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New Horizons in Quantum Matter Physics Next: from Quantum Fields to Condensed Matter

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New Horizons in Quantum Matter Physics Next: from Quantum Fields to Condensed Matter New Horizons in Quantum Matter Physics Next: From Quantum Fields to Condensed Matter Hyatt Place Long Island Hotel, NY Aug 24-26, 2017 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point VOI vM+ $5s +vMQ&R PHYSIC:AI. REVIEW LETTERS 11 AvGvsY 1980 ew et od for High-Accuracy Determination of th e Fine--Structure Constant Based on Quantized Hall Resistance K. v. Klitzing Hsysikalisches Institut der Universitat Wurzburg, D-8700 ~iirgburg,urgburg, FederalI'ederal RepublicRe b of Germany, and IIochfeld-Ma gn etlabor des Max-Planckx- anc --Insnstitutstitut pier PestkorPerforsckung, P 38048-Grenoble, Prance G. Dorda Forschungslaboratorien der Siemens AG, D-80000 Mununcken,ThePedera/ integerRePublic of quantumGermany Hall effect and VOI vM+ $5s +vMQ&R PHYSIC:AI. REVIEW LETTERS 11 AvGvsY 1980 M. Pepper Cavendish Laboratory, Cambridge CB30HZ Unoted Kingdom ew et od for High-Accuracy Determination of th e Fine--Structure Constant (Received 30 May 1980) ' Based on Quantized Hall Resistance Measurements of the Hall voltage of a two-diwo- imensiona 1 electronI gas, realized with a si~ ]icon0 metal-oxide-semiconductor~ ~ field-effect transistor, showow thata thee Halla resistanceresi K. v. Klitzing Hsysikalisches Institut der Universitat Wurzburg, D-8700 ~iirgburg,urgburg, FederalI'ederal RepublicRe b of Germany, and at particular, experimentall y wewell-d- e ined surface carrier concentrations has f'ixed va ues ' IIochfeld-Ma gn etlabor des Max-Planckx- anc --Insnstitutstitut pier PestkorPerforsckung, P 38048-Grenoble, Prance which de pend onl y on the fine-structure constant and speed ofo liig,ht and is insensitive to ~ ~ ~ the gcome trry of the device. Preliminary data are reported. G. Dorda PACS numbers: 73.25.+i, 06.20.Jr, 72.20.My, 73.40.Qv Forschungslaboratorien der Siemens AG, D-80000 Mununcken, Pedera/ RePublic of Germany In this paper we report a new, potentially high- and accuracy method for determining the fine-struc- p-SUBSTRATE UHI N Upp lmV M. Pepper HALL PROBE ture constant, n. The new approach is based on Cavendish Laboratory, Cambridge CB30HZ Unoted li Kingdom the fact that the degenerate electron gas in the in- --ORAIN (Received 30 May 1980) 25 -2.5 ' version layer of a MOSFET (metal-oxide-semi- Measurements of the Hall voltage of a two-diwo- imensiona 1 electronI gas, realized with a SURFACE CHANNEL $~ ~ 0 ~ ~ conductor field-effect transistor) is fully cluan- ~ ~ g &n' si]icon metal-oxide-semiconductor field-effect transistor, showow thata thee Halla resistanceresi at particular, experimentall y wewell-d- e ined surface carrier concentrations has f'ixed va ues tized when the transistor is operated at helium SOURCE GATE ' which de pend onl y on the fine-structure constant and speed ofo liig,ht and is insensitive to 20.-2.0 ~ ~ ~ and in of / the come the temperatures a strong magnetic field POTENTIAL PROBES g trry of device. Preliminary data are reported. order 15 T.' The inset in Fig. 1 shows a schem- PACS numbers: 73.25.+i, 06.20.Jr, 72.20.My, 73.40.Qv atic diagram of a typical MOSFET device used in this work. The electric field perpendicular to the 15-1.5 In this paper we report a new, potentially high- surface field) produces subbands for the mo- accuracy method for determining the fine-struc- 2 p-SUBSTRATE (gate UHI N Upp lmV ture constant, n. The new approach is based on HALL PROBE tion normal to the semiconductor-oxide interface, li ne the fact that the degenerate electron gas in the in- --ORAIN and the magnetic field produces Landau quantiza- -1. 10 0 version layer of a MOSFET (metal-oxide-semi-σ = 25 -2.5 xy SURFACE CHANNEL $~ tion of motion den- ~ ~ parallel to the interface. The conductor field-effect transistor) is fully cluan- g &n' sity of states D(E) consists of broadened 5 func- tized when the transistor is operated at helium h SOURCE GATE tions'; minimal overlap is achieved if the mag- and in of 20.-2.0 / 5--0.5 temperatures a strong magnetic field POTENTIAL PROBES netic field is sufficiently high. The number of order 15 T.' The inset in Fig. 1 shows a schem- states, NL, within each Landau level is given by atic diagram of a typical MOSFET device used in this work. The electric field perpendicular to the 15-1.5 V„=ea/I, (&) 0; surface (gate field) produces subbands for the mo- 0:; 10 15 20tion normal25 to the semiconductor-oxide interface, where we exclude the spin and valley degenera- n=Q -n=l n=2 and the magnetic field produces Landau quantiza- -1. = 10 0 cies. If the density of states at the Fermi ener- Vg/Vtion of motion parallel to the interface. The den- gy, N(EF), is zero, an inversion layer carrier sity of states D(E) consists of broadened 5 func- tions'; minimal if the cannot be scattered. , and the center of the cyclo- overlap is achieved mag- 5--0.5 tron orbit drifts in the direction perpendicular to FIG. l. Recordings of the Hall voltage UH,neticanand fieldth e is sufficiently high. The number of vol within each Landau level the electric and magnetic field. If N(FF) is finite tage drop between the potential probo es, U&&,states,asaNL, is given by function of the gate voltage V at T = 1.5 K. The con- but small, an arbitrarily small rate of scattering V„=ea/I, (&) 0; stant magnetic field {B)is 18 T and the source drain 0:; 10 15 20 25 cannot occur and localization produced by th e long n=Q -n=l n=2 current, l, is 1 p,A.. The inset shows a top viewwhereof wethe exclude the spin and valley degenera- lxf etarne is the same as a zero scattering = rate, device with a length of I =400 pm, a width ofcies.8' =50If pm,the density of states at the Fermi ener- Vg/V i.e. the same absence of current-carrying states and N(EF), is zero, an inversion layer carrier , a distance between the potential probeses ogy,f I && =130 occurs. ' Thus, when the Fermi level is between p,m. cannot be scattered. , and the center of the cyclo- tron orbit drifts in the direction perpendicular to FIG. l. Recordings of the Hall voltage UH, anand th e vol 494 the electric and magnetic field. If N(FF) is finite tage drop between the potential probo es, U&&, asa function the V = but small, an arbitrarily small rate of scattering of gate voltage at T 1.5 K. The con- stant magnetic field {B)is 18 T and the source drain cannot occur and localization produced by th e long current, l, is 1 p,A.. The inset shows a top view of the lxf etarne is the same as a zero scattering rate, device with a length of I =400 pm, a width of 8' =50 pm, i.e. the same absence of current-carrying states and , a distance between the potential probeses of I && =130 occurs. ' Thus, when the Fermi level is between p,m. 494 The fractional quantum Hall effect VOLUME 48, NUMBER 22 PHYSICAL REVIEW LETTERS $1 MA+ 1982 Two-Dimensional Magnetotransport in the Extreme Quantum Limit D. C. Tsui, '" '"' H. L. Stormer, '" and A. C. Gossard Bell Laboratories, Murray Hill, New Jersey 07974 VOLUME 48, NUMBER 22 PHYSICAL-- REVIEW LETTERS $1 MAY 1982 (Received 5 March 1982) A quantized Hall plateau of —31'/e, accompanied a minimum in was observed F I LLING FACTOR v ILI 1.0 p» by p„, at &Q & 5 K in magnetotransport of high-mobility, bvo-dimensional electrons, when the low- 43 2 1 2/3 1/2 1/3 O ~ 4 II I I I I . I est-energy, spin-polarized Landau level is 3 filled. The formation of a Wigner solid or 4— 0.48 K 1.00K charge-density-wave state with triangular symmetry is suggested as a possible explana- 1.65K tion. ~ 1.23 x 10 crn-2 4.15 K 4— ~ PACS numbers: 72.~20. 71.~45.1.11-d,x 73.10 40.cm 73.60.Fw .2— y My, Lq, K ~ +1.38 x 10 Gill CV O II 2 Z In the presence of an intense perpendicular shows a dip at v = —,', which becomes stronger at ~ ~ magnetic field B, a system of two-dimensional lower T. For v & —,', p„„ follows an approximately (2D) electrons is expected to form a Wigner sol- exponential increase with inverse T. The Hall Cg id' at low temperaturesII (T). In the infinite-B resistivity p„„on the other hand, approaches a 0 ' an can be drawn to the of Sh/e' v = —, as 0 limit, analogy classical step at T decreases, but re- 0 electronOOK gas on the surface of liquid helium, mains essentially2 independent of T away from 0 which crystallizes into a solid' when the ratio of this⌫eHall plateau.
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