V OLUME 93, N UMBER 3
2.4 Cryogenics
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DQW wafers), we can fully deplete the upper 2DES directly underneath that gate.
Thus, the ohmic contact in that arm will only be connected to the central region via the bottom layer. By applying a large bias to the bottom arm gate for another arm, we will similarly deplete the bottom layer within a localized region in that arm.
The ohmic contact associated with that arm will then be connected to the central region only through the top layer. An ohmic contact can be fully disconnected from the central region by applying a large bias to its matching top arm gate (generally
−1.2 V) to deplete both layers.
The central region itself is covered by one or more top and bottom gates to in- dependently control the electron density in either layer within this central region.
Through proper application of biases to the arm gates, we can for example measure interlayer tunneling within the central region using one contact to the upper layer and another contact to the bottom layer. In order to reduce fringe fields to a tolerable level, we must bring our bottom gates to within 50 µm of the bilayer system. To do this, we thin the wafer piece to a thickness of 50µm using a bromine-methanol etch.
Once the sample is thin, the bottom gates can be deposited. We must then carefully solder and epoxy wires to the contact pads for each gate and ohmic contact. The wires are then soldered to an 18-pin header, which can be plugged into the sample holder of a dipping stick or dilution refrigerator.
This allows us to test the ohmic contacts and gates at 4.2 K. Our lab has a number of dipping sticks that can be used to lower a sample into a standard liquid helium storage dewar. Each of these dipping sticks is essentially an enclosed tube with a series of wires connecting the sample holder with a breakout box attached to the upper part of the stick. The end of the tube holding the sample is dipped into the dewar while the breakout box remains at room temperature. The breakout box consists of a number of BNC connectors and switches that permit electrical connection to the sample while it sits in the liquid helium.
The dipping stick should be lowered slowly into the liquid helium dewar in order to minimize any thermal shocks to the sample as well as to avoid violent boil-offs that ultimately waste liquid helium. To warm up the sample, the stick should be raised slowly: about six inches per minute. Once the stick has been fully raised, the sample space is likely to be below 0◦ C and there is the danger that ice can form on it if it is exposed to air. Such ice can be harmful to sensitive samples. Generally it is sufficient to remove the dipping stick once it is fully raised and then quickly insert its bottom tip into a can through which dry nitrogen flows. To completely avoid exposure to water vapor while the sample is still cold, we can instead install an isolation chamber on top of the liquid helium dewar and clamp the dipping stick onto the top of the chamber. The isolation chamber has a gate valve that can be closed once the sample has been fully raised and spigots to permit the flow of nitrogen gas through the chamber. In either case, the nitrogen should flow for at least 15 minutes to fully warm up the sample before its removal from the dipping stick.
2.4.2
3He Cryostat: T = 300 mK
Colder temperatures can be reached using a helium-3 cryostat. Although limited to 300 mK, the helium-3 cryostat in our lab is top loading and allows us to quickly cool, test, and warm fup a sample. Often this entire process can be completed in a single
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day. Equipped with a superconducting magnet capable of reaching 14 T, the helium- 3 cryostat permits magnetotransport studies and more careful characterization of samples than is possible in liquid helium-4 dips.
The principle behind the helium-3 cryostat is conceptually straightforward. The sample is immersed in liquid helium-3. By then pumping on the helium-3 and reducing its vapor pressure, the liquid is evaporatively cooled to T ≈ 0.3 K. This is a lower temperature than can be obtained with helium-4 for two reasons. First, the helium-3 atom is lighter than the helium-4 atom. Consequently, the vapor pressure of helium-3 will be higher than that of helium-4 at any temperature [78]. Second, helium-3 is a fermion while helium-4 is a boson. Thus, helium-4 can form a superfluid film that acts as a heat link and can limit the ultimate temperature for evaporative cooling [78]. Helium-3, however, does not form a superfluid until its temperature has fallen below 3 mK [87, 86].
Helium-3 is a rare and expensive isotope of liquid helium. To conserve helium-3, we use a sorb pump to perform the evaporative cooling. The sorb pump is a chunk of activated charcoal with enormous effective surface area. By flowing liquid helium-4 around it, the charcoal adsorbs the helium-3 atoms and allows for evaporative cooling.
Applying heat to the sorb releases the helium-3 so that it can be liquified once more.
2.4.3 Dilution Refrigerator: T = 15 mK
While rudimentary signs of νT = 1 physics are observable at 300 mK, we must go to even lower temperatures to clearly observe the effects of excitonic condensation.
The dilution refrigerator is the standard instrument for reaching T ≤ 100 mK. Our lab has two dilution fridges in operation, with base temperatures of 15 mK and 50 mK. A third is being developed with a demagnetization stage, with projected base temperatures of T ≤1 mK.
The heart of the dilution refrigerator is the mixing chamber, which contains liqui- fied helium-3 and helium-4 during operation. Below T = 0.86 K, this mixture will physically separate into two distinct phases: a phase rich in helium-3 (the concen-
mechanical ground phase and inert. Only the helium-3 phase is thermodynamically and hydrostatically relevant. The removal of helium-3 from the dilute phase will en- courage the passage of helium-3 atoms from the concentrated phase into the dilute phase. This provides cooling power analogous to evaporative cooling. However, the concentration of helium-3 in the dilute phase remains finite even at absolute zero, sat- urating at the value of nn3
3+n4 = 0.064 [78]. Thus, while the vanishing vapor pressure Pvapor ≈ e−∆/kbT of most liquids will cause evaporative cooling to become exponen- tially suppressed, the raw cooling power of a dilution refrigerator is proportional to T2 [78]. To allow for continuous operation, the pumped-away helium-3 is recooled and returned to the mixing chamber. A more detailed explanation of the physics and mechanics of dilution refrigeration is given in chapter 3 in reference [78].