the
Weizmann Institute of Science The Weizmann Institute of Science ( he, מכון ויצמן למדע ''Machon Vaitzman LeMada'') is a public research university in Rehovot, Israel, established in 1934, 14 years before the State of Israel. It differs from other Israeli unive ...
in
Rehovot Rehovot ( he, רְחוֹבוֹת ''Rəḥōvōt'', ar, رحوڤوت ''Reḥūfūt'') is a city in the Central District of Israel, about south of Tel Aviv. In it had a population of . Etymology Israel Belkind, founder of the Bilu movement, ...
,
Israel Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...
, and at the
Commissariat à l'énergie atomique The French Alternative Energies and Atomic Energy Commission or CEA (French: Commissariat à l'énergie atomique et aux énergies alternatives), is a French public government-funded research organisation in the areas of energy, defense and securit ...
laboratory near
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
, detected such quasiparticles carrying an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
, through measuring quantum shot noise Both of these experiments have been confirmed with certainty. A more recent experiment, which measures the quasiparticle charge extremely directly, appears beyond reproach.


Impact of fractional quantum Hall effect

The FQH effect shows the limits of Landau's
symmetry breaking In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
theory. Previously it was long believed that the symmetry breaking theory could explain all the important concepts and essential properties of all forms of matter. According to this view the only thing to be done is to apply the
symmetry breaking In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
theory to all different kinds of phases and phase transitions. From this perspective, we can understand the importance of the FQHE discovered by Tsui, Stormer, and Gossard. The existence of FQH liquids indicates that there is a whole new world beyond the paradigm of
symmetry breaking In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
, waiting to be explored. The FQH effect opened up a new chapter in condensed matter physics. Different FQH states all have the same symmetry and cannot be described by symmetry breaking theory. The associated
fractional charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
,
fractional statistics In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than the two kinds of standard elementary particles, fermions and bosons. In general, the operation of exchangi ...
, non-Abelian statistics,
chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
edge states, etc. demonstrate the power and the fascination of
emergence In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergence ...
in many-body systems. Thus FQH states represent new states of matter that contain a completely new kind of order—
topological order In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian ...
. For example, properties once deemed isotropic for all materials may be anisotropic in 2D planes. The new type of orders represented by FQH states greatly enrich our understanding of quantum phases and
quantum phase transitions In physics, a quantum phase transition (QPT) is a phase transition between different quantum phases ( phases of matter at zero temperature). Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physi ...
.


See also

* Hall probe *
Laughlin wavefunction In condensed matter physics, the Laughlin wavefunction pp. 210-213 is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium ...
*
Macroscopic quantum phenomena Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and sup ...
*
Quantum anomalous Hall effect Quantum anomalous Hall effect (QAHE) is the "quantum" version of the anomalous Hall effect. While the anomalous Hall effect requires a combination of magnetic polarization and spin-orbit coupling to generate a finite Hall voltage even in the abse ...
*
Quantum Hall Effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exh ...
*
Quantum spin Hall effect The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin o ...
*
Topological order In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian ...


Notes


References

* * * {{DEFAULTSORT:Fractional Quantum Hall Effect Hall effect Correlated electrons Quantum phases Mesoscopic physics Unsolved problems in physics Unexplained phenomena